Well-designed AP Board Solutions Class 7 Maths Chapter 2 Fractions and Decimals InText Questions offers step-by-step explanations to help students understand problem-solving strategies.
AP 7th Class Maths 2nd Chapter Fractions and Decimals InText Questions
Try These (Page No. 44)
Question 1.
Find
a) \(\frac { 2 }{ 7 }\) × 3
b) \(\frac { 9 }{ 7 }\) × 6
c) 3 × \(\frac { 1 }{ 8 }\)
d) \(\frac { 13 }{ 11 }\) × 6
If the product is an improper fraction express it as a mixed fraction.
Solution:
a) \(\frac { 2 }{ 7 }\) × 3 = \(\frac{2 \times 3}{7}\) = \(\frac { 6 }{ 7 }\)
b) \(\frac { 9 }{ 7 }\) × 6 = \(\frac{9 \times 6}{7}\) = \(\frac { 54 }{ 7 }\) = 7\(\frac { 5 }{ 7 }\)
c) 3 × \(\frac { 1 }{ 8 }\) = \(\frac{3 \times 1}{8}\) = \(\frac { 3 }{ 8 }\)
d) \(\frac { 13 }{ 11 }\) × 6 = \(\frac{13 \times 6}{11}\) = \(\frac { 78 }{ 11 }\) = 7\(\frac { 1 }{ 11 }\)
Question 2.
Represent pictorially : 2 × \(\frac { 2 }{ 5 }\) = \(\frac { 4 }{ 5 }\)
Solution:
Try These (Page No. 44)
Question 1.
Find:
i) 5 × 2\(\frac { 3 }{ 7 }\)
ii) 1\(\frac { 4 }{ 9 }\) × 6
Solution:
i) 5 × 2\(\frac { 3 }{ 7 }\) = 5 × \(\frac { 17 }{ 7 }\) = \(\frac { 85 }{ 7 }\) = 12\(\frac { 1 }{ 7 }\)
ii) 1\(\frac { 4 }{ 9 }\) × 6 = \(\frac { 13 }{ 9 }\) × 6 = \(\frac { 78 }{ 9 }\) = 8\(\frac { 2 }{ 3 }\)
Try These (Page No. 46)
Question 1.
Can you tell, what is
i) \(\frac { 1 }{ 2 }\) of 10?
Solution:
\(\frac { 1 }{ 2 }\) of 10 = \(\frac { 1 }{ 2 }\) × 10 = 5
ii) \(\frac { 1 }{ 4 }\) of 16?
Solution:
\(\frac { 1 }{ 4 }\) of 16 = \(\frac { 1 }{ 4 }\) × 16 = 4
iii) \(\frac { 2 }{ 5 }\) of 25?
Solution:
\(\frac { 2 }{ 5 }\) of 25 = \(\frac { 2 }{ 5 }\) × 25 = 2 × 5 = 10
Try These (Page No. 54)
Question 1.
Fill in the boxes:
Try These (Page No. 56)
Question 1.
Find : \(\frac { 1 }{ 3 }\) × \(\frac { 4 }{ 5 }\); \(\frac { 2 }{ 3 }\) × \(\frac { 1 }{ 5 }\)
Solution:
\(\frac { 1 }{ 3 }\) × \(\frac { 4 }{ 5 }\) = \(\frac{1 \times 4}{3 \times 5}\) = \(\frac { 4 }{ 15 }\)
\(\frac { 2 }{ 3 }\) × \(\frac { 1 }{ 5 }\) = \(\frac{2 \times 1}{3 \times 5}\) = \(\frac { 2 }{ 15 }\)
Try These (Page No. 56)
Question 1.
Find :
\(\frac { 8 }{ 3 }\) × \(\frac { 4 }{ 7 }\); \(\frac { 3 }{ 4 }\) × \(\frac { 2 }{ 3 }\)
Solution:
\(\frac { 8 }{ 3 }\) × \(\frac { 4 }{ 7 }\) = \(\frac{8 \times 4}{3 \times 7}\) = \(\frac { 32 }{ 21 }\)
\(\frac { 3 }{ 4 }\) × \(\frac { 2 }{ 3 }\) = \(\frac { 3 }{ 2 }\) × \(\frac { 1 }{ 3 }\) = \(\frac { 1 }{ 2 }\) × \(\frac { 1 }{ 1 }\) = \(\frac{1 \times 1}{2 \times 1}\) = \(\frac { 1 }{ 2 }\)
Try These (page No. 66)
Question 1.
Find
i) 7 ÷ \(\frac { 2 }{ 5 }\)
Solution:
7 ÷ \(\frac { 2 }{ 5 }\) = 7 × \(\frac { 5 }{ 2 }\) = \(\frac{7 \times 5}{2}\) = \(\frac { 35 }{ 2 }\)
ii) 6 ÷ \(\frac { 4 }{ 7 }\)
Solution:
6 ÷ \(\frac { 4 }{ 7 }\) = 6 × \(\frac { 7 }{ 4 }\) = \(\frac{3 \times 7}{2}\) = \(\frac { 21 }{ 2 }\)
iii) 2 ÷ \(\frac { 8 }{ 9 }\)
Solution:
2 ÷ \(\frac { 8 }{ 9 }\) = 2 × \(\frac { 9 }{ 8 }\) = \(\frac{1 \times 9}{4}\) = \(\frac { 9 }{ 4 }\)
Try These (Page No. 66)
Question 1.
Find :
i) 6 ÷ 5\(\frac { 1 }{ 3 }\)
Solution:
6 ÷ 5\(\frac { 1 }{ 3 }\) = 6 ÷ \(\frac { 16 }{ 3 }\) = 6 × \(\frac { 3 }{ 16 }\) = \(\frac { 18 }{ 16 }\) = \(\frac { 9 }{ 18 }\)
ii) 7 ÷ 2\(\frac { 4 }{ 7 }\)
Solution:
7 ÷ 2\(\frac { 4 }{ 7 }\) = 7 ÷ \(\frac { 18 }{ 7 }\) = 7 × \(\frac { 7 }{ 18 }\) = \(\frac { 49 }{ 18 }\)
Try These (page No. 66)
Question 1.
Find:
i) 7 ÷ \(\frac { 2 }{ 5 }\)
Solution:
7 ÷ \(\frac { 2 }{ 5 }\) = 7 × \(\frac { 5 }{ 2 }\) = \(\frac{7 \times 5}{2}\) = \(\frac { 35 }{ 2 }\)
ii) 6 ÷ \(\frac { 4 }{ 7 }\)
Solution:
6 ÷ \(\frac { 4 }{ 7 }\) = 6 × \(\frac { 7 }{ 4 }\) = \(\frac{3 \times 7}{2}\) = \(\frac { 21 }{ 2 }\)
iii) 2 ÷ \(\frac { 8 }{ 9 }\)
Solution:
2 ÷ \(\frac { 8 }{ 9 }\) = 2 × \(\frac { 9 }{ 8 }\) = \(\frac{1 \times 9}{4}\) = \(\frac { 9 }{ 4 }\)
Try These (page No. 66)
Question 1.
Find:
i) 6 ÷ 5\(\frac { 1 }{ 3 }\)
Solution:
6 ÷ 5\(\frac { 1 }{ 3 }\) = 6 ÷ \(\frac { 16 }{ 3 }\) = 16 × \(\frac { 3 }{ 16 }\) = \(\frac { 18 }{ 16 }\) = \(\frac { 9 }{ 18 }\)
ii) 7 ÷ 2\(\frac { 4 }{ 7 }\)
Solution:
7 ÷ 2\(\frac { 4 }{ 7 }\) = 7 ÷ \(\frac { 18 }{ 7 }\) = 7 × \(\frac { 7 }{ 18 }\) = \(\frac { 49 }{ 18 }\)
Try These (page No. 66)
Question 1.
Find:
i) \(\frac { 3 }{ 5 }\) ÷ \(\frac { 1 }{ 2 }\)
Solution:
\(\frac { 3 }{ 5 }\) ÷ \(\frac { 1 }{ 2 }\) = \(\frac { 3 }{ 5 }\) × \(\frac { 2 }{ 1 }\) = \(\frac{3 \times 2}{5 \times 1}\) = \(\frac { 6 }{ 5 }\)
ii) \(\frac { 1 }{ 2 }\) ÷ \(\frac { 3 }{ 5 }\)
Solution:
\(\frac { 1 }{ 2 }\) ÷ \(\frac { 3 }{ 5 }\) = \(\frac { 1 }{ 2 }\) × \(\frac { 5 }{ 3 }\) = \(\frac{1 \times 5}{2 \times 3}\) = \(\frac { 5 }{ 6 }\)
iii) 2\(\frac { 1 }{ 2 }\) ÷ \(\frac { 3 }{ 5 }\)
Solution:
2\(\frac { 1 }{ 2 }\) ÷ \(\frac { 3 }{ 5 }\) = \(\frac { 5 }{ 2 }\) ÷ \(\frac { 3 }{ 5 }\) = \(\frac { 5 }{ 2 }\) × \(\frac { 5 }{ 3 }\) = \(\frac{5 \times 5}{2 \times 3}\) = \(\frac { 25 }{ 6 }\)
Try These (page No. 72)
Question 1.
Find
i) 2.7 × 4
Solution:
\(\frac { 27 }{ 10 }\) × 4 = \(\frac { 108 }{ 10 }\) = 10.8
ii) 1.8 × 1.2
Solution:
\(\frac { 18 }{ 10 }\) × \(\frac { 12 }{ 10 }\) = \(\frac { 216 }{ 100 }\) = 2.16
iii) 2.3 × 4.35
Solution:
\(\frac { 23 }{ 10 }\) × \(\frac { 435 }{ 100 }\) = \(\frac { 10,005 }{ 1000 }\) = 10.005
Question 2.
Arrange the products obtained in (1) in descending order.
Solution:
Descending order of Q.No. (1) products is 10.8, 10.005, 2.16
Try These (page No. 76)
Question 1.
Find :
i) 0.3 × 10
Solution:
0.3 × 10 = 3
ii) 1.2 × 100
Solution:
1.2 × 100 = 120
iii) 56.3 × 1000
Solution:
56.3 × 1000 = 56300
Try These (page No. 78)
Question 1.
Find
i) 235.4 ÷ 10
Solution:
\(\frac { 235.4 }{ 10 }\) = 23.54
ii) 235.4 ÷ 100
Solution:
\(\frac { 235.4 }{ 100 }\) = 2.35
iii) 235.4 ÷ 1000
Solution:
\(\frac { 235.4 }{ 1000 }\) = 0.2354
Try These (page No. 78)
Question 1.
Find:
i) 235.4 ÷ 10
Solution:
\(\frac { 235.4 }{ 10 }\) = 23.54
ii) 235.4 ÷ 100
Solution:
\(\frac { 235.4 }{ 100 }\) = 2.35
iii) 235.4 ÷ 1000
Solution:
\(\frac { 235.4 }{ 1000 }\) = 0.2354
Try These (page No. 78)
Question 1.
Find:
i) 35.7 ÷ 3 = ?
Solution:
\(\frac { 35.7 }{ 3 }\) = 11.9
ii) 25.5 ÷ 3 = ?
Solution:
\(\frac { 25.5 }{ 3 }\) = 8.5
Try These (Page No. 78)
Question 1.
Find:
i) 43.15 ÷ 5 = ?
Solution:
\(\frac { 43.15 }{ 5 }\) = 8.63
ii) 82.44 ÷ 6 = ?
Solution:
\(\frac { 82.44 }{ 6 }\) = 13.74
Try These (Page No. 80)
Question 1.
Find:
Try These (page No. 80)
Question 1.
Find
i) \(\frac{7.75}{0.25}\)
Solution:
\(\frac{7.75}{0.25}\) = \(\frac{775}{100 \times \frac{25}{100}}\) = \(\frac { 82.44 }{ 6 }\)
ii) \(\frac{42.8}{0.02}\)
Solution:
\(\frac{42.8}{0.02}\) = \(\frac{428}{10 \times \frac{2}{10}}\) = \(\frac{4280}{2}\) = 2140
iii) \(\frac{5.6}{1.4}\)
Solution:
\(\frac{5.6}{1.4}\) = \(\frac{56}{10 \times \frac{14}{10}}\) = \(\frac{56}{14}\) = 4