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