# Worksheet on Simplification of Numerical Expressions

We will practice the questions given in the worksheet on simplification of numerical expressions. We know to simplify a numerical expression having two or more operations, we perform operation like: Division first, followed by Multiplication, Addition and then Subtraction.

1. Simplify the following numerical expression involving whole numbers:

(i) 12 + 4 - 8 ÷ 2 × 3

(ii) 7 - 5 + 14 ÷ 2 + 6

(iii) 37 - 6 × 4 + 32 ÷ 8

(iv) 64 - 48 ÷ 6 × 4 + 8

2. Simplify the following numerical expression involving fractional numbers:

(i) 3$$\frac{1}{2}$$ + $$\frac{5}{8}$$ ÷ $$\frac{3}{4}$$ - $$\frac{1}{2}$$ × 2$$\frac{1}{2}$$

(ii) 4$$\frac{1}{4}$$ + 3$$\frac{1}{8}$$ ÷ 1$$\frac{1}{4}$$ - 1$$\frac{1}{4}$$

(iii) $$\frac{5}{6}$$ ÷ $$\frac{1}{3}$$ + $$\frac{3}{4}$$ - $$\frac{5}{4}$$

3. Simplify the following numerical expressions involving decimal numbers:

(i) 0.2 + 1.3 - 0.4 × 1.5

(ii) 0.3 × 0.4 - 2.4 ÷ 6 + 1.2 × 4

(iii) 0.72 ÷ 1.2 + 3.5 × 4.2 - 1.6

(iv) 9.2 + 3.5 - 4.9 - 3.5 ÷ 0.7 × 1.2

(v) 5.01 × 1.2 - 2.4 ÷ 2

4. Simplify the following numerical expressions:

(i) 8{1 - {3 + (5 - 6 + 7)}}

(ii) 4$$\frac{7}{8}$$[3$$\frac{1}{2}$$ + {8$$\frac{17}{24}$$ - (1$$\frac{1}{2}$$ + 5$$\frac{1}{2}$$ + 1$$\frac{1}{2}$$)}]

(iii) 10 + [5 - {4 - 2(3 + $$\frac{1}{2}$$ - $$\frac{1}{4}$$) ÷ 5$$\frac{1}{2}$$}]

(iv) 0.8{0.75 ÷ (1.35 - 0.6)} - 0.8

(v) 1 - [0.3 - {0.5 - (0.2 - 0.7) - 0.1}]

(vi) 30 - [15 - {6$$\frac{1}{2}$$ - ($$\frac{4}{3}$$ - $$\frac{1}{2}$$)}]

(vii) 0.5 + {10.5 ÷ 0.5 + 6}

(viii) 7 - [6 - {5 - (4 - 3)}] ÷ 2

(ix) 2$$\frac{1}{3}$$ ÷ 4$$\frac{2}{5}$$ + 6$$\frac{1}{2}$$ ÷ 7 × 5

Answers for the worksheet on simplification of numerical expressions are given below.

1. (i) 4

(ii) 15

(iii) 17

(iv) 40

2. (i) $$\frac{37}{12}$$ or 3$$\frac{1}{12}$$

(ii) $$\frac{11}{2}$$ or 5$$\frac{1}{2}$$

(iii) 2

3. (i) 0.9

(ii) 4.52

(iii) 13.7

(iv) 1.8

(v) 4.812

4. (i) 10

(ii) $$\frac{1}{8}$$

(iii) 12$$\frac{1}{4}$$

(iv) 0

(v) 1.6