How To Use Fractions in Math

Introduction for How to use Fractions in Math:
A fraction (from the Latin fractus, broken) 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, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.) and which consist of a numerator and a denominator.

Source – Wikipedia.


How to use Fractions in Math -Type 1:

We can use the fractions in math by the following types.

Math -Example 1:

Addition of two fractions: `1/12+1/12` .

Solution:

Step 1:

From the given fractions the denominators are same.

Step 2:

Adding the numerators and use the same denominators.

= `1/12+1/12`

= `(1+1)/12`

Step 3:

By simplifying the fractions

= `2/12`

= `1/6` is the solution for them.

Math-Example 2:

Subtraction of two fractions: `5/24-10/13` .

Solution:

Step 1:

The LCD for the denominators 24, 13 is 312.

Step 2:

Multiplying and subtracting the numerators and use the same denominators.

= `(13*5)/312-(24*10)/312`

= `(65-240)/312`

Step 3:

By simplifying the fractions

=` -175/312` is the solution for them.

Math-Example 3:

Simplify the two fractions: `(23x)/13-(29x)/18` .

Solution:

Step 1:

LCD for the denominators 13 and 18 is 234.

=` (18*23x)/234-(13*29x)/234`

= `(414x)/234-(377x)/234`

Step 2:

Simplify the numerators.

= `(414x-377x)/234`

Step 3:

Subtract the numerators.

= `(37x)/234` is the solution.

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How to use Fractions in Math - Type 2:


Example 1:

Compare two fractions which are smaller: `11/9` or `23/17` ?

Solution:

Step 1:

LCD for the given denominators 9, 17 is 153.

Step 2:

Multiply the fractions as `(17*11)/153` and `(9*23)/153` .
Step 3:

The solutions for them as

`187/153` and` 207/153`

When comparing two fractions `11/9` is smaller.

Example 2:

Compare two fractions which are greater: `26/12` or `32/15` ?

Solution:

Step 1:

We can convert the given fractions in to decimal form.

Step 2:

Divide the fractions as (26÷12) and (32÷15).

Step 3:

Now we get the solutions for the given fractions.

`26/12` = 2.166 and `32/15` = 2.133

When comparing two fractions `26/12` is greater.