# Simplification of Fractions

Still now we have learnt about addition, subtraction, multiplication and division of fractions separately and have also discussed about the properties of each of them separately. However, now we move onto simplification of fraction. What does it mean?

The basic four operations that is addition, subtraction, multiplication or division are present in a single sum and hence we will have to carry out all the four operations together one by one. For doing so we have to remember ‘BODMAS

What does ‘BODMAS’ stands for?

B = Brackets

O = Of

D = Division

M= Multiplication

S = Subtraction

We will carry out the task of simplification in this order.

However, there are three types of brackets:

()= first bracket

{} = second bracket

[]= third bracket

The rule is that anything in the bracket should be simplified first and in accordance with the brackets. The operation of first bracket should be done first then followed by second and third bracket.

Here are few examples showing simplification of fractions:

1. (21/3 + 52/3) × (6/7  ÷  12/14)

= (7/3 + 17/3) × (6/7  × 14/12)

= ((7+17)/3) × ((6 ×14)/(7 ×12))

= 24/3 × 84/84

= 8 × 1

= 8

Explanation:

Here in this sum the operations in the brackets are carried out first according to the rule of ‘BODMAS’. Hence the addition and division in the first bracket have been carried out first and then both the answers of addition and division is multiplied. The answer from division is 1. And we know according to the properties of multiplication that if any fraction/ number  is multiplied by 1 then the result is the fraction/ number itself.

80 – 17/2 × 2 + 13 ÷ 13/7

= 80 – 17/2 × 2+ 13 ÷ 13/7

= 80 – 17/2 × 2 + 13 × 7/13

= 80 – 17/2 × 2 + 7

= 80 – 17 + 7

= 80 + 7 – 17

=87 – 17

= 70

Explanation:

The sum is done following the rule of ‘BODMAS’. Four basic operations that is addition, subtraction, multiplication and division all are involved in this sum. According to ‘BODMAS’

First division is carried out then multiplication and then followed by subtraction and addition.

If we do not follow this sequence and carry out the operation according to the sequence in which the sum is given then we will get the answer wrong.

3. 12 7/8 + 6 2/3 × 24/16

= 103/8 + 20/3 × 24/16

= 103/8 + (20 ×24)/(3 ×16)

= 103/8 +  480/48

= (103 ×6+480 ×1)/48

= 1098/48

= (1098 ÷6)/(48 ÷6)

= 183/8

= 22 7/8

Explanation:

The sum is done following the rule of ‘BODMAS’. The basic operation that is addition and multiplication is involved in this sum. According to ‘BODMAS’ rule first multiplication is done and then addition is carried out. After multiplying the answer is first expressed in lowest terms and then into mixed fraction as it was an improper fraction.

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