Exercise 2.1 (Revised) - Chapter 2 - Fractions & Decimals - Ncert Solutions class 7 - Maths

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Chapter 2: Fractions & Decimals - NCERT Solutions for Class 7 Maths

Ex 2.1 Question 1.

Which of the drawings (a) to (d) show:
(i) $2 \times \frac{1}{5}$
(ii) $2 \times \frac{1}{2}$
(iii) $3 \times \frac{2}{3}$
(iv) $3 \times \frac{1}{4}$

Answer:

(i) - (d) Since $2 \times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}$
(ii) - (b) Since $2 \times \frac{1}{2}=\frac{1}{2}+\frac{1}{2}$
(iii) - (a) Since $3 \times \frac{2}{3}=\frac{2}{3}+\frac{2}{3}+\frac{2}{3}$
(iv) - (c) Since $3 \times \frac{1}{4}=\frac{1}{4}+\frac{1}{4}+\frac{1}{4}$

Ex 2.1 Question 2.

Some pictures (a) to (c) are given below. Tell which of them show:
(i) $3 \times \frac{1}{5}=\frac{3}{5}$
(ii) $2 \times \frac{1}{3}=\frac{2}{3}$
(iii) $3 \times \frac{3}{4}=2 \frac{1}{4}$

Answer:

(i) - (c) Since $3 \times \frac{1}{5}=\frac{1}{5}+\frac{1}{5}+\frac{1}{5}$
(ii) - (a) Since $2 \times \frac{1}{3}=\frac{1}{3}+\frac{1}{3}$
(iii) - (b) Since $3 \times \frac{3}{4}=\frac{3}{4}+\frac{3}{4}+\frac{3}{4}$

Ex 2.1 Question 3.

Multiply and reduce to lowest form and convert into a mixed fraction:
(i) $7 \times \frac{3}{5}$
(ii) $4 \times \frac{1}{3}$
(iii) $2 \times \frac{6}{7}$
(iv) $5 \times \frac{2}{9}$
(v) $\frac{2}{3} \times 4$

(vi) $\frac{5}{2} \times 6$
(vii) $11 \times \frac{4}{7}$
(viii) $20 \times \frac{4}{5}$
(ix) $13 \times \frac{1}{3}$
(x) $15 \times \frac{3}{5}$

Answer:

(i) $7 \times \frac{3}{5}=\frac{7 \times 3}{5}=\frac{21}{5}=4 \frac{1}{5}$
(ii) $4 \times \frac{1}{3}=\frac{4 \times 1}{3}=\frac{4}{3}=1 \frac{1}{3}$
(iii) $2 \times \frac{6}{7}=\frac{2 \times 6}{7}=\frac{12}{7}=1 \frac{5}{7}$
(iv) $5 \times \frac{2}{9}=\frac{5 \times 2}{9}=\frac{10}{9}=1 \frac{1}{9}$
(v) $\frac{2}{3} \times 4=\frac{2 \times 4}{3}=\frac{8}{3}=2 \frac{2}{3}$
(vi) $\frac{5}{2} \times 6=5 \times 3=15$
(vii) $11 \times \frac{4}{7}=\frac{11 \times 4}{7}=\frac{44}{7}=6 \frac{2}{7}$
(viii) $20 \times \frac{4}{5}=4 \times 4=16$
(ix) $13 \times \frac{1}{3}=\frac{13 \times 1}{3}=\frac{13}{3}=4 \frac{1}{3}$
(x) $15 \times \frac{3}{5}=3 \times 3=9$

Ex 2.1 Question 4.

Shade:
(i) $\frac{2}{3}$ of the triangles in box (a)
(ii) $\frac{3}{5}$ of the squares in box (b)
(i) $\frac{1}{2}$ of the circles in box (c)

$\text { Answer: (i) } \frac{2}{3} \text { of } 9 \text { triangles }=\frac{2}{3} \times 9=2 \times 3=6 \text { triangles }$

$\text { (ii) } \frac{3}{5} \text { of } 15 \text { squares }=\frac{3}{5} \times 15=3 \times 3=9 \text { squares }$

$\text { (iii) } \frac{1}{2} \text { of } 12 \text { circles }=\frac{1}{2} \times 12=6 \text { circles }$

Ex 2.1 Question 5.

Find:
(a) $\frac{1}{2}$ of (i) 24 (ii) 46

(b) $\frac{2}{3}$ of (i) 18 (ii) 27
(c) $\frac{3}{4}$ of (i) 16
(ii) 36
(d) $\frac{4}{5}$ of (i) 20
(ii) 35

Answer:

(a)
(i) $\frac{1}{2}$ of $24=12$
(ii) $\frac{1}{2}$ of $46=23$
(b)
(i) $\frac{2}{3}$ of $18=\frac{2}{3} \times 18=2 \times 6=12$
(ii) $\frac{2}{3}$ of $27=\frac{2}{3} \times 27=2 \times 9=18$
(c)
(i) $\frac{3}{4}$ of $16=\frac{3}{4} \times 16=3 \times 4=12$
(ii) $\frac{3}{4}$ of $36=\frac{3}{4} \times 36=3 \times 9=27$
(d)
(i) $\frac{4}{5}$ of $20=\frac{4}{5} \times 20=4 \times 4=16$
(ii) $\frac{4}{5}$ of $35=\frac{4}{5} \times 35=4 \times 7=28$

(d)
(i) $\frac{4}{5}$ of $20=\frac{4}{5} \times 20=4 \times 4=16$
(ii) $\frac{4}{5}$ of $35=\frac{4}{5} \times 35=4 \times 7=28$

Ex 2.1 Question 6.

Multiply and express as a mixed fraction:
(a) $3 \times 5 \frac{1}{5}$
(b) $5 \times 6 \frac{3}{4}$
(c) $7 \times 2 \frac{1}{4}$
(d) $4 \times 6 \frac{1}{3}$
(e) $3 \frac{1}{4} \times 6$

(f) $3 \frac{2}{5} \times 8$

Answer:

(a) $3 \times 5 \frac{1}{5}=3 \times \frac{26}{5}=\frac{3 \times 26}{5}=\frac{78}{5}=15 \frac{3}{5}$
(b) $5 \times 6 \frac{3}{4}=5 \times \frac{27}{4}=\frac{5 \times 27}{4}=\frac{135}{4}=33 \frac{3}{4}$
(c) $7 \times 2 \frac{1}{4}=7 \times \frac{9}{4}=\frac{7 \times 9}{4}=\frac{63}{4}=15 \frac{3}{4}$
(d) $4 \times 6 \frac{1}{3}=4 \times \frac{19}{3}=\frac{4 \times 19}{3}=\frac{76}{3}=25 \frac{1}{3}$
(e) $3 \frac{1}{4} \times 6=\frac{13}{4} \times 6=\frac{13 \times 3}{2}=\frac{39}{2}=19 \frac{1}{2}$
(f) $3 \frac{2}{5} \times 8=\frac{17}{5} \times 8=\frac{17 \times 8}{5}=\frac{136}{5}=27 \frac{1}{5}$

Ex 2.1 Question 7.

Find:
(a) $\frac{1}{2}$ of
(i) $2 \frac{3}{4}$
(ii) $4 \frac{2}{9}$
(b) $\frac{5}{8}$ of
(i) $3 \frac{5}{6}$
(ii) $9 \frac{2}{3}$

Answer:

(a)
(i) $\frac{1}{2} o f 2 \frac{3}{4}=\frac{1}{2} \times \frac{11}{4}=\frac{11}{8}=1 \frac{3}{8}$
(ii) $\frac{1}{2}$ of $4 \frac{2}{9}=\frac{1}{2} \times \frac{38}{9}=\frac{19}{9}=2 \frac{1}{9}$

(b)
(i) $\frac{5}{8}$ of $3 \frac{5}{6}=\frac{5}{8} \times \frac{23}{6}=\frac{115}{48}=2 \frac{19}{48}$
(ii) $\frac{5}{8}$ of $9 \frac{2}{3}=\frac{5}{8} \times \frac{29}{3}=\frac{145}{24}=6 \frac{1}{24}$

Ex 2.1 Question 8.

Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}$ of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?

Answer:

Given: Total quantity of water in bottle $=5$ litres

(i) Vidya consumed $=\frac{2}{5}$ of 5 litres $=\frac{2}{5} \times 5=2$ litres

Thus, Vidya drank 2 litres water from the bottle.
(ii) Pratap consumed $=\left(1-\frac{2}{5}\right)$ part of bottle $=\frac{5-2}{5}=\frac{3}{5}$ part of bottle Pratap consumed $\frac{3}{5}$ of 5 litres water $=\frac{3}{5} \times 5=3$ litres

Thus, Pratap drank $\frac{3}{5}$ part of the total quantity of water.