The DAV Maths Book Class 5 Solutions and DAV Class 5 Maths Chapter 8 Brain Teasers Solutions of Simplification of Numerical Expressions offer comprehensive answers to textbook questions.
DAV Class 5 Maths Ch 8 Brain Teasers Solutions
Question 1.
Tick (✓) the correct answer.
(a) 8 – 5 + 2 = ______
(i) 4
(ii) 5
(iii) 1
(iv) 10
Solution:
8 – 5 + 2
= 10 – 5
= 5
So, option (ii) is correct.
(b) 2 + \(\frac{1}{2} \times \frac{1}{2}\) = ______
(i) 1\(\frac{1}{2}\)
(ii) \(\frac{5}{4}\)
(iii) 2\(\frac{1}{4}\)
(iv) 3
Solution:
So, option (iii) is correct.
(c) 1.7 + 1.8 × 2
(i) 5.3
(ii) 1
(iii) 5.2
(iv) 7.3
Solution:
1.7 + 1.8 × 2
= 1.7 + 3.6
= 5.3
So, option (i) is correct.
(d) 5.3 + 1.5 ÷ 5 × 2
(i) 3.6
(ii) 5.9
(iii) 1.8
(iv) 9
Solution:
5.3 + \(\frac{1.5}{5}\) × 2
= 5.3 + 0.3 × 2
= 5.3 + 0.6
= 5.9
So, option (ii) is correct.
(e) 3 + .3 × 4 ÷ 2
(i) 4.3
(ii) 3.6
(iii) 6.6
(iv) 9.2
Solution:
3 + .3 × 4 ÷ 2
= 3 + .3 × \(\frac{4}{2}\)
= 3 + .3 × 2
= 3 + 0.6
= 3.6
So, option (ii) is correct.
Question 2.
Simplify the following expressions.
(a) 108 ÷ 12 + 46 – 14
Solution:
108 ÷ 12 + 46 – 14 (108 ÷ 12)
= 9 + 46 – 14 (9 + 46)
= 55 – 15
= 41
(b) 16 + 9 – 3 × 12 ÷ 6 – 5
Solution:
16 + 9 – 3 × 12 ÷ 6 – 5 (12 ÷ 6)
= 16 + 9 – 3 × \(\frac{12}{6}\) – 5
= 16 + 9 – 3 × 2 – 5 (3 × 2)
= 16 + 9 – 6 – 5 (16 + 9)
= 25 – 6 – 5 (6 – 5)
= 25 – 11
= 14
(c) 2 × 1 – \(\frac{1}{4} \times \frac{1}{4}\) ÷ 2
Solution:
(d) \(2 \frac{1}{5}+2 \frac{5}{7} \times \frac{7}{19}-\frac{1}{4} \times 3\)
Solution:
(e) 3.5 + 6 ÷ 0.6 × 2.5
Solution:
3.5 + 6 ÷ 0.6 × 2.5
= 3.5 + 10 × 2.5 (10 × 2.5)
= 3.5 + 25
= 28.5
(f) 1.8 × 2.4 – 2 × 2.1 + 0.12
Solution:
1.8 × 2.4 – 2 × 2.1 + 0.12 (1.8 × 2.4 & 2 × 2.1)
= 4.32 – 4.2 + 0.12
= 4.32 + 0.12 – 4.2 (4.32 + 0.12)
= 4.44 – 4.2
= 0.24
(g) 36 – 11 – 15 – 2
Solution:
36 – 11 – 15 – 2 (-15 – 2)
= 36 – 11 – 17 (-11 – 17)
= 36 – 28
= 8
(h) 7 + 7 × 7 ÷ 7 – 7 + 7
Solution:
7 + 7 × 7 ÷ 7 -7 + 7 (7 ÷ 7)
= 7 + 7 × 1 – 7 + 7 (7 × 1)
= 7 + 7 – 7 + 7
= 7 + 7 + 7 – 7 (7 + 7 + 7)
= 21 – 7
= 14
Question 3.
Simplify and compare the pairs of numerical expressions.
(a) 15 – 3 × 2 + 3 ______ 15 – 3 + 2 × 3
Solution:
L.H.S. = 15 – 3 × 2 + 3
= 15 – 6 + 3
= 18 – 6
= 12
R.H.S. = 15 – 3 + 2 × 3
= 15 – 3 + 6
= -3 + 6 + 15
= -3 + 21
= 18
Hence, 15 – 3 × 2 + 3 < 15 – 3 + 2 × 3
(b) \(\frac{3}{5} \times \frac{2}{3}+\frac{7}{10}\) < \(\frac{3}{5}+\frac{2}{3} \times \frac{7}{10}\)
Solution:
Additional Questions
Question 1.
Simplify the following numerical expressions.
(a) 10 × 29 – 30
Solution:
10 × 29 – 30 (10 × 29)
= 290 – 30
= 260
(b) 25 ÷ 5 + 59 – 20
Solution:
25 ÷ 5 + 59 – 20 (25 ÷ 5)
= 5 + 59 – 20 (5 + 59)
= 64 – 20
= 44
(c) 20 + 5 ÷ 5 – 15
Solution:
20 + 5 ÷ 5 – 15 (5 ÷ 5)
= 20 + 1 – 15 (20 + 1)
= 21 – 15
= 6
Question 2.
Solve the following numerical expressions.
(a) \(\frac{1}{5}-\frac{2}{5}+\frac{8}{5}\)
Solution:
(b) \(\frac{3}{5} \div \frac{12}{5} \times \frac{7}{3}-\frac{1}{2}\)
Solution:
\(\frac{3}{5} \div \frac{12}{5} \times \frac{7}{3}-\frac{1}{2}\)
(c) \(1 \frac{1}{3} \div \frac{3}{5}-\frac{1}{6}+1 \frac{3}{5}\)
Solution:
Question 3.
Simplify the following numerical expressions:
(a) 3.5 + 2 × 0.02 – 3.1
Solution:
3.5 + 2 × 0.02 – 3.1
= 3.5 + 0.04 – 3.1
= 3.54 – 3.1
= 0.44
(b) 30.2 × 2 + 7.1 ÷ 14.2 – 10.3
Solution:
30.2 × 2 + 7.1 ÷ 14.2 – 10.3 (7.1 ÷ 14.2)
= 30.2 × 2 + \(\frac{7.1}{14.2}\) – 10.3
= 30.2 × 2 + 0.5 – 10.3 (30.2 × 2)
= 60.4 + 0.5 – 10.3 (60.4 + 0.5)
= 60.9 – 10.3
= 50.6
(c) 2.7 ÷ 0.9 × 1.01 – 3
Solution:
2.7 ÷ 0.9 × 1.01 – 3 (2.7 ÷ 0.9)
= 3 × 1.01 – 3 (3 × 1.01)
= 3.03 – 3
= 0.03
Question 4.
Simplify and compare the pairs of numerical expressions.
(a) 20 – 3 × 6 + 23 ______ 27 ÷ 3 × 5 – 20
Solution:
L.H.S. = 20 – 3 × 6 + 23
= 20 – 18 + 23
= 43 – 18
= 45 – 20
= 25
R.H.S. = 27 ÷ 3 × 5 – 20
= 9 × 5 – 20
= 45 – 0
= 25
Hence, 20 – 3 × 6 + 23 = 27 ÷ 3 × 5 – 20
(b) \(\frac{2}{5} \times \frac{10}{3}+\frac{7}{3}\) ______ \(1 \frac{2}{5} \times \frac{1}{5} \div \frac{1}{3}-\frac{1}{2}\)
Solution:
L.H.S. = \(\frac{2}{5} \times \frac{10}{3}+\frac{7}{3}\)
Question 5.
Tick (✓) the correct answer.
(a) 1.3 × 2 – 0.3
(i) 3.3
(ii) 0.3
(iii) 2.3
(iv) 1.3
Solution:
(iii) 2.3
(b) 75 – 30 ÷ 15 + 26
(i) 101
(ii) 98
(iii) 97
(iv) 99
Solution:
(iv) 99
Question 6.
Put (✓) which is right or (✗) which is wrong.
(a) \(\frac{3}{7}-\frac{5}{7}+\frac{2}{7}=\frac{5}{6}-\frac{3}{7} \times \frac{1}{7}\)
Solution:
✗
(b) \(\frac{3}{6} \div \frac{1}{2} \times \frac{2}{7}>\frac{7}{6} \times \frac{1}{6}+\frac{5}{6}\)
Solution:
✗
(c) \(\frac{12}{5}+\frac{15}{7} \div \frac{3}{7}+\frac{1}{5}>\frac{1}{5}+\frac{27}{13} \div \frac{3}{13}-\frac{2}{5}\)
Solution:
✗