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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

Addition

Subtraction.

strictly in that order.

So do the operations in that order
in simplifying Fractions.

Get The Best Grades With the Least Amount of Effort : Simplifying Fractions

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Simplify
4 ^{5}⁄_{6}
+ 2⁄3 ÷ 3⁄4 of 2⁄9
- 1⁄2 x 2 ^{3}⁄_{4}
÷ 3 ^{7}⁄_{9}
of (4 ^{7}⁄_{17} - 3 ^{1}⁄_{2})

Solution :
The given expression
= 4 ^{5}⁄_{6}
+ 2⁄3 ÷ 3⁄4 of 2⁄9
- 1⁄2 x 2 ^{3}⁄_{4}
÷ 3 ^{7}⁄_{9}
of (4 ^{5}⁄_{17} - 3 ^{1}⁄_{2})

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 ^{3}⁄_{8}. Ans.

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Problem for practice on Simplifying Fractions

Solve the following problem on Simplifying Fractions

Progressive Learning of Math : Simplifying Fractions

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