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:

✗