SIMPLIFICATION

INTRODUCTION

With a simple sum that only has two numbers and one single operation, or sign, it’s easy to see how to calculate the answer. Either you add, subtract, multiply, or divide.

But what about when there are several numbers, and different operations? Maybe you need to divide and multiply, or add and divide. What do you do then?

Fortunately, mathematics is a logic-based discipline. As so often, there are some simple rules to follow that help you work out the order in which to do the sum.

Do you know how to solve the two examples given below?

EXAMPLES:

1) Simplify: 21 - 12 ÷ 3 × 2

ANSWER: Given expression:

= 21 - 12 ÷ 3 ⨯ 2

= 21 - 4 ⨯ 2 [Performing division]

= 21 - 8 [Performing multiplication]

= 13 [Performing subtraction]

2) Simplify: 16 + 8 ÷ 4 − 2 × 3

ANSWER: Given expression:

= 16 + 8 ÷ 4 - 2 ⨯ 3

= 16 + 2 - 2 ⨯ 3 [Performing division]

= 16 + 2 - 6 [Performing multiplication]

= 18 - 6 [Performing addition]

= 12 [Performing subtraction]

We can solve it using DMAS rule.

(Division->Multiplication->Addition->Subtraction)

LET'S PRACTICE

QUESTION 1) Simplify:

(a) 16 − 14 ÷ 7 + 6 × 2 (f)54 ÷ 3 × 6 + 9

(b) 15 + 24 ÷ 3 − 1 × 6 (g)16 + 12 ÷ 4 × 5 − 2

(c) 21 − 12 ÷ 3 × 2 (h)15 -2 × 5+ 9

(d) 21 ÷ 7 + 16 − 5 × 3 (i) 30 ÷ 6 + 8 × 3 − 10

(e) 49 − 57 + 8 ÷ 4 × 4 (j) 6 × 20 ÷ 5 + 15 − 10

QUESTION 2) Put >,< or = in the blanks given:

(a)2 x 32 + 46_________ 62 + 4 x 9

(b)120 – 6 x 7_______ 6 x 7 + 40

(c)140 + 4 x 7 ________32 x 5 + 5

(d)8 + 8 x 6 ________6 + 8 x 8