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