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.
Answers:
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
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