 # Proper fraction

Fraction:

Fraction is defined as an element of quotient field, where fraction can be represented as "x/y", here fraction variable 'x' denotes the value called as numerator and fraction variable 'y' denotes the value called as denominator.

Note: the denominator 'y' is not equal to zero. It is a fraction which has a numerator less than its denominator and the value of that fraction is less than one.

Examples:

`3/5` , `1/8` , `24/25`

Improper fraction:

Improper fraction is a fraction, where the top number of fraction that the numerator is greater than or equal to its own denominator (bottom number) and the value of that fraction is greater than or equal to one.

Examples:

3/2, 12/8,  123/12

Arithmetic operation rules are same for proper and improper fractions.

## Addition & Subtraction of fractions:

Adding fractions:

Step1: Check whether the denominators are the same or not (If not, then take LCD by cross-multiplying)

Step2: Add the numerators and write the answer on the same denominator

Step3: Finally reduce the fraction (if needed)

Example:

## 2 / 2 + 1 / 2

Step1: The denominators are the same.

Step2: Add the numerators

2 / 2 + 1 / 2 = (2+1) / = 3 / 2

Step3: No need of reduction. So,

= 3 / 2

Subtracting fractions:

Step1: Check whether the denominators are the same or not (If not, then take LCD by cross-multiplying)

Step2: Subtract the numerators and write the answer on the same denominator

Step3: Finally how to reduce fractions (if needed)

Example:

7 / 5 – 1 / 6

Step1: The denominators are not same. So take LCD by cross-multiplying as follows.

7/5 – 1/6 = (42-5)/30

Step2: Next subtract the numerator

= 37/30

Step3: the fraction is in simplified form. So no need for simplification:

= 37/30

## Multiplication & Division of fractions:

Multiplying fractions:

Step1: Multiply the numerators

Step2: Multiply the denominators

Step3: Finally reduce the fraction (if needed)

Example:

9 / 4 * 7 / 2

Step1: Multiply the numerators:

9 /4 * 7 /2 = 9 *7 / = 63 /

Step2: Multiply the denominators.

= (63) / (4 *2) = 63 /8

Step3: No reduction is needed.

2 /20 = 1 /10

Dividing fractions:

Step1: Change the second fraction as a reciprocal of itself.

Step2: Then multiply the first fraction with the reciprocal fraction

Step3: Finally reduce the fraction (if needed)

Example:

(9/3) /(6/6)

Step1: Change the second fraction upside-down that is the reciprocal of itself:

6 /6 = 6 /6

Step2: Then multiply the first fraction with that reciprocal.

(9 /3) * (6 /6) = ((9 *6) /(3 *6)) = 54 /36

Step3: Reduce the fraction:

= 3/2