Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 2 Fractions and Decimals Ex 2.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.1

1. Solve the following fractions :

Question (i).

4 + \(\frac {7}{8}\)

Answer:

4 + \(\frac {7}{8}\)

= \(\frac{4 \times 8+7}{8}\)

= \(\frac{32+7}{8}\)

= \(\frac {39}{8}\)

= 4\(\frac {7}{8}\)

Question (ii).

\(\frac{9}{11}-\frac{4}{15}\)

Answer:

\(\frac{9}{11}-\frac{4}{15}\)

= \(\frac{9 \times 15-4 \times 11}{11 \times 15}\)

= \(\frac{135-44}{165}\)

= \(\frac {91}{165}\)

Question (iii).

\(\frac{11}{16}-\frac{2}{5}+\frac{8}{10}\)

Answer:

\(\frac{11}{16}-\frac{2}{5}+\frac{8}{10}\)

LCM of 16, 5 and 10

= 2 × 2 × 2 × 2 × 5

= 80

= \(\frac{11 \times 5-2 \times 16+8 \times 8}{80}\)

= \(\frac{55-32+64}{80}\)

= \(\frac {87}{80}\)

= 1\(\frac {7}{80}\)

Question (iv).

\(2 \frac{1}{5}+6 \frac{1}{2}\)

Answer:

\(2 \frac{1}{5}+6 \frac{1}{2}\)

= \(\frac{11}{5}+\frac{13}{2}\)

= \(\frac{11 \times 2+13 \times 5}{5 \times 2}\)

= \(\frac{22+65}{10}\)

= \(\frac {87}{10}\)

= 8\(\frac {7}{10}\)

Question (v).

\(8 \frac{1}{2}-3 \frac{5}{8}\)

Answer:

\(8 \frac{1}{2}-3 \frac{5}{8}\)

= \(\frac{17}{2}-\frac{29}{8}\)

= \(\frac{17 \times 4-29}{8}\)

= \(\frac{68-29}{8}\)

= \(\frac {39}{8}\)

= 4\(\frac {7}{8}\)

Question (vi).

\(\frac{9}{10}-\frac{9}{100}+\frac{9}{1000}\)

Answer:

\(\frac{9}{10}-\frac{9}{100}+\frac{9}{1000}\)

= \(\frac{9 \times 100-9 \times 10+9}{1000}\)

= \(\frac{900-90+9}{1000}\)

= \(\frac {810}{1000}\)

2. Arrange the following in ascending order :

Question (i).

\(\frac{2}{17}, \frac{10}{17}, \frac{3}{17}, \frac{16}{17}, \frac{5}{17}, \frac{8}{17}\)

Answer:

Ascending order of \(\frac{2}{17}, \frac{10}{17}, \frac{3}{17}, \frac{16}{17}, \frac{5}{17}, \frac{8}{17}\) is:

\(\frac{2}{17}, \frac{3}{17}, \frac{5}{17}, \frac{8}{17}, \frac{10}{17}, \frac{16}{17}\)

Question (ii).

\(\frac{1}{5}, \frac{3}{7}, \frac{7}{10}\)

Answer:

\(\frac{1}{5}, \frac{3}{7}, \frac{7}{10}\)

L.C.M of 5, 7 , 10 = 2 × 5 × 7

= 70

3. The three sides AB, BC and CA of a triangle ΔABC are \(\frac {5}{6}\)cm, \(\frac {2}{3}\)cm and \(\frac {7}{10}\) cm respectively. Find the perimeter of the triangle.

Answer:

Slides of ΔABC are

AB = \(\frac {5}{6}\) cm,

BC = \(\frac {2}{3}\)

CA = \(\frac {7}{10}\)

L.C.M. (6, 3, 10) = 2 × 3 × 5 = 30

Perimeter of ΔABC = AB + BC + CA

4. Ramesh studies for 5\(\frac {2}{3}\) hours daily. He devotes 2\(\frac {4}{5}\) hours of his time for science devotes for other subjects ?

Answer:

Total daily time for all subjects

= 5\(\frac {2}{3}\) hours = \(\frac {17}{3}\) hours

Time for science and mathematics

= 2\(\frac {4}{5}\) hours = \(\frac {14}{5}\) hours

Time for other subjects

5. Sonia jogs once around the rectangular park of sides 10\(\frac {2}{3}\)m and 12\(\frac {1}{2}\)m. Find the total distance covered by the Sonia.

Answer:

Length of rectangular park

= 12\(\frac {1}{2}\)m = \(\frac {25}{2}\)m

Breadth of rectangular park

= 10\(\frac {2}{3}\)m = \(\frac {32}{3}\)m

Total distance covered by Sonia = 2 [Length + Breadth]

= \(2\left(\frac{32}{3}+\frac{25}{3}\right) \mathrm{m}\)

= \(2\left(\frac{32 \times 2+25 \times 3}{3 \times 2}\right) \mathrm{m}\)

= \(2\left(\frac{65+75}{6}\right) \mathrm{m}\)

= \(\frac {278}{6}\) m

= \(\frac {139}{3}\) m

= 46\(\frac {1}{3}\) m

6. Ritu coloured a picture in \(\frac {7}{12}\) hours. Vaibhav coloured the same picture in \(\frac {3}{4}\) hours. Who worked for a longer time and by what fraction ?

Answer:

Time taken by Ritu to colour

= \(\frac {7}{12}\) hours

Time taken by Vaibhav = \(\frac {3}{4}\) hours

= \(\frac {3}{4}\) × \(\frac {3}{3}\)

= \(\frac {9}{12}\) hours

Since 9 > 7

∴ \(\frac {9}{12}\) > \(\frac {7}{12}\)

∴ Vaibhav worked for more time.

Difference between time taken by

Vaibhav and Ritu = \(\frac{3}{4}-\frac{7}{12}\)

= \(\frac{3 \times 3-7}{12}\)

= \(\frac{9-7}{12}=\frac{2}{12}\)

= \(\frac {1}{6}\) of an hour.

7. Multiple Choice Questions :

Question (i).

Fraction \(\frac {2}{5}\), \(\frac {7}{5}\) are :

(a) Like fractions

(b) Unlike fractions

(c) Equivalent fractions

(d) None of these

Answer:

(a) Like fractions

Question (ii).

What fraction do 8 hours of a day represents ?

(a) \(\frac {1}{2}\)

(b) \(\frac {1}{3}\)

(c) \(\frac {8}{60}\)

(d) \(\frac {2}{3}\)

Answer:

(b) \(\frac {1}{3}\)

Question (iii).

Equivalent fraction of \(\frac {3}{5}\) is :

(a) \(\frac {13}{15}\)

(b) \(\frac {5}{3}\)

(c) \(\frac {9}{15}\)

(d) \(\frac {5}{13}\)

Answer:

(c) \(\frac {9}{15}\)

Question (iv).

Shaded area of given triangle represents the fractions:

(a) \(\frac {1}{3}\)

(b) \(\frac {3}{4}\)

(c) \(\frac {1}{4}\)

(d) \(\frac {2}{3}\)

Answer:

(b) \(\frac {3}{4}\)

Question (v).

Sum of fractions \(\frac {2}{7}\), \(\frac {3}{4}\) is equal to :

(a) \(\frac {5}{28}\)

(b) \(\frac {1}{3}\)

(c) \(\frac {5}{11}\)

(d) \(\frac {29}{28}\)

Answer:

(d) \(\frac {29}{28}\)