Math 40 Solving Problems

Introduction to Math 40 Solving Problems:
In mathematics, numeration is one of the main sources describing about numerals such as number system. The number is also used for abstract object and symbolic representations of numbers. There is addition, multiplication, division, subtraction operation in math. The common usage of math is to solve the problem and finding the solution. The given problem can be performed by any one of the above operation. Let us see about math 40 solving problems in this article.

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Example Problems for Math 40 Solving Problems


Solving the below problem using addition, subtraction, multiplication and addition operation in math.

Using Addition Operation in Math

Example 1:

Add 40 and 60?

Solution:

Let us add the given problem.

Write the given whole number 40 first and then write the given whole number 60 second one by one.

40 (addend)

(+)   60 (addend)

--------------

100

--------------

The sum for adding 40 and 60 is 100.

Using Subtraction Operation in Math

Example 2:

Subtract 40 and 10?

Solution:

Let us subtract the given problem.

Write the given whole number 40 first and then write the given whole number 10 second one by one.

40 (minuend)

(-)   10 (subtrahend)

--------------

30 (difference)

---------------

The difference for subtracting 40 and 10 is 30.

Using Multiplication Operation in Math

Example 3:

Multiply 40 and 8?

Solution:

Let us write the given problem as in the below form. Here, 40 is multiplicand and 8 is multiplier.

40 ×

8

----------------

320

----------------

The product for multiplying 40 × 8 is 320.

Using Division Operation in Math

Example 4:

Divide 40 by 10?

Solution:

Let us write the given problem is in form of 40 ÷ 10 and put the divisor on the left side of the division bracket and dividend on the right side of the division bracket.

Check whether the 10 goes into 4 or not. The number 10 cannot go into 4. So that takes the dividend as two digit number. Now the divisor 10 goes into 40 for 4 times. Continue with the division method for the given problem.

10)40(4

0

----------------

40

40

----------------

0

-----------------

The quotient for dividing 40 by 10 is 4.



Practice Problems for Math 40 Solving Problems


1. Add 40 and 80.

Answer: 120

2. Subtract 80 and 40.

Answer: 40

3. Multiply 40 and 5.

Answer: 200

4. Divide 40 by 5.

Answer: 8

Free Math Practice Integers

Introduction to free math practice integers:

An integer is a set of whole numbers. Whole numbers above zero is said to be positive integers denoted as ‘+’ sign and whole numbers below zero is said to be negative integers denoted as ‘-‘. An integer with zero is said to be neither negative nor positive and it does not have any sign in math. Here, integers can be performed with four basic operations such as addition, subtraction, multiplication, and division. The positive integers can be written with or without the sign. Let us see free math practice integers in this article.



Practice Integer Problems - Practice Adding Integers in Math


Adding same signed free Integers:

Example 1:

15 + 9

Solution:

The absolute value of 15 and 9 is 15 and 9. Put the positive sign before the result.

15 + 9 = 24

Example 2:

(-5) + (-7)

Solution:

The absolute value of -5 and -7 is 5 and 7. Put the negative sign before the result.

(-5) + (-7) = - (5 + 7) = - 12

Adding different signed free Integers:

Example 3:

2 + (-8)

Solution:

The absolute value of -8 and 2 is 8 and 2. Put the larger number sign before the answer.

8 –2 = 6

Therefore, the solution for adding 2 + (-8) is -6.


Practice Subtracting Integers in Math


Example 4:

20 - (-8)

Solution:

The absolute value of 20 and -8 is 20 and 8. Subtract the integers and put the larger number sign.

20 – (-8) = 20 + 8 = 28


Practice Multiplying Integers in Math


Multiplying same signed free Integers

Example 5:

3 × 6

Solution:

The absolute value of 3 and 6 is 3 and 6. Put the same sign as it is in the given problem.

3 × 6 = 18

Example 6:

(-5) × (-5)

Solution:

The absolute value of -5 and -5 is 5 and 5.

5 × 5 = 25

Put the same sign as it is in the given problem – 25.

Multiplying different signed free Integers:

Example 7:

(-6) × (8)

Solution:

The absolute value of -6 and 8 is 6 and 8.

6 × 8 = 48

Put the negative sign if it is sign of one of the integer in the given problem. Therefore, the solution is -48.



Practice Dividing Integers in Math


Dividing same signed Integers:

Example 8:

36 ÷ 6

Solution:

The absolute value of 36 and 6 is same. Therefore, the solution for dividing 36 ÷ 6 is 6.

Dividing different signed Integers:

Example 9:

42 ÷ -7

Solution:

The absolute value of 42 and -7 is 42 and 7. Put the negative sign in the result, because there is a negative sign in front of the integers.

Therefore, the solution for dividing 42 ÷ -7 is -6.

Algebra Ags Answer

Introduction to algebra ags answers:
Algebra ags answers deals with solving basic algebra problems whereas ags is the publication name in which one of the algebra problems with answers are published by ags. In ags, algebra is defined as the branch of mathematics which deals with finding unknowns with the help of known values. The ags algebraic problems with answers are discussed below. Alphabets are used for variable representation and numbers are considered as constants.


Algebra ags answers example problems:


Example 1:

Solve the ags algebraic expression.

-2(n - 1) - 4n - 1 = 3(n + 5) - 2n

Solution:

Given expression is
-2(n - 1) - 4n - 1 = 3(n + 5) - 2n

Multiplying the factor terms
-2n + 2 - 4n - 1 = 3n + 15 - 2n

Grouping the above terms
-6n + 1 = n + 15

Subtract 1 on both sides
-6n + 1 - 1 = n + 15 -1

Grouping the above terms
-6n = n + 14

Subtract n on both sides
-6n - n = n + 14 -n

Grouping the above terms
-7n = 14

Multiply by – `1/ 7` on both sides, we get
n = - `14/7`

N = 2

Conclusion:

n = 2 is the solution for the given expression.

Example 2:

Solve the ags algebraic expression.

-4(n + 2) = n + 12

Solution:

Given expression is
-4(n + 2) = n + 12

Multiply factors in left term
-4n - 8 = n + 12

Add 8 on both sides
-4n - 8 + 8 = n + 12 + 8

Grouping the above terms
-4n = n + 12

Subtract n on both sides
-4n - n = n + 20 -n

Grouping the above terms
-5n = 20

Multiply -`1/5 ` on both sides
n = -`20/5 `

N = -4

Conclusion:

n = - 4 is the solution for the given expression.


Algebra ags answers practice problems:


1) Solve the ags algebraic expression.

-3(n - 2) - 2n - 3 = 2(n + 5) - 4n

Answer:  n = -`7/3` is the solution for the above given expression.

2) Solve the ags algebraic expression.

-2(n + 3) = 5n + 8

Answer:   n = - 2 is the solution for the above given expression.

What Do X Mean in Math

Introduction to math variable x means:

In mathematics a variable is a symbol that stands for a value that may vary; the term usually occurs in opposition to constant, which is a symbol for a non-varying value, i.e. completely fixed or fixed in the context of use. The concepts of constants and variables are fundamental to all modern mathematics, science, and engineering .Here we are going to study about what is math variable x means and how to solve the value of x with example problems.    (Source from Wikipedia).

Example problems :


Math example: 1

Find the value of |x+3| = 0

Solution:

Here x means the modulus value

We have take -(x+3) and x +3

-x -3 = 0

Add the +3 both sides

-x = 3

x = -3

Similarly   x + 3 = 0

Add both sides -3

x + 3-3 = -3

x = -3

Therefore the solution x = -3, -3

Math example 2:

Solve for x in the equation 4x + 6 + 6x = 46

Solution:

Here x means unknown value we have to find the x value.

First we have to combine the like terms here the like terms are x.

4x + 6x = 10x

10x + 6 = 46

Add both sides -6 we get

10x + 6 - 6 = 46 -6

10x = 40

Divide both sides 10 we get

x = 40/10

x = 4

Therefore the value of x = 4



Some more examples of x mean in math:


Math problem 3:

4x+3+2x + 5 > 2x+4

Solution:

Here x means inequality variable we have to find the x value

In the left hand side combine the like term first

4x+3+2x +5 > 2x+4

6x + 8 > 2x + 4

Add both sides -4 we get

6x + 8 - 4 > 2x + 4 - 4

In right hand side 4 - 4 will be cancelling

6x+ 4 > 2x

Add both sides -2x

6x -2x + 4 > 2x -2x

4x + 4 > 0

Add both sides -4 we get

4x + 4 -4 > -4

4x > -4

Divide both sides 4 we get

(4x / 4) > - `(4/4)`

x > - `(4/4)`

x > -1

Therefore the x value greater than -1

Second Derivative

The derivative of the derivative of a given function is the second derivative. Given a function f(x), the 2nd derivative is represented as f’’(x) of [f(x)]. The definition of second derivative of a function f(x) at a point a is, f’’(x) = lim(x?a [f’(x) – f(a)]/(x-a)

It gives how fast the rate of change of a function is changing. It gives the information about the concavity.
Second Derivative Curvature
The curvature of a given function is described by the second-derivative of the function.  If the function curves upwards then the curvature of the function is concave up and if the function curves downwards then the curvature of the function is concave down.

The function behavior corresponding to its 2nd derivative can be given as follows:
If f’’(x)>0, then the curvature of the function f(x) is concave up
If f’’(x)<0 br="" concave="" curvature="" down="" f="" function="" is="" of="" the="" then="" x="">If f’’(x)=0, then it corresponds to a possibility of an inflection point
The inflection point is the point where there is a change in the concavity of the function f(x).

Calculate Second Derivative

While calculating the 2nd derivative the 1st derivative becomes the function.

The two basic steps involved in finding the second of the derivative are as follows:
Step1:  first the derivative of the function is found. The result thus obtained becomes the function to find it
Step2: the derivative of the first derivative gives the required derivative
If y=4x3- 3x^2 + 5x
Step1: The first derivative is given by y’ = [4x3 – 3x^2 + 5x]. Taking derivative of each of the terms,
y’= [4x3] – [3x^2] + [5x]
= 12x^2 – 6x + 5
Step2: Now the function is y’= 12x^2 – 6x + 5. The second-derivative would be,
y’’ = [y’]
= [12x^2 – 6x + 5] taking derivative of each of the terms,
= [12x^2] – [6x] + [5]
= 24x – 6 + 0
So, y’’ = 24x- 6 required 2nd derivative of y



Acceleration Second Derivative

Instantaneous velocity of a particle along a line at time t is the first derivative of a function which represents its position along a line at a particular time t. The derivative of this velocity is the second-derivative of the function which is the instantaneous acceleration of the particle at a time t.
For instance, let y= p(t) is the position of the particle, then  the instantaneous velocity which is the first derivative is v=p’(t)and the instantaneous acceleration of the particle at time t which is the second derivative is a=v’(t) = p’’(t).

Variable in Math

Introduction to variable in math:

In mathematics, the term “variable” is used in algebra. Variable is nothing but the letter which represents the some numerical value. For example consider the algebraic expression 4x. Here 4 is the constant and x is the variable.

Discuss:

(a)   Consider x + y = 10.

The variable x and y are variables and they has some numerical values that makes the above statement true.

Examples:

1. P = 4s    2. x + 5 = 10

Here

4, 5, 10 are constants.

P, s, x are variables.

Note:

The numbers are constants.

To denote variable in math we use the alphabets A to Z or a to z.

Let us see some example problems.


Variable in math - Example problems:


1. Pick out the constants in the following:

8, a, x, y, – 25, 0, z, 35, 2.7,

Solution:

The constants are 8, – 25, 0, 35, 2.7 and

2. Pick out the variables in the following:

63, x, 27, m, p, q, 10, 0, y

Solution:

The variables are x, m, p, q and y

2. Pick out the variables and constants: A, – 15, q, l, 22.3, 73

Solution:

The variables are A, q and l

The constants are – 15, 22.3 and 73.

Practice problems:

1) Pick out the variables in the following:

6, c, – 12, h, k, 16, m, n, – 22, p, s, 30

2) Write any five variables:



Power of the variable in math:


In math, the product of 18 and a is 18 × a and it is written as 18a .Similarly the product of two literals a and b is a × b = ab

Now let us see how the repeated product of a literal with itself is written in math.

Multiply a with a. We get a × a and is denoted by a2.

We read a2 as a to the power of 2. Similarly d × d × d = d3, which is read as m to the

Power of 3

In a2, 2 is the power and a is the base.

In d3, 3 is the power and d is the base.

Example problems using the variables:

a + 5 = 10. Find the value of a.

Solution:

To find the value of a, we have to move the like terms in one side

For that, subtract 5 on both sides

a + 5 – 5 = 10 – 5

Simplify,

a + 0 = 5

a = 5.

Answer to 4th Grade Math

Introduction about answer to 4th grade math:

In mathematics, the following topics are covered under 4 th grade, these 4th grade mostly deals with the number system, algebra terms, basic geometry shapes and their way of solving techniques , order of operations. Now, here we are going to discuss about the different type of problems and their answers.



Description to answer to 4th grade math:


The following areas are covered under the 4th grade  math:

Natural Numbers

The natural numbers are normal numbers which starts with 1,2,3…we can call these numbers as a counting numbers.

Even and odd numbers

When a number is divisible by 2 then its called as even number and the remaining numbers are all odd numbers.

Even numbers are 2,4,6… and odd numbers are 1,3,5…

Fractions

Fraction is looking line division operation in which the denominator is always less than the numerator and this is a proper fraction. For example: 6/3.The opposite of proper fraction is called improper fraction. For example 5/7. Here we have another type of fraction is said to be mixed fraction. A mixed fraction is a combination of whole number and proper fraction, for example 5 8/4

Algebraic equation

It can be any equation with the arithmetic operation operators.

Algebraic expression

Here we have the different term with the different sign and operations.

Geometry shapes:

In 4th grade we have lot of geometry shapes like square, rectangle, circle, etc….



Problems with answers to 4th grade math:


Some of 4th grade math problems with answers:

Example 1:

Solve: 5( 4+1) – 9 + 3( 7 ) + 26

Answer:

5( 4+1 ) – 9 + 3( 7 ) + 26

=  5( 5 ) – 9 + 21 + 26

=  25 - 9 + 47

=  63



Example 2:

Simplify : 4/12 +5/15

Answer:

4/12+6/12 = 4+6/12

=10/12

=5/6


Example 3:

Simplify:      5( x + 6 )  =  65

Answer:

5( x + 6 )  =  65

5x + ( 5 x 6 )  =  65

5x + 30  =  65

5x   =  35

x   =  7


Example 4:

Martin bought a bike  for 40 and he sold it for 47. calculate the gain?

Answer:

Original cost price of bike =  $ 40

sold price of bike =  $ 47

Gain  =  sold price - Cost Price

=  47 - 40

=  $ 7

So he the gain as $7.

4th Grade Math Probability

Introduction to 4th grade math probability:

Generally probability is defined as the ratio of the number do ways of an event occur to the total number of possible outcomes, probability is used in the area of statistics, finance, gambling and science.

Probability formula for 4th grade math probability

The probability of event P (A) = no of possible events n (a) `//` the total number of the events n(s)

Example problem -4th grade math probability


Suppose a single die is rolled find the probability of getting odd number and also even number? ii) Probability of getting each number?

Solution:

Generally the die has 6 sides ,they are numbered as 1,2,3,4,5,6

From the six  number  we can tell the odd number as  1,3,5 and even number as 2,4,6

Here the possible outcomes of these experiments are 1, 2, and 3,4,5,6.

First we have to find the probability of getting odd number, the die as 3 odd numbers

So the probability p (odd) =3/6

Here 6 is the total number

Similarly the probability of even number will be written as

Probability p (even) =3/6

ii) Probability of getting each number it will be shown as below,

P (1) =1/6

P (2) =1/6

P (3) =1/6

P (4) =1/6

P (5) =1/6

P (6) =1/6

Example problem -4th grade math probability

Here the circle is divided into 8 equal parts and they are colored using the different color find the probability of choosing green color?

Solution:

It is divided into equal parts so the total number will be present in the denominator and counts the how many colors are shaded using green, here colors are shade in a green so it must be come in the numerator parts

Then the answer is 4/8



Example problem -4th grade math probability


A basket contains the fruits, it has 5 apples, 3 orange, 11 mango and 1plum what is the probability of choosing mango without looking the basket?

Solution:

The total number of fruits is 5 apples, 3 orange, 11 mango and 1plum so the total number of fruits in the basket is 5+3+11+1=20

P (mango) =11/20

Here numerator represents the count of apple and denominator represents the total count of fruits

Doing Math Problem

Introduction for Mathematics:

Mathematics is one of the most important terms in our daily life. We have seen so many different concepts in mathematics.  In mathematics, many formulas are present.  The formulas are used to solve all types of problems.  Here, we are going to see some mathematical problems in some different concepts.



Example problems – Doing math problem


Example for doing math problem 1:

Writing the simple mathematical form: 36/6.

Solution:

Given 36/6

First, we are going to factor the numerator value and then factor the value of denominator.

At last, decrease the fraction value by removing the common value.

In the given problem, 36 is the numerator and 6 is denominator

Here, 6 is the common for numerator and denominator.

36 / 6 = 6

Now, we get the answer 6.

Answer: 6

Example for doing math problem 2:

Subtract 34mn + 20n – 28m from 40mn - 22n + 24m.

Solution:

The given equations are 34mn + 20n – 28m and 40mn - 22n + 24m

Subtract these two equations

34mn + 20n – 28m – (40mn - 22n + 24m)

Process 1: Add the subtract value within the parenthesis

Now, we get 34mn + 20n – 28m – 40mn + 22n - 24m

Process 2:

Arranging the values in term

= 34mn – 40mn + 20n + 22n – 28m – 24m

= -6mn + 42n – 52m

The correct answer is -6mn + 42n – 52m.



Example for doing math problem 3:

Solve (10p + 17q) + (12p – 14q)

Solution:

Process 1:

First, we are going to solve within the parenthesis,

10p + 17q + 12p – 14q

Process 2:

Now, we are going to arrange in terms,

= 10p + 17q + 12p – 14q

= 10p + 12p + 17q – 14q

Process 3:

Here, we are going to add,

= 10p + 12p + 17q – 14q

= 22p + 3q

The correct answer is 22p + 3q.

Example for doing math problem 4:

Find a in the 24a + 3b + 3a = 0, the value of b is a - 10.

Solution:

The given equation is 24a + 3b + 3a = 0

Substitute the value b in this given equation

24a + 3(a - 10) + 3a = 0

24a + 3a – 30 + 3a = 0

Arranged in terms

24a + 3a + 3a – 30 = 0

30a – 30 = 0

30a = 30

a = 30/30

a = 1

Answer:  The value of a is 1.


Practiced problem – Doing math problem


Doing math practiced problem 1:

Solve (2p + 3q) - (4p – 5q)

Answer: -2p +8q

Doing math practiced problem 2:

Find x in the 15x + 5y – 5x = 0, the value of y is x - 1.

Answer:  1/3

Properties Of Math

Introduction to math properties:

Mathematics is the important study which is applied in all fields. There are many properties in math. These properties define some of the rules and methods for solving the problems. Some of the properties in math are,

Associative property
Distributive property
Commutative property
Reflexive property
Transitive property
Addition property
Multiplication property
Additive identity
Symmetric property
Multiplication identity
Substitution property.



Math properties


Properties in math:

Here we are going to discuss about some of the properties in math.

Associative property:

In the associative property we does not consider the way that how the numbers are grouped with others. In this property when we rearrange the parenthesis it does not changes the value. This property is common for both addition and multiplication. The associative property is given as,

( p + q ) + r = p + ( q + r)

( p * q ) * r = p * ( q * r)

Commutative property:

In this commutative property we can swap the numbers after performing the operation. Since the value does not change even after the swapping or interchanging. This property is also common for both addition and multiplication. This commutative property is given as,

p + q = q + p

p * q = q * p

Distributive property:

In this distributive property, we can split and broken up the number of parts. The distributive property is given as,

p * (q +r) = p * q +p * r

Additive identity:

When we add zero to a number it results the same number as the answer. This property is referred as additive identity.

p + 0 = p.

Multiplicative identity:

When we multiply one to a number then it will result the same number as the answer which is referred as property of multiplicative identity. This property is given as,

( p ) 1 = p.

Addition property:

When two numbers such as p = q is given then if we add r to both numbers p and q then this property is referred as addition property. The addition property is given as,

p = q, p + r = q + r.

Multiplication property:

This property is same as the addition property but in this instead of addition we want to do multiplication. This multiplication property is given as,

p = q, pr = qr.


Example problems


Example problems by using the properties of math:

Problem 1: Simplify the given equation 4x – 5y + 8x.

Solution:

Given: 4x – 5y + 8x.

Step 1: By using the commutative property write the given equation as,

4x + 8x – 5y

Step 2: According to the associative property, write the equation as,

(4x + 8x) – 5y

Step 3: By using distributive property write the equation as,

x ( 4 + 8) – 5y

Step 4: Finally according to the commutative property and by doing the simplification, the equation is given as

12x – 5y

Problem 2: simplify: 7 ( x + 4).

Solution:

Given: 7(x + 4)

Step 1: By using the distributive property write the given equation as,

7x + 7 * 4 – 6x

Step 2: After doing simplification according to the commutative property, write the equation as,

7x – 6x +28

Step 3: By using associative property write the equation as,

( 7x – 6x ) + 28

Step 4: According to the distributive property, the equation is given as

x( 7 – 6) + 28

Step 5: According to the commutative property, the equation is given as,

x + 28.

6th Grade Answers for Math

Introduction 6th grade answers for math:
In this article we see 6th grade practice problems. According to 6th grade syllabus we have to see the following problems.

1) Addition and subtraction

2) Fraction and decimal

3) Perimeter and circumference

4) Area and volume

6th grade answers for math:


Addition

6th grade addition are little advanced from 5th grade.

When adding two numbers in that one value may not be known and needs to be determined. The unknown term may be represented by a letter x (example: 432 + x = 422). We have to find the x value using the steps,

Example: x + 343 = 432

Subtract 343 on both side

x + 343 – 343 = 432 – 343

x = 89

Now add 89 + 343 = 432.

Subtraction

6th grade subtraction are little advanced from 5th grade. Subtraction is also same like addition.

Example: x - 343 = 432 find the x value

Add 343 on both side

x - 343 + 343 = 432 + 343

x = 775

Now subtract 775 - 343 = 432.

Fraction

In fraction there are two numbers numerator and denominator

Adding fraction with same denominator is seen in 5th grade. In 6th grade we see addition of fraction with different denominator.

Fraction addition

Example

`3/5` + `(4)/(10)`

take lcm as 10 for both fraction numbers

In `3/5` numerator is 5 so to get 10. we have to multiply by 2 in both numerator and denominator

`(6 + 4)/(10)` = `(10)/(10)` = 1

Decimal:

In 6th grade we see decimal addition and decimal subtraction.

Example:

0.342

(+) 0.421

0.763

0.754

(-) 0.721

0.033

Perimeter and circumference

Perimeter for square and rectangle

Formula for square and rectangle

Perimeter for square = 4s

Perimeter for rectangle = 2(l+w)

Circumference of a circle = 2πr

Example to find the perimeter of the rectangle whose l =4m and w =6m

Perimeter = 2(l + w)

= 2(4+6)

= 2(10)

Answer = 20

Example for circumference of a circle radius = 6cm

Circumference of the circle = 2 π r

= 2 × 3.14 × 6

Answer = 37.68

Area and volume:

In 6th grade we see volume of cube and volume rectangular prism

Formula for volume of cube = a ^3

Formula for volume of rectangular prism = l × w × h

Example for finding volume of the cube side = 8cm

Solution;

volume of cube = a ^3

= 8^3

Answer = 512cm^3

Example for finding volume of the rectangular prism l = 8cm, w =5cm and h = 7cm

Solution;

volume of rectangular prism = l ×w ×h

= 8 × 5 × 7

= 280cm3



6th grade practice problem with answers for math:


Practice problems for 6th grade

1) Add the values and find the unknown value x + 43 = 134

2) Subtract the values and find the unknown values x -87 = 234

3) Add the fraction numbers and `3/2` and `7/4`

4) Subtract the fraction numbers and `7/6` and `(12)/(9)`

5) Add the decimal values 0.369 and 0.765

6) Subtract the decimal values 0.923 and 0.345

7) Find the perimeter of the square side s = 9cm

8) Find the perimeter of the rectangle l =6m and w =12cm

9) Find the circumference of the circle radius = 12cm.

10) Find the volume of the cube side a = 12m

11) Find the volume of the rectangular prism l =4m, w= 6m and h= 7m.

Answers

1) 91

2) 147

3) `(13)/(4)`

4) `5/2`

5) 1.134

6) 0.578

7) 36

8) 36

9) 75.36

10) 1728 cubic meter

11) 168 cubic meter

Help Doing Math Problems

Introduction to doing math help problems:

Mathematics is the study of magnitude, structure, space, and modify. Mathematicians search for examples, formulate new inferences, and found truth by accurate deduction from correctly chosen theorems and explanation.

Students are allowed to solve the mathematics problems such as homework problems, practice problems and also providing the formulas and definitions. Homework problems are used to develop the knowledge of solving problems themselves. It includes algebra variant, geometry and so on...

Example problems of doing math help problems:


Math help problem 1:

Writing the simple form: `25/5`

Solution:

Given `25/5`

Method 1:

First we are factoring the values of numerator and then factoring a denominator values.

Finally reduce the fraction by cancelling the common value.

Method 2:

Find the Greatest common divisor for the given fraction values and then simplifying them.

Therefore we can simply the given problem using the second method.

Greatest common divisor of 25, 5 = 5

So, `25/5=5/1`

Answer: 5

Math help problem 2:

Find the area of following triangle:

Solution:

Given base= 12 cm and height= 10 cm

We can find the area of triangle by using the following formula:

Area `A=` ` 1/2 (base * height) or 1/2bh`

Substitute the value of base and height into the above formula and then we get the final answer.

`Area A= 1/2(12*10)`

`= 1/2(120)`

`= 120/2`

` = 60`

Answer: 60 cm2

Math help problem 3:

If sixteen inches correspond to 44 centimeters, how many centimeters are there in twenty eight inches?

Solution:

By using the proportion concept,

Here inches/ centimeters: `16/44=28/x`

`16x= 44xx28` (cross multiplication)

Multiply 44 and 28

`16x=1232`

Divide by 16 on both sides.

`(16x)/16= 1232/16`

`x= 77`

Answer: 77 cm

Math help problem 4:

What is 12% of 1800 centimeters?

Solution:

Percentage means division of 100.

We can find the number with the 12% of 1800.

That is, 12% of 1800

`= 12/100xx1800`

Here we can divide the values 12 and 100 and then we get

`= 0.12xx1800`

Again we can multiply 0.12 with 1800. Then we get the final answer.

`= 216`

Answer: 216



Practice problems doing math help problems:


Writing the simple form: `18/10`
Find the area of square with side value 7.2 cm.
Answer:

`9/5`
51.84 cm2

What are Ratios in Math

Introduction-what are ratios in math:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)     (Source: Wikipedia)



Definition in ratio geometry - what are ratios in math:


When two objects are related to, the geometric ratio of the interval of a come together of linked sides is the identical as the ratio in geometry of any other team of equivalent linear measurements of the two objects. It is known as geometric ratios.

Therefore:

1)   Lengths of comparable sides are equal.

2)   The ratio in geometry of the interval end to end of any pair of equivalent sides is the identical as the ration of comparable perimeters, altitudes, or medians in.

Concept -what are ratios in math:

The numeric ratio of two numbers x and y(y?0) is the quotient of the numbers. The numbers x and y referred to as the conditions of the numeric ratio.

Types of ratios- what are ratios in math:

Compounded ratios in math.

Duplicate ratios in math.

Triplicate ratios in math.

Define compounded ratios in math:

Ordinary format for compounded numeric ratio is

`w/x` *`y/z`=`(wy)/(xz)`

Example for compounded numeric ratios in math:

How to calculate ratios: `5/1`*`2/3`=`(5*2)/(1*3)`  or `10/3`or 10:3

Practice problems for compounded ratios in math:

How to calculate ratios:  `4/1`  * `3/2`    Answer: `(4*3)/(1*2)` or `4/2` or 4:2

How to calculate ratios: `5/2` * `3/2` Answer: `(5*3)/(2*2)` or `5/4` or 5:4

Define duplicate numeric ratios in math:

General format for duplicate ratio is

`(x/y)*(x/y)` = `(x^2)/(y^2)`

Example for duplicate numeric ratios in math:

How to calculate numeric ratios: `9/2` *`9/2` = `(9*9)/(2*2)` or `(9^2)/(9^2)`   or `9^2` :`2^2`

Practice problem:

How to calculate numeric ratios: `(11/2)*(11/2)`    answer: `(11^2)/(2^2)` or `11^2` :`2^2`

Define triplicate numeric ratios in math:

General format for triplicates ratio is

`x/y`  `x/y` `x/y` =`(x^3)/(y^3)`

Example for triplicate numeric ratios in math:

How to calculate numeric ratios: `3/2` * `3/2` * `3/2`=`(3*3*3)/(2*2*2)`=`(3^3)/(2^3)` or `3^3`:`2^3`

Practice problem:

How to calculate numeric ratios: `3/2` * `3/2` *`3/2`   answer: `(3^3)/(2^3)` or `3^3`:`2^3`



Define Inverse numeric ratios in math:

It is often want to guesstimate the numbers of a numeric ratio in the inverse order. To do this, we simply swap the numerator and the denominator. Therefore, the inverse of 5:10 is 10:5. When the terms of a ratio are swap, the INVERSE NUMERIC RATIO results.

For example, in problems 1 through 6, write down the ratio as a fraction and reduce to lowest terms. In problems 1 through 6, write the inverse of the given ratio.

Example problem for inverse ratios in math:

In math, how to calculate inverse numeric ratios:  `5/25`

Solution:

=`5/25`    (5 Divided by both the numerator and denominator)

=`1/5`

Answer is `1/5` or 1:5

Simple Math Fractions

Introduction to simple fractions in math:

A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, etc…A fraction consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole.

SOURCE: WIKIPEDIA


Examples problems of simple fractions in math:


Simple math fraction example 1:

Solve `7/4+5/2`

Solution:

We can add the given fractions by using the following methods.

First we can see the denominator part.

If denominator values are same we can not make any change in the numerator.

But if denominator values are different we can find the L.C.M of denominators and then change the numerator value depends on L.C.M value.

In the above problem, denominators are different.

So we can take the L.C.M of 4, 2.

L.C.M (4, 2) = 4

Therefore, `(7*2)/ (4*2) + (5*4)/(2*4)`

`= 14/8+20/8`

Now denominators are equal. Then we can add the fractions easily.

That is, `(14+20)/8`

`= 34/8`

After simplifying,

`= 17/4`

Answer: `17/4`

Simple math fraction example 2:

Solve `9/2- 5/3`

Solution:

We can subtract the given fractions by using the following methods.

Before we can go to subtracting, we can see the denominator part.

If denominator values are equal we need not to change the numerator.

But if denominator values are different we can find the L.C.M of denominators and then change the numerator value depends on L.C.M value.

In the above problem, denominators are different.

So we can take the L.C.M of 2, 3.

L.C.M (2, 3) = 6

Therefore, `(9*3)/(2*3)-(5*2)/(3*2)`

`= 27/6-10/6`

Here denominators are equal.

That is, `(27-10)/6`

`= 17/6`

Answer: `17/6`

Simple math fraction example 3:

Solve `1/2* 3/2`

Solution:

We can multiply the given fractions by using the following method.

Fractions are multiply by the multiplication of both numerators and also both denominators.

That is, `(1*3)/ (2*2)`

` = 3/4`

Answer: `3/4`

Practice problems of simple fractions in math:


Simple math problems:

Solve `9/2+ 4/3 `
Solve `3/4-1/2 `
Solve `6/2*7/3`
Answer:

`35/6`
`1/4`
`7`

How to Distribute Math

Introduction to how to distribute math:
Distribution functions in mathematics are mainly used for generalizing the functions. By distributing the function, the derivatives cannot exists in the classical sense. The formulations of partial differential equations are done by using the distribution function. In the partial differential equation, the classical solutions are very difficult to use. But when we using the distribution function it is very easy.

Various types for how to distribute math


There are many types of functions are used to distribute math. They are given in the following,

Distribute test function
Distribute operations
Distribute the localization functions



Explanation for how to distribute math


Distribute test function:

Distribution functions are defined as one of the types of distribution in the mathematics. For example, the distribution function on U is given by S: (U) `|->` R has the values in the R function. Then it can be given by,

`lim_(n->oo)` S(φn ) = S ( `lim_(n->oo)` φn )

where,

φn = convergent sequence present in D(U).
D' (U) = continuous dual space
Distribute of operations:

Distributions of operations are also one of the types of the distribution function in mathematics. Therefore, most of the operation is mainly defined on the smooth functions. Therefore the formula is given by,

T : D(U) `|->` D(U)

The above function is defined as the linear mapping functions.where, T is used to represent the topology.

By extending the function og T we get,

T  : D' (U) `|->` D' (U)

Distribute of localization functions:

Localization is also one of the distribution functions of mathematics. The value of U present in the distribution function is not given easily in D' (U) . Some restrictions are given to the U value. Therefore the open function of U is given as distribution function. The restrictions formula is given by,

Solve Math Problems

Introduction to solve math problems

Solve math problems is very simple. Math is very biggest subject and interesting subject which are very important for our life. Many topics of math problem are there to find and solve according to the problems given. To solve math problems we have different sequence of steps, methods, functions and formulae every thing. Solve math problems includes topics like algebra, arithmetic operations, functions, limits, calculus trigonometry etc. Many other topics are also involved in mathematics that have different models of problems that are to be solved.  Here some of the math problems are solved.

solve math problems


1. Solve 1 0 5 7 x 3

Solution

1 0 5 7
3 x
-----------
3 1 7 1
----------
2. Solve

a) 15 +46 =? – 8

b) 25 – 17 = 4 +? +1

Solution

a) 15 + 46 =? – 8

61 =? – 8

61 + 8 = 69

So the answer is 69

15 + 46 =69 – 8

b)  25 – 17 = 4 +? +1

25 – 17 = 5 +?

8 = 5 +?

8 – 5 =?

So the answer is 3

25 – 17 = 4 +3 +1

3. Solve 3x + 5 = 20

Solution

3 x + 5 = 20

Subtract 5 on both sides

3 x + 5 – 5 = 20 – 5

3x = 15

Divide by 3

x = 3.

Additional solve math problems:


4. Solve math problem using PEMDAS rule

(5*6) + 9 – 8 / 2 *2 + 3

Solution

30 + 9 – 8 / 2 * 2 + 3 ------------ (Parenthesis first)

30 + 9 – 8 / 4 + 3------------------ (No exponents so net multiplication)

30 + 9 – 2 +3 --------------------- (Division)

39-5--------------------------------- (Addition)

34

5. SOLVE 35 x 8

3 5 x 8

Solution

3 5
8  x
---------------
2 8 0
---------------
6. Solve 578 * 23

Solution

5 7 8
2 3 *
----------------
1 7 3 4
1 1 5 6
-------------------
1 3 2 9 4
------------------
Practice problems

1. Solve math problems

a) 231 * 42

b) 78 * 245

Answer

1 a) 9702

b) 19110

Biased Problems Math

Introduction to biased problems in math:

Normally biased problems in math are nothing but a question wondered the answers are favored over others such a way. And the main thing in biased math problems are it will make some assumptions. These assumptions on a biased problems may or may not be true.

Example:

Do you want t eat pizza or burger? This is an unfair question, because it favors pizza over burger.

Let us see some examples for biased problems in math.

Examples foe biased problems in math:


Example 1:

If the following question is a biased then say the answer as 0 or 1. Where yes mean 1 and no mean 0.

Do you like math subject?

Solution:

The given question is Do you like math subject?

The answer is 0. Because here it won’t take any assumption or I didn’t take any answers over another answer. So it is an unbiased question.

Example 2:

A survey among the importance of the elder’s health care conducted. The percentage of the health care and age of the elders is given. These percentage and age gives the sample. From this find which sample is a biased one.

Sample 1:

Percentage (%)    28    25    22    23
Age limit    30 - 45    46 - 50    50 - 60    61 - 80
Sample 2:

Percentage (%)    32    28    34    6
Age limit    30 - 45    46 - 50    50 - 60    61 - 80
Sample 3:

Percentage (%)    18    19    25    26
Age limit    30 - 45    46 - 50    50 - 60    61 - 80
Sample 4:

Percentage (%)    10    15    22    20
Age limit    30 - 45    46 - 50    50 - 60    61 - 80

Solution:


From the above we understand a sample is nothing but a population sample.

When a population survey has to take mean we have to take the population sample we have to study.

Here the percentage of sample which is above 80 is 6 %. And it does not represent the opinions about the previous elders. So sample 2 is a biased one.

Negative and Positive Math

Introduction:

Negative and positive signs are the important concepts in mathematics.  In mathematics addition and subtraction and multiplication and division are the important basic arithmetic operations. Subtraction is represented as the symbol ‘-‘and addition is represented as the symbol ‘+’. In this topic we have to discuss about the negative and positive signs of math.

The Basic operations in math are

Positive (+)
Negative (-)
Multiplication (x)
Division (/)

Brief Description of Negative operation in math


Negative Operation:

Negative operation is ‘-’. It is used to subtract two or values.

For Example Subtract (5, 3) means 5-3 =8.

The most common key words used to represent subtraction are

Subtract
Difference
Minus
Negative
Less
Left
Example Problem:

Subtract 34-18

Solution:

Here the following steps to be followed,

Step 1: These are the two digit numbers.

Step 2: First we can subtract the unit digits.

Step 3: here the unit digits are 4 and 8

Step 4: 8 is greater than 4

Step 5: So we are not able to subtract directly.

Step 6: Borrow one from the ten’s digit value 3

Step 7: Now the tern’s digit value be 2

Step 8: one’s digit value be 14

Step 9: now 8 is subtracted from 14 that is 6

Step 10: therefore the unit digit is 6

Step 11: ten’s digit subtraction values are 2 and 1

Step 12: Therefore the ten’s unit digit be 1

Step 13: Therefore the difference of 34 and 18 is 16.



Brief Description of Positive operation in math


Positive Operation:

Positive operation is ‘+’. It is used to add two or values.

For Example Add (5, 3) means 5+3 =8.

The most common keywords used to represent addition are

Sum
Add
Plus
Increase
Increment
Total
Positive
More
Example Problem:

Find the sum of 15, 18.

Solution:

Here the following steps to be followed,

Step 1: These are the two digit numbers.

Step 2: First we can add the unit digits.

Step 3: The sum of the unit digits be 5 + 8 is 13.

Step 4: Then keep 3 and keep 1 as remainder to the next two digit term.

Step 5: Then the sum of ten’s digit number is 1 + 1 =2

Step 6: We can add this 2 to the remainder value 1

Step 7: Therefore the ten’s place value is 3

Step 8: And then unit place value is 3

Step 9: So the total sum of 15 + 18 be equal to 33.

Math Compatible Numbers

Introduction:

Well matched numbers are compatible numbers. Each compatible number friendly with other compatible numbers. If we want to estimate the mental computation, use the compatible numbers. The problem have actual numbers with closely related value. Addition, subtraction, product or division are estimated by using compatible numbers. Math compatible numbers have the end integers as 0 or 5.


Explanation for math compatible numbers


Examples of math compatible number:

1). If we take the 12 and 4, they are called as math compatible numbers. Because 4 divides 12 without any remaining.

2). The compatible numbers 1200 and 6 because 6 divides the 12 quickly and give the answer 2. At the end of 2, we put two zeros.

3).  100 and 20 are math compatible numbers because multiplying 1 and 2 to get 2 quickly. At the end of 2 put three zeros.

4). If we get the compatible numbers for 33 and 28, round the values. That is,compatible number for both 33 and 28 may be (35, 30) or (30, 25). The compatible number sum is 65 or 55.

Estimate the division using compatible numbers:

We cant get the exact numbers when we divide the compatible numbers. It is used for reasonable estimation. If we want to reduce the one number value, we should reduce the another one also.We must increase the value of one number when another number increased. It give the close value.

Example with division:

1). 228 divided by 4.

230 and 5 are compatible numbers for 228 and 4. Here compatible number’s value are increased. The number 5 divide the 230 to get 26.

2). 198 divided by 3.

200 and 4 are math compatible numbers for 198 and 3. Here also the values are increased. Divide the 20 by 4 and get 5. Then add one zero to 5.

Estimate the multiplication using compatible numbers:

Multiplication also follow the same procedure as division.

Example with multiplication:

1). 68 multiply with 3.

The compatible numbers for 68 and 3 are 70 and 5. The value 7 multiply with 5 to get 35. Add one zero to 35.

2). 585 multiply with 190.

The compatible numbers for 585 and 195 are 600 and 200. Multiply 6 and 2 to 12 and put four zeros.

Exercise problem for math compatible numbers:

1). Add 63 and 42.

Answer: The compatible numbers are 60 and 40.

2). Divide 450 by 25.

Answer: The compatible numbers are 500 and 30.

What Does Mean in Math Terms

Introduction of mean in math terms:

In statistics, the mean key word refers to the value of the total values and the total value is made to divide with the number of terms present in the terms. The means also termed as arithmetic mean, which equals the value on the either side of the terms. The other terms are statistics are named as median and mode. The mean is simple term in the statistics to calculate the results.


Mean in math term:


The list of values in which its sum is made to divide through the total number of values present in the list is known as mean. The mean is also known as arithmetic mean. The terms mean and average are similar. The difference of the two means are nothing but the subtraction of the first mean vale with the another mean value.

Mean = sum of the values/total number of values

The mean of the grouped data is nothing but the two list of values are made to given on the question. In which the mean are calculated through the formulae of

Mean of grouped data = SfX / Sf

The SfX is nothing but the product of values present in the both list of elements, and the sum of the total lists are denoted.

The Sf is nothing but the sum of the values present in the second list of elements.

Example problems for mean in math terms:


Example 1:

Heights in centimeters of thirteen students are:

126, 127, 145, 140, 157, 149, 130, 136, 166, 129, 143, 134, 129

Solution:

If we can find the mean, using the following formula in math:

Mean: sum of all values/total numbers

Mean= 1811/13

=139.307

Answer: 139.307

Example 2:

The highest scores of the first ten players in ICC ODI are:

198,195,192,190,186,184,182,180,179,178.

Solution:

We can find the mean, using the formula found below in math terms

Mean = sum of all values/total numbers.

= 1864/10

Answer: 186.4

4th Grade Math Practice

Introduction to 4th grade math practice:

Study of arithmetic operation and numbers system is called basic mathematics. 4th grade math practice is nothing but, it is used to practicing some basic math operation. Math practice is used to growth our mathematical knowledge.

Addition, subtraction, division and multiplication are called basic arithmetic operations of mathematics. The 4th grade math practice is deals with basic algebra, in the 4th grade math practice is involves a basic math operation only. This article we are discussing about 4th grade math practice problems.

Basic addition problems for 4th grade math practice:


1. Find the total value of the given numbers, using addition operation, 455 + 266 + 767.

Solution:

Given numbers using addition operation for, 455 + 266 + 767

First step, we are going to add the first two numbers,

455 + 266 = 721

Then add third number with first two numbers of sum values,

721 + 767 = 1488

Finally we get the answer for given numbers are 1488.


Basic subtraction problems for 4th grade math practice:


2. Find the subtract value of the given numbers, using subtraction operation, -60 - 750 – 224.

Solution:

Given numbers using subtraction operation for, -60 - 750 – 224

First step, we are going to add the first two numbers,

- 60 - 750 = -810

Then subtract third number with first two numbers of subtracted values,

- 810 - 224 = -1034

Finally we get the answer for given numbers are -1034.


Basic multiplication problems for 4th grade math practice:

3. Find the multiply value of the given numbers, using multiplication operation, 20 * 12 * 8.

Solution:

Given numbers, using multiplication operation for, 12 * 20 * 8.

First step, we are going to multiply the first two numbers,

12 * 20 = 240

Then multiply the third number with first two numbers of multiplied values,

240 * 8 = 1920

Finally we get the answer for given numbers are 1920.



4th grade math practice problems:


1. Find the add value of the given numbers, using addition operation, 55 + 26 + 74.

Answer is 155.

2. Find the add value of the given numbers, using addition operation, 31 + 26 + 69.

Answer is 126.

3. Find the subtract value of the given numbers, using subtraction operation, -54 - 7 - 16.

Answer is -77.

4. Find the subtract value of the given numbers, using subtraction operation, -5 - 7 - 22.

Answer is -34.

5. Find the multiply value of the given numbers, using multiplication operation, 2 * 5 * 9.

Answer is 90.

6. Find the multiply value of the given numbers, using multiplication operation, 6 * 5 * 2.

Answer is 60.

Answer Pre Algebra Questions

Introduction to answer pre algebra questions:

Pre algebra is a method of calculating the number system by different methods like linear equations and geometry methods. In algebra each and every systems has a common formula to explain its all concepts.
Pre algebra is a easiest number system where we can implement the techniques for any algebra calculations.
Pre algebra describes about the fraction, decimals, polynomials, ratios, geometry, measurements and integers and other number formats.

Example for answer pre algebra questions :


1)  solve the question:   g + 79 = 194

Answer:

g + 79 = 194

g + 79 - 79 = 194 - 79 ( add -79 on both sides, we get)

g = 115.

2)    Solve:   n - 56 = 604

Answer:

n - 56 = 604

n - 56 + 56 = 604 + 56 ( add 56 on both sides,we get)

n = 660

3)    compute:   `m / 5` = 10

Answer:

`m / 5` = 10

5`(m / 5)` = 10(5) ( multiply by 5 on both sides, we get)

m = 50

4)    fine the value of s in the given question:   7s - 7 = 42

Answer:

7s - 7  = 42

7s - 7 + 7 = 42 + 7 (  add 7 on both sides, we get)

7s = 49

(7s) / 7 = 49 / 7 ( divide by 7 on both sides, we get)

s = 7

5)    find:   5(h + 2) = 25

Answer:

5(h + 2) = 25

[5(h + 2]/5 = 25/5 (divide by 5 on both sides, we get)

h + 2 = 5

h + 2 -2 = 5 -2 ( add -2 on both sides, we get)

h = 3

6)    The amount of twice a digit plus 13 is 75.  Find the number.

Answer:
Answer:

•    The word "is" represents equals.

•    The word "and" represents plus.

•    Therefore, we can rewrite the problem like the following:

•    The total of twice a number and 13 equals 75.

•     Using figures and a variable that denotes something, D in this case (for digit),

•    we can write an equation that represents the same thing as the given problem.

2D + 13 = 75

By solving this equation by isolating the variable.

2D + 13 = 75 Equation.

- 13 = -13 Add (-13) to both sides.

-------------------

2D = 62

D = 31 Divide 2 on both sides.

So the number is 31.


Answer pre algebra questions: Practice problems


1) (9n 2 + 15n + 9) + (14n 2 + 12n + 8) = ?

Answer: 23n 2 + 27n + 17  (after solving the question)

2) (2a + b) + ( –a + 4b) = ?

Answer: a + 5b ( after solving the question)

Sunshine Math Answers

Introduction to sunshine math answers:-

SUNSHINE MATH, this course is planned to improve your child’s voyage from first to last in mathematics. It is a math fortification course offered by Somerset Academy. Mission of Sunshine Maths is to put forward each and every students the chance to defy themselves in all category of math conception by giving them additional learning activities.

Sunshine Math Word Problems with Answers:-


Prob 1 :

Ram can cut a piece of wood in to three pieces in 20 minutes. How long it takes for him to cut the piece of wood in to 6 pieces.

Sol :

Given:-

Ram can cut a piece of wood in to three pieces in 20 minutes.

Find in how many minutes ram cut 6 pieces of wood.

3 pieces = 20 minutes. ------------> (1)

6 pieces = ? Minutes

6 is two times of 3.

So he takes double the time he took for cutting the piece in to three pieces.

The time taken to cut the wood in to three pieces is 20 minutes.

Double the times of 20 minutes is 40 minutes.

The time taken to cut the wood in to six pieces is 40 minutes.

Ans : 40 minutes



More examples:-Sunshine Math Equation Problems with Answers:-


Prob 2 :

When I was at the park I saw some girls and cats. Counting heads and legs I got 32 and 104 respectively. Find the total number of girls and cats in the park.

Sol :

Given there are totally 32 heads and 104 legs respectively.

The equation for head can be written as x + y = 32.

Let x – girls, y – cats.

The equation for legs can be written as 2x + 4y = 104.

By solving the above two equation we get

y = 20 and x = 12 .

Ans : The number of girls in the park is 12 and number of cats in the park is 20.

Prob 3 :

23 + 21 + 5+ 3 + 56 = 159.

Find the given expression correct or not.

Sol :

The given expression is 23 + 21 + 5+ 3 + 56 = 159.

The sum of numbers in right hand side is 106.

Ans : So the given expression is algebraically wrong .

Prob 4 :

13 + 41 + 51+ 32 + 34 = 171.

Find the given expression correct or not.

Sol:-

The given expression is 13 + 41 + 51+ 32 + 34 = 171.

The sum of numbers in right hand side is171.

Ans : So the given expression is algebraically correct.

Prob 5 :

3 + 1 + 5+ 32 - 34 = 11.

Find the given expression correct or not.

Sol :

The given expression is 3 + 1 + 5+ 32 - 34 = 11.

The sum of numbers in right hand side is 7.

Ans :So the given expression is algebraically wrong.

Prime Numbers 1-100

Introduction to prime numbers 1-100:

Prime numbers are the numbers it can be divided only by 1 and the number itself.Prime numbers cannot have any thing or factors except one and the number by itself. The +ve(positive) integers are divided into two such as prime numbers and composite integers.Totally there is  25 prime numbers between 1 and 100. So remaining are the composite numbers.

The numbers are like 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 are 25 prime numbers between 1 to 100.That twenty five prime numbers are in between 1-100 These numbers cannot be divide by any other number except 1 and the number itself.And the same is called prime numbers.


The prime numbers from 1-100


In the prime number composite numbers have thing or factors  compare than other is one and itself Except the 25 prime numbers between 1 to 100 all the other numbers are composite numbers.In that,the list of  composite numbers 4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,

62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100.......

These were the composite numbers between 1 to 100.


Problems of prime numbers between 1-100


solving prime numbers 1-100:

Here we mentioned the prime numbers from 1 to 100 only

So many prime numbers are there.

Let us see some examples,

Example 1:

To determine the given number is prime or not :one hundred forty-three ?

The factors of 143 are 1, 11, 13,143

So here we have factors for 143 other than 1 and 143

So this is not a prime number

The remaining prime number compare than other numbers are called composite number

So 143 is a composite number

Example 2:

To determine the one hundred thirty-one is prime or not?

Solution

The factors of 131 is 1, 131

So here we don’t have any other factor except 1 and the number 131

So the number 131 is a prime number

Example 3

To determine the prime numbers between thirty to thirty-five?

Solution

30    - Factors  - 1,2,3,5,6,10,15,30 – Not a prime number

31    – Factors – 1,31 – Prime number

32    – Factors – 1,2,,4,8,16,32 –Not a prime number

33     - Factors  - 1,3,11,33  - Not a prime number

34     - Factors  - 1,2,,17,34 – Not a prime number

35     - Factors – 1,5,7,35 –Not a prime number

So from 30 to 35 we have only one prime number

31 is only prime between 30 to 35

Definition of Conclusion

Introduction on definition of conclusion:

The term definition of conclusion in maths is used to define us about the problem that we solve and when we produce the final result at the end then that stage of processes is called as conclusion. In this chapter let us discuss about the term definition of conclusion in detail with suitable examples and explanations.

Representation of Definition of Conclusion:

The final result that we produce or the result that we produce at the end of the sum is called as conclusion.

Example Problems Based on Definition of Conclusion:

Example 1: Based on definition of conclusion

Solve the given problem by giving a conclusion by finding the value of A if A=33/2?

Solution:

Given: `A=33/2`

To produce an conclusion by finding the value of A

Step 1: The term division to found to be calculated in the given problem

Step 2: The conclusion or result will be given after finding the value of `A`

`A= 33/2`

`A= 16.5`

Hence, we conclude the problem by finding the value of `A=16.5`

Example 2: Based on definition of conclusion

Solve the given problem by giving a conclusion by finding the value of X if X=150/9?

Solution:

Given:` X=150/9`

To produce an conclusion or result

Step 1: The term division to found to be calculated in the given problem

Step 2: The conclusion or result will be given after finding the value of `X`

`X=150/9`

`X=16.66`

Hence, we conclude the problem by finding the value of `X =16.66`



Exercise Problems Based on Definition of Conclusion:

Solve the given problem by giving a conclusion by finding the value of Z if Z=330/5?
Answer: We conclude the problem by finding the value of Z=66

Solve the given problem by giving a conclusion by finding the value of Y if Y=88/2?
Answer: We conclude the problem by finding the value of Y=44

Summation Math

Introduction for summation math:

Summation math is assumed to be the sequence form of addition. Summation is the process of combine a sequence of numbers by means of addition. The summation can be written as n1 + n2 + n3 + n4 + n5 + ……… nn. Summation math is a continuous function for one variable in closed interval. Summation  of an infinite series of value is not constantly possible. In this topic we will discuss the some examples  problems.

Summation Math Rules:

Summation of infinite numbers is called summation,

`sum_(n=1)^oo`  =  1 + 2 + 3 + 4 + 5 + 6 + ...... + `oo`

Summation Rules:

Summation of a number

`sum_(n=1)^oo` a = a + a + a + ...... a (infinite times) = a * (`oo` )

Summation of square of infinite number.

`sum_(n =1)^oo`  i2 = 12 + 22 + 32 + 42 + 52 + ….. n2 = `(n (n + 1) (2n + 1))/(6)`
Summation of cube of infinite number.

`sum_(n=1)^oo` i3 = 13 + 23 + 33 + 43 + 53 + ….. n3 = `(n^2 (n + 1)^2/4) `

`sum_(i=1)^n`  si = s1 + s2 + s3 + … + sn

(n times) = sn, where s is constant.

`sum_(i=1)^n` i = 1 + 2 + 3 + … + n = `(n (n +1)) /(2) `

Example for Summation Math:

Example 1: Determine the value of the summation math `sum_(n=1)^4` ` (3 + 4n)`

Solution:

`sum_(n=1)^oo`  `= 1 + 2 + 3 + 4 + 5 + 6 + ...... + n`

`sum_(n=1)^5` `(3 + 4n) = (3 + 4(1)) + (3 + 4(2)) + (3 + 4(3)) + (3 + 4(4)) `

`= (3 + 4) + (3 + 8) + (3 + 12) + (3 + 16) `

`= 7 + 11 + 15 + 19 = 52`

Answer: 52

Example 2: Determine the value of the summation math `sum_(n=1)^6` `(n + 1)^2`

Solution:

Here, `(n + 1)^2`

`(n + 1)^2 = n^2 + 2n +1`

so, we wirte the summation as `sum_(n=1)^6` ` (n^2 + 2n+ 1)`

the summation, we get

`sum_(n=1)^6` `n^2` + `sum_(n=1)^6` `2n` +  `sum_(n=1)^6`

`= {12 + 22 + 32 + 42 + 52 + 6 ^2} + {(2 * (1)) + (2 * (2)) + (2 * (3)) + + (2 * (4)) + + (2 * (5)) + + (2 * (6))} + (1 * (6))`

= `((6 (6 + 1) ((2 * (6)) + 1))/(6)) + 42 + 6` 


`=91 + 42 + 6`

Answer: 139

Simple Solution Math Book

Introduction for simple solution mathematics book:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.  The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Arithmetic operations and numbers are mainly used in mathematics. Let us see some simple solution math book.  (Source: Wikipedia)



Example Problems for Simple Math Book:

Let us see some simple math book here:

Problem 1:

Solve the equation 2x - 24 = 78

Solution:

Given equation 2x - 24= 78

Add 24 on both the sides of the equation, we get

2x = 102

Divide the obtained equation by 2 on both the sides, we get

x = `102 / 2` = 51

Therefore the final answer for this equation is x =51

Problem 2:

Solve:

Given function `(x / 4)` = 14

Solution:

Given, `(x / 4)` = 14

Multiply the above equation by 4 on both the sides, we get

x = 14 * 4

x = 56

Therefore the final answer is x = 56

Problem 3:

Divide 75 by 5

Solution:

Given, 75 divided by 5

It can be written as,

75 ÷ 5

Divide the value of 75 by 5, we get

75 ÷ 5 = 15

Therefore the final answer for the division is 15

Problem 4:

Add this two equations x - y2 + 4 and x2 + 2x + y2 - 22

Solution:

The given equations are, x - y2 + 4 and x2 + 2x + y2 - 22

Now we have add the two equations, we get

= x - y2 + 4 + x2 + 2x + y2 - 22

= x2 + 3x - 18

Therefore the final equation will be x2 + 3x - 18

Problem 5:

Subtract the two equations (x - 2y + 18) and (3x + 8y + 60)

Solution:

Given equations are (x - 2y + 18) and (3x + 8y + 60)

Subtract the two equations, we get

= (x - 2y + 18) - (3x + 8y + 60)

Expand the above equation, we get

= x - 2y + 18 - 3x - 8y - 60

= - 2x - 10y - 42

Divide the obtained equation by - 2, we get

= x + 5y + 21

Therefore the final answer is x + 5y + 21



Practice Problems for Simple Math Book:

Problem 1:

Solve x + 24 = 3x - 38

Solution:

Therefore x = 31

Problem 2:

Solve x2 - 144 = 0

Solution:

Therefore x = ± 12

Problem 3:

x + y = 23, find the value of x at y = 2

Solution:

Therefore x = 21

Long Math Problem

Introduction on long math problem

This article is about long math problem. Long math problem will contain a lot of step in solving the problem to obtain the final solution. In some of the long math problem we use different formula to obtain the solution. There are many long math problem in many different math chapters. Each topics of mathematics have different solving properties theorem methods and formulas. There are many websites and online tutors to help with long math problem. Many stiudents favorite and best website to solve long math problem is tutor vista. Below we can see one long math problem.

Long Math Problem

Long math problem does not means that the given problem must be long. It also means the steps taken to solve some problems lead to long math problem. Below we solved one math problem which have a long steps to obtain the entire solution.
1. Solve the equations: p + 2q + 3r = 14, 3p + q + 2r = 11, 2p + 3q + r = 11.

Solution: Let the given equations be identified as follows:

p + 2q + 3r = 14------- (1)

3p + q + 2r = 11------ (2)

2p + 3q + r = 11------ (3)

Consider the equations (1) and (3)

(1) ? p + 2q + 3r = 14

(3) × 3 ? 6p + 9q + 3r = 33 subtracting

–5p – 7q = –19

5p + 7q = 19 (4)

Consider the equations (2) and (3)

(2) ? 3p + q + 2r = 11

(3) × 2 ? 4p + 6q + 2r = 22 subtracting

–p – 5q = –11

p + 5q = 11 (5)

Consider the equations (4) and (5)

(4) ? 5p + 7q = 19

(5) × 5 ? 5p + 25q = 55 subtracting

–18q = –36; ?q = 2

Substitute q = 2 in (5) we get

p + 5(2) = 11; p + 10 = 11; ?p= 1

Substitute p = 1, q = 2 in (3) we get

2(1) + 3(2) + r = 11; 2 + 6 + r = 11 ? r = 3

The solution is p = 1, q = 2, r = 3.


Long Math Problem

Similar to the above problem there are more number of math problems to solve with long steps. In some problems the given math problem will be long and the solution will be a shorter one. In some cases the solution and the problem both will be a longer one. Here are some problem similar to the solved problem above for your practice. The solution also given below and you have to try the steps similar to the problem solved above.

1. Solve: 3x – 3y + 4z = 14; –9x – 6y + 2z = 1; 6x + 3y + z = 5

Answer: The solution is x = 1, y = –1, z = 2

2. Solve: a + b = 3, b + c = –5, c + a = 2.

Answer: The solution is a = 5, b = –2, c = –3.

Multiply Symbol

Introduction of multiply symbol:

Multiplication or Times is fundamental operation on whole numbers. The fundamental operations on whole numbers are addition, subtraction, multiplication, and division. The time is the process of repeated addition of a number. Times or multiply denoted by the symbol × or *. Elementary school students use the symbol × for multiplication (multiply) or times. Leibniz uses the cap symbol `nn`  for multiplication or times. This symbol is used to indicate intersection in set.

Multiplication Example

Multiplication or times indicates by placing the quantities to be multiplied side by side (juxtaposition). Multiplication or times is a short form of addition of the same number several times. The important of multiplication or times process is to place the digits value of the factors in the proper columns. That is, units number must be placed in the units column, tens in tens column, and hundreds in hundreds column. Notice that it is not essential to write the zero in the case of 15 tens (150) since the 1 and 5 are written in the proper columns.

Ex 1:   Multiply 283 by 101

Sol:    283 × 101 means 101 times 283

Or 100 times 283 + one time 283

Or 28300 + 283

Or 28583

Therefore 283 × 101 = 28583

Ex 2:  John earns four times, of what his brother earns. If his brother earns $1800 in a month, how much does John earn?

Sol :  John brother earn $1800

John earn three times more than his brother that is $1800 times 4 (Here the times indicate the symbol ×)

Therefore $1800 × 4

John earn $7200

Ex 3: Multiply 650 × 99

Sol :  650 × 99 means 99 times 650

Or 100 times 650 – one time 650 (Here the times indicate the symbol ×)

Or 65000 – 650

Or 64350

Therefore 650 × 99 = 64350

Practice Problem

1. Kim earns 5 times, of what his brother earns. If his brother earns $1500 in a month, how much does Kim earn?

Ans :  $7500

2. Multiply 350 × 470

Ans : 164500

3. In a town have four post offices. In each post office there are six workers. How many workers do the post offices have in total?

Ans : 24

4. Four children are playing cricket. They all brought 7 balls. How many balls do they have totaled?

Ans : 28

Ones Tenths Hundredths

Introduction to Ones Tenth Hundredths:

These ones, tenths and hundredths are representing the place value of the number. The number which has place value of ones is the number less than ten. That is the number in place value of ones  starts from 0 to 9. The number which has the place value of tenths is that number multiplied by `(1)/(10)` . The number which has the place value of hundredths is that number multiplied by `(1)/(100)` .

Ones Tenths Hundredths:

The standard form of place value exists in decimal number and fraction form. Generally in decimal number, digit place before the decimal point is called as ones and digit after the decimal point is called as tenths and digit after the tenths place is called as hundredths.

Example: x.yz, here

x is the digit placed before the decimal point – Ones.

y is the digit placed after the decimal point – Tenths = x *`(1)/(10)`

z is the digit placed after the tenths place – Hundredths = y * `(1)/(100)`

Example Problem – Ones Tenth Hundred:

Example 1:

Write the place value of ones in following numbers.

a)      2.9

b)      1123

c)      0.01

Solution:

a) 2.9

Given the number is the decimal number, and the digit before the decimal point is 2.

2 is the number having ones Place.

Answer: 2

b) 1123

Here the given number is not the decimal number, it is the whole number.

Step 1: Make the whole number as decimal number without changing the value as 1123.0

Now the ones place of the number 1123 is 3

Answer: 3

c) 0.01

Given the number is the decimal number, and the digit before the decimal point is 0.

0 is the number having ones Place.

Answer: 0

Example 2:

Say the ones tenth and hundredths of the following numbers.

a)      2.34

b)      17.456

Solution:

a) 2.34

The digit before the decimal point = 2 = Ones

The digit after the decimal point = 3 = tenths

The digit after the tenths place = 4 = hundredths.

b) 17.456

The digit before the decimal point = 7 = Ones

The digit after the decimal point = 4 = tenths

The digit after the tenths place = 5 = hundredths.

Tangent Line Formula

Introduction To Tangent Line Formula:

Normally Tangent Line is defined as the line which locally just touches a curve particularly at one and only one point .Specifically We have to know that there is no intersection at all in any other points in a curve.Tangent Line Formula is used to represnt the tangent line in an efficient manner.In this article we will see about the tangent line formula with some practice example problems.

Tangent Line Formula:
The tangent line  to a curve at a given point is the straight line that just touches the curve particular point. The point of tangency means that the tangent line is going in the same direction with the curve, and  it is the best straight-line approximation to the curve at that point.

Normally To find the formula for the Tangent line to the curve y=f(x) at point `p(x_o,f(x_0))` ,We need to find out the slope of the curve . Slope of the curve is also called as the gradient of the curve.

Slope of the curve  calculated by using the following two steps:

1.First we need to take the derivative of the curve equation,

`dy/dx=f'(x)`

2. Then evaluate the above equation at the point p(x_o,f(x_0))

`dy/dx=f'(x_0)=slope`

The Equation for the line if we are knowing the slope and point

`y-y_1=m(x-x_1)`

Here the points are`(x_0,f(x_0)` and slope is `f'(x_0)`

So the Tangent line formula is

`y-f(x_0)=f'(x_0)(x-x_0)`

Tangent Line Formula Example1:

Find the equation of the tangent line to the curve y = x4 at the point (2, 8).

Solution:

`dy/dx= 4x^2`

Slope of the Curve when  x = 2 is

4 × 22 = 16.
So apply the slope and points in the slope point formula of the line.

`y-y_1=m(x-x_1)`

`y - 8 = 16(x - 2)`

y = 16x – 24

This is the equation of the tangent line

Tangent Line Formula Example2:

Find the equation of the tangent line to the curve `y = 5x^3-4y^2`  at the point (1, 2).

Solution:

`dy/dx= 15x^2-8y`
Slope of the Curve  when the points are (1,2) is

`dy/dx=15-16`

`m =-1`

So apply the slope value and x and y values into the slope point formula of the line.

`y-y_1=m(x-x_1)`

` y - 2 = -1(x - 1)`

`y-2 = -x +1`

y+x=3

This is the equation of the tangent line

Define Loss Ratio

Introduction for define of loss ratio:

A relation is getting form the comparison of two quantities like in some wisdom is called a ratio. Ratio will be show by the terms of fraction, that is, a: b is equal to `a/b` for example 25 is `1/4` of the hundred; Therefore, the ratio of 25 to 100 is `1/4.` We can write it in ratio as 1:4. The loss ration is calculated as the total money paid out is divided by the sum of the money is taken for the premium is multiplied by the 100.

Loss ratio = `"total money paid out"/"sum of money taken for premium"` `xx` 100

Example for Define of Loss Ratio:

Example:

A company has paid out `$` 65000 in claims of a previous year to john. But the company has taken in a total of  `$` 100000 in premiums during a particular year. Calculate the loss ratio to define.

Solution:

Total money paid out = `$` 65000

Sum of money taken for premium = `$` 100000

Loss ratio = `"total money paid out"/"sum of money taken for premium"` `xx` 100

= `65000/100000` `xx` 100

= `65/100` `xx` 100

= .65 `xx` 100

= 65%

Therefore the loss ratio for the company is 65% .

Practice Problems for Definition of Loss Ratio:

Problem 1:

A company has paid out `$` 70000 in claims of a previous year to Martin. But the company has taken in a total of `$` 150000 in premiums during a particular year. Calculate the loss ratio to define.

Solution: The loss ratio for the company is 46.67%

Problem 2:

A company has paid out `$` 75000 in claims of a previous year to Paul. But the company has taken in a total of  `$` 200000 in premiums during a particular year. Calculate the loss ratio to define.

Solution: The loss ratio for the company is 37.5%

Problem 3:

A company has paid out `$` 80000 in claims of a previous year to Sarra. But the company has taken in a total of `$` 250000 in premiums during a particular year. Calculate the loss ratio to define.

Solution: The loss ratio for the company is 32%

Percent Word Problem Solving

Introduction to percent word problem solving:

In math, percent is an expression, expressing the fraction as a percent (that is "per" "cent" means "per" "hundred"). The percentage is represented as "%" sign. The percentage of the number is expressed as 7%. Percentage expresses whether one quantity is larger or smaller with respect to the other quantity. The word problem is expressed in which it fits the equation.

There are three steps to solving math word problems:

Translate into equations
Solve the equations and
Check the answer
In math percent word problems, we have to translate the simple English statements into mathematical expressions. For example “of” indicates multiplication (times). Percentage word problems can be easily solved by using the rule, If suppose,

"(x) is (some percentage) of (y)", which translates to "(x) = (some decimal) × (y)"



Formula for Percent Word Problem Solving:
Formula for percentage:

The formula for percentage is the following and it must be easy to use:

`"is"/"of" = "%"/"100"`

Example 1:

What percent of 40 is 50?

Solution:

The given statement is

Percent * 40 = 50

Therefore,

x % `xx` 40 = 50

`x/100` `xx` 40 = 50

`(40x)/100` = 50

Now cross multiply to get

40x = 50*100 = 5000

x = `5000/40`

x = 125

Therefore, Fifty is 125% of 40

Example 2:

25% of what is 30?

Solution:

The statement is

25% `xx` x = 30

Therefore,

`25/100` `xx` x = 30

`(25x)/100" ` = 30

x = `3000/25`

= 120

Answer: 30 is 25% of 120

Examples of Percent Word Problem Solving:

Example 3:

In a college, 30% of students are studying computer science. If their total number is 120, how many students are studying in that college totally?

Solution:

There are 30% of students are studing computer science. We understood that 30% of all students in college are equal to number of students studying computer science.

Therefore, the equation is

30% of x = 120

`30/100`` xx x` = 120

30 x = 120 * 100

30 x = 12000

x = 12000/30

x = 400

Therefore, we have 400 students in the college.

Practice Percentage Word Problems

Practice problem 1:

What percent of 15 is 20?

Answer key: 133.33

Practice problem 2:

40% of what is 70?

Answer key: 175

Practice problem 3:

In a test there are 30 questions in total. If john gets 70% correct, how many questions did john missed?

Answer key: John missed 9 questions

Equations with Variables on both Sides Calculator

Introduction for equations with variables on both sides calculator:

Equation with variable are the important part of algebra, generally the equation with same variable are said to be equation with  variables on both sides. Fro example x+2x+4 = x+8 here x is the variable in this equation we need to find the value of variable using calculator. In this article we will discuss about equation with variables on both sides calculator with suitable example problem.

Problem on Equations with Variables on both Sides Calculator:

Simplify the following equations with variables on both sides calculator

Problem(i) : The equation  is 2x+4 = 4x+6+8.

Solution

The given equation  is 2x+4 = 4x+6+8.

Step 1: In this given equation collect the variable

2x-4x+4 = 6+8

Step2: Collecting the constant

2x-4x+4 = 14

2x-4x = 14-4.

Step 3: simplifying the equation

-2x = 10

Step 4: Dividing both sides by -2

`(-2x)/-2` =`10/-2`

x= -5

Step 5: The variable of x is -5.

Problem(ii) : The equation  is 3x= 4x+6+1.

Solution

The given equation  is 3x = 4x+6+1.

Step 1: In this given equation collect the variable

3x-4x = 6+1

Step 2: Collecting the constant

3x-4x = 7

3x-4x = 7.

Step 3: simplifying the equation

-x = 7

Step 4: The variable of x is -7.

Problem on Equations with Variables on both Sides Calculator:

Simplify the following equations with variables on both sides calculator

Problem (i) The equation is -5x+7+8 = -9x +15+10

Solution

The given equation  is -5x+7+8 = -9x +15+10

Step 1: In this given equation collect the variable

-5x+9x+15 = 15+10

Step2: Collecting the constant

-5x+9x+15 = 25

-5x+9x = 25-15.

Step 3: simplifying the equation

4x = 10

Step 4: Dividing both sides by 4

`(4x)/4` = `10/4`

x = `5/2`

Step 5: The variable of x is `5/2` .

Problem (ii) The equation is -2x+7+13 = 4x +14

Solution

The given equation  is -2x+7+13 = 4x +14

Step 1: In this given equation collect the variable

-2x-4x+7+13 = 14

Step2: Collecting the constant

-2x-4x+20 = 14

-6x = 14-20

Step 3: simplifying the equation

-6x = -6

Step 4: Dividing both sides by -6

`(-6x)/-6` =`(-6)/(-6)`

x = 1

Step 5: The variable of x is 1.

Simple Regression Formula

Introduction to simple regression formula:

In mathematics, one of the most important topics in statistics is regression. Regression is determining the relationship between two variables. Regression math are used to analysis the several variables. Regression is one of the statistical analysis methods that can be used to assessing the association between the two different variables.

Example of Simple Regression Formula:
Here we study about the simple regression formula are,

Formula for regression analysis:

Regression Equation (y) = a + bx

Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`

Intercept`(a) = (sumY-b(sumX))/N`


Where,
x and y are the variables.
b = the slope of the regression line is also defined as regression coefficient
a = intercept point of the regression line where is in the y-axis.
N = Number of values or elements
X = First Score
Y = Second Score
`(sumXY)` = Sum of the product of the first scores and Second Scores
`(sumX)` = Sum of First Scores
`(sumY)` = Sum of Second Scores
`(sumX^2)` = Sum of square First Scores.

Example Problem for Simple Regression Formula:

Problem for simple regression formula:

Example 1:

Find the regression slope coefficient, intercept value and create a regression equation by using the given table.

X Values   Y Values

10            11

20            22

30            33

40            44

50            55


For the given data set of data, solve the regression slope and intercept values.

Solution:

Let us count the number of values.
N = 5
Determine the values for XY, X2

X Value  Y Value    X*Y      X*X

10        11        110      100

20        22        440      400

30        33        990      900

40        44       1760     1600

50        55       2750     2500


Determine the following values `(sumX), (sumY), (sumXY), (sumX^2).`
`(sumX) = 150`
`(sumY)= 165`
`(sumXY)= 6050`
`(sumX^2) = 5500`



Plug values in the slope formula,


Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`


`= (5 xx(6050)-(150)xx(165))/((5)xx(5500)-(150)^2)`


`= (30250 - 24750)/(27500-22500)`


`= 5500/5000`

`b= 1.1`

Plug the values in the intercept formula,


Intercept `(a) = (sumY- b(sumX))/N`


`= (165-(1.1xx150))/5`


`= (165 - 165)/5`


`= 0/5`


`a = 0`

Plug the Regression coefficient values and intercept values in the regression equation,
Regression Equation(y) = a + bx
= 0 + 1.1x

Answer:

Slope (or) Regression coefficient (b) = 1.1

Intercept (y) = 0

Regression equation y = 0 + 1.1x