# 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.

## You might like these

• ### Ribosomes and Inclusion Bodies | Definition | Stored Food | Pigments

Definition of ribosome- Ribosome is the organelles which is associated with protein synthesis. It is made up of two subunits. The larger one is spherical in shape and the smaller one is oval in shape. Ribosomes are attached with the endoplasmic reticulum and formed rough

• ### Worksheet on Divisibility Rules | Questions on Test of Divisibility

This is a worksheet which will provide few problems on the divisibility rule of 2, 3, 4, 5, 6, 7, 8, 9, and 10. 1. Check whether the following numbers are divisible by 2 or 3 or both? (i) 2562 (ii) 5693 (iii) 2201 (iv) 7480 (v) 5296 (vi) 4062 (vii) 4568 (viii) 1425 (ix) 1110

• ### Problems on Divisibility Rules | Rules to Test of Divisibility | Test

Here are few problems on the divisibility rules of 2, 3, 4, 5, 6, 7, 8, 9, and 10 which will help the learners in revising their concepts on the divisibility rules. 1. Check whether 3456 is divisible by 2? Solution: The last digit is an even number (i.e. 6) hence 3456 is

• ### Divisible by 10|Test of Divisibility by 10|Rules of Divisibility by 10

The divisibility rule of 10 states that If the last digit of a number is 0 then the given number is divisible by 10. For eg: Check whether 5400 is divisible by 10 or not? Solution: As the last digit of the number is 0 hence, 5400 is divisible by 10

• ### Divisible by 9 | Test of Divisibility by 9 |Rules of Divisibility by 9

This rule states that a number is divisible by 9 if the sum of its digits of the number is divisible by 9 For eg: Check whether 729 is divisible by 9 or not? Sum of the digits = 7 + 2 + 9 = 18 Now 18 is divisible by 9 hence, 729 is also divisible by 9 Here are few examples

• ### Divisible by 8 | Test of Divisibility by 8 |Rules of Divisibility by 8

The most common method to check whether a number is divisible by 8 is to divide and see if the quotient is a whole number or not? If the quotient is a whole number then the given number is divisible by 8. But there is an easier way to check by using the divisibility rule.

• ### Divisible by 7 | Test of Divisibility by 7 |Rules of Divisibility by 7

This rule states that if the difference between twice the digit at units place and the number formed from the remaining digits of the given number is divisible by 7 then the whole number is divisible by 7.

• ### Divisible by 6 | Test of divisibility by 6 |Rules of Divisibility by 6

This topic on divisible by 6 will discuss about the divisibility rule of 6 and few example on the same. Divisibility rule of 6: A number is divisible by 6 if the prime factor of that is 2 & 3 is divisible by 6. For Example: 216 216 is divisible by 2 as the last digit 6 is

• ### Divisible by 5 | Test of divisibility by 5 |Rules of Divisibility by 5

This topic on divisible by 5 will discuss on the divisibility rule of 5 and illustrate few example on the same. Divisibility Rule of 5: If a number ends with 0 or 5 then the number is divisible by 5. For Example: 550 Since the number ends with 0 hence the number is divisible

• ### Divisible by 4 | Rules of Divisibility by 4|Divisibility Rules & Tests

This topic i on divisibility rule of 4 and will provide examples on the same. Divisibility Rule of 4: If the last two digits of the number is divisible by 4 then the whole number is divisible by 4 For eg: 524 The last two digit of the number is 24 which is divisible by 4.

• ### Divisible by 3 | Rules of Divisibility by 3|Divisibility Rules & Tests

This topic is on the divisibility rule of 3 and few examples based on the topic. If the sum of the digits is divisible by 3 then the whole number is divisible by 3. For example 519 The sum of the digits = 5 + 1 + 9 = 15 15 is divisible by 3 hence 519 is also divisible by 3

• ### Divisible by 2 | Divisibility Rule of 2 | Test of Divisibility by 2

This topic would deal with the divisibility rule of 2 and few sums on divisibility rule of 2. Numbers that are ending with 0, 2, 4, 6, and 8 are divisible by 2. That means numbers ending with 0 or multiples of 2 are divisible by 2. We know that numbers which are multiples of

• ### Properties of Divisibility | Divisibility Property |Divisibility Rules

This topic deals with the properties of divisibility which will help us in doing our multiplication and division easy. These rules will help us to determine quickly the factors of certain number, the divisibility criteria of certain number and helps in overall strengthening

• ### Worksheet on Multiples and Factors | List the First Five Multiples

1. List the first five multiples of the following numbers: 2. Choose the numbers that are factors of 24. 3. 3. Choose the numbers that are multiples of 15. 4. Choose the numbers which are multiple of 3 as well as factor of 36