# SIMPLIFYING FRACTIONS MADE EASY - LUCID EXPLANATION OF FRACTION PROBLEMS OF SIMPLIFICATION

Fractions before simplifying Fractions
if you have not already done so.

There we studied about half, quarter, three fourth with examples and exercises.

Learn/Teach
Fractions through Fun Games.
For details, see near

There we studied about concept of fraction in general with examples and exercises.

The knowledge of

Conversion of Improper to Mixed and Mixed to Improper Fractions

and

Least Common Multiple (L.C.M.)

is also used here.

To learn how to simplify a single fraction go to

Equivalent Fractions.

Here we see how to simplify a numerical expression involving fractions.

A combination of fractions connected by one or more of the symbols +, -, x, ÷ and 'of', is called a numerical expression with fractions.

Each of these symbols represent an operation.

Performing these operations and getting the value of the expression of fractions is known as simplifying the expression of fractions.

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## BODMAS rule in simplifying fractions

For simplifying an expression, we must perform these operations strictly in the following order : (i) Brackets (ii) Of (iii) Division (iv) Multiplication (v) Addition (vi) Subtraction. To remember the order, remember the word 'BODMAS' which is formed by the first letters of the operations in an order.

Remember this as the 'BODMAS' rule which says
the order of priority of operations as :

• Brackets
• Of
• Division
• Multiplication
• Subtraction.
strictly in that order.

So do the operations in that order
in simplifying Fractions.

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### Solved Example of Simplifying Fractions

Simplify
4  56 + 2⁄3 ÷ 3⁄4 of 2⁄9 - 1⁄2 x 2  34 ÷ 3  79 of (4  717 - 3  12)

Solution :
The given expression
= 4  56 + 2⁄3 ÷ 3⁄4 of 2⁄9 - 1⁄2 x 2  34 ÷ 3  79 of (4  517 - 3  12)

First, let us convert mixed fractions to improper fractions

= 29⁄6 + 2⁄3 ÷ 3⁄4 of 2⁄9 - 1⁄2 x 11⁄4 ÷ 34⁄9 of (73⁄17 - 7⁄2)

Now, let us remove Brackets (B in BODMAS)

= 29⁄6 + 2⁄3 ÷ 3⁄4 of 2⁄9 - 1⁄2 x 11⁄4 ÷ 34⁄9 of (2 x 73 - 7 x 17)⁄34
= 29⁄6 + 2⁄3 ÷ 3⁄4 of 2⁄9 - 1⁄2 x 11⁄4 ÷ 34⁄9 of 27⁄34

Now, let us evaluate 'of' (O in BODMAS)

= 29⁄6 + 2⁄3 ÷ 1⁄6 - 1⁄2 x 11⁄4 ÷ 3

Now, let us evaluate Division (D in BODMAS)

= 29⁄6 + 2⁄3 x 6⁄1 - 1⁄2 x 11⁄4 x 1⁄3
= 29⁄6 + 4⁄1 - 1⁄2 x 11⁄12

Now, let us evaluate Multiplication (M in BODMAS)

= 29⁄6 + 4⁄1 - 11⁄24

Now, let us evaluate Addition (A in BODMAS)

= ( 29 x 1 + 4 x 6)⁄6 - 11⁄24
= 53⁄6 - 11⁄24

Now, let us evaluate Subtraction (S in BODMAS)

= ( 53 x 4 - 11 x 1)⁄24 = 201⁄24 = 67⁄8 = 8  38. Ans.

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### Problem for practice on Simplifying Fractions

Solve the following problem on Simplifying Fractions

Simplify
7  12 + 1⁄2 ÷ 1⁄2 of 1⁄4 - 2⁄5 x 2  13÷ 1  78of (1  25 - 1  13)

For Answer, see at the bottom of the page.

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