Numerical Expressions Involving Decimal Numbers

We will learn how to simplify the numerical expressions involving decimal numbers. We know how to perform the fundamental operations, namely addition, subtraction, multiplication and division involving decimal numbers and now we will learn to perform two or more operations together.

Solved examples to simplify the numerical expressions involving decimal numbers:

Simplify the following:

(i) 0.75 ÷ 1.5 + 3.4 × 2.5 - 1.6

= 0.75 × 1/1.5 + 3.4 × 2.5 - 1.6 (Divide 0.75 by 1.5 = 0.5)

= 0.5 + 3.4 × 2.5 - 1.6 (Multiply 3.4 × 2.5 = 8.5)

= 0.5 + 8.5 - 1.6 (Add 0.5 + 8.5 = 9.5)

= 9 - 1.6 (Subtract 9 - 1.6 = 7.4)

= 7.4

Therefore, 0.75 ÷ 1.5 + 3.4 × 2.5 - 1.6 = 7.4

(ii) 0.05 + 2 × 1.02 ÷ 0.2 - 0.5

= 0.05 + 2  × 1.02 × 1/0.2 - 0.5 (Divide 1.02 by 0.2 = 5.1)

= 0.05 + 2 × 5.1 - 0.5 (Multiply 2 × 5.1 = 10.2)

= 0.05 + 10.2 - 0.5 (Add 0.05 + 10.2 = 10.25)

= 10.25 - 0.5 (Subtract 10.25 - 0.5 = 9.75) 

= 9.75

Therefore, 0.05 + 2 × 1.02 ÷ 0.2 - 0.5 = 9.75

(iii) 0.01 + 2 × 1.02 ÷ 0.2 - 0.5

= 0.01 + 2  × 1.02 × 1/0.2 - 0.5 (Divide 1.02 by 0.2 = 5.1)

= 0.01 + 2 × 5.1 - 0.5 (Multiply 2 × 5.1 = 10.2)

= 0.01 + 10.2 - 0.5 (Add 0.01 + 10.2 = 10.21)

= 10.21 - 0.5 (Subtract 10.21 - 0.5 = 9.71) 

= 9.71

Therefore, 0.01 + 2 × 1.02 ÷ 0.2 - 0.5 = 9.71

(iv) 9 - 2.5 ÷ 5 × 0.3 + 1

= 9 - 2.5 × 1/5 × 0.3 + 1 (Divide 2.5 by 5 = 0.5)

= 9 - 0.5 × 0.3 + 1 (Multiply 0.5 × 0.3 = 0.15)

= 9 - 0.15 + 1 (Rearrange)

= 9 + 1 - 0.15 (Add 9 + 1 = 10)

= 10 - 0.15 (Subtract 10 - 0.15 = 9.85)

= 9.85

Therefore, 9 - 2.5 ÷ 5 × 0.3 + 1 = 9.85

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