NCERT Solutions for exercise 2.2 class 7 maths

 

NCERT Solutions for Class 7 Maths Exercise 2.2

NCERT Solutions for exercise 2.2 class 7 maths Chapter 2 Fractions and Decimals in simple solutions are given here. exercise 2.2 class 7 maths of NCERT Solutions for Maths Class 7 Chapter 2 contains all the topics containing the basic information of Fractions. exercise 2.2 class 7 maths provide students the study of fractions including proper, improper and mixed fractions as well as their addition and subtraction. NCERT Solutions for exercise 2.2 class 7 maths provides necessary material for solving different range of questions that test the students capability of understanding the concepts. It also helps the students of CBSE Class 7 Maths students

Question 1. 

Which of the drawings (a) to (d) show:

(i) 2 × $({\displaystyle \frac{1}{5}})$ (ii) 2 × $({\displaystyle \frac{1}{2}})$ (iii) 3 × $({\displaystyle \frac{2}{3}}$ (iv) 3 × $({\displaystyle \frac{1}{4}})$

Solution:-

(i) 2 × $({\displaystyle \frac{1}{5}})$ represents the addition of 2 figures, each represents 1 shaded part out of the given 5 equal parts.

∴ 2 × $({\displaystyle \frac{1}{5}})$ is represented by fig (d).

(ii) 2 × $({\displaystyle \frac{1}{2}})$ represents the addition of 2 figures, each represents 1 shaded part out of the given 2 equal parts.

∴ 2 × $({\displaystyle \frac{1}{2}})$ is represented by fig (b).

(iii) 3 × $({\displaystyle \frac{2}{3}}$ represents the addition of 3 figures, each represents 2 shaded part out of the given 3 equal parts.

∴ 3 × $({\displaystyle \frac{2}{3}}$ is represented by fig (a).

(iii) 3 × $({\displaystyle \frac{1}{4}})$ represents the addition of 3 figures, each represents 1 shaded part out of the given 4 equal parts.

∴ 3 × $({\displaystyle \frac{1}{4}})$ is represented by fig (c).

Question 2. 

Some pictures (a) to (c) are given below. Tell which of them show:

(i) 3 × $({\displaystyle \frac{1}{5}})$= $({\displaystyle \frac{3}{5}})$ (ii) 2 × $({\displaystyle \frac{1}{3}})$ = $({\displaystyle \frac{2}{3}})$ (iii) 3 × $({\displaystyle \frac{3}{4}})$ = 2 $({\displaystyle \frac{1}{4}})$

Solution:-

(i) 3 × $({\displaystyle \frac{1}{5}})$ represents the addition of 3 figures, each represents 1 shaded part out of the given 5 equal parts and (3/5) represents 3 shaded parts out of 5 equal parts.

∴ 3 × $({\displaystyle \frac{1}{5}})$ = $({\displaystyle \frac{3}{5}})$ is represented by fig (c).

(ii) 2 × $({\displaystyle \frac{1}{3}})$ represents the addition of 2 figures, each represents 1 shaded part out of the given 3 equal parts and (2/3) represents 2 shaded parts out of 3 equal parts.

∴ 2 × $({\displaystyle \frac{1}{3}})$ = $({\displaystyle \frac{2}{3}})$ is represented by fig (a).

(iii) 3 × $({\displaystyle \frac{3}{4}})$  represents the addition of 3 figures, each represents 3 shaded part out of the given 4 equal parts and 2 ¼ represents 2 fully and 1 figure having 1 part as shaded out of 4 equal parts.

∴ 3 × $({\displaystyle \frac{3}{4}})$ = 2 $({\displaystyle \frac{1}{4}})$ is represented by fig (b).

Question 3. 

Multiply and reduce to lowest form and convert into a mixed fraction:

(i) 7 × $({\displaystyle \frac{3}{5}})$

Solution:-

= $({\displaystyle \frac{7\times 3}{1\times 5}})$ 

= $({\displaystyle \frac{21}{5}})$ 

(ii) 4 × $({\displaystyle \frac{1}{3}})$ 

Solution:-

4 × $({\displaystyle \frac{1}{3}})$

= $({\displaystyle \frac{4}{1}})\times ({\displaystyle \frac{1}{3}})$ 

= ${\displaystyle \frac{(4\times 1)}{1\times 3}}$

= $({\displaystyle \frac{4}{3}})$

(iii) 2 × $({\displaystyle \frac{6}{7}})$ 

Solution:-

= $({\displaystyle \frac{2}{1}})\times ({\displaystyle \frac{6}{7}})$ 

= ${\displaystyle \frac{(2\times 6)}{1\times 7}}$

= $({\displaystyle \frac{12}{7}})$

(iv) 5 × $({\displaystyle \frac{2}{9}})$

Solution:-

= $({\displaystyle \frac{5}{1}})\times ({\displaystyle \frac{2}{9}})$ 

= ${\displaystyle \frac{(5\times 2)}{1\times 9}}$

= $({\displaystyle \frac{10}{9}})$

(v) (2/3) × 4

Solution:-

= $({\displaystyle \frac{2}{3}})\times ({\displaystyle \frac{4}{1}})$ 

= ${\displaystyle \frac{(2\times 4)}{3\times 1}}$

= $({\displaystyle \frac{8}{3}})$

(vi) $({\displaystyle \frac{5}{2}})$ × 6

Solution:-

= $({\displaystyle \frac{5}{2}})\times ({\displaystyle \frac{6}{1}})$ 

= ${\displaystyle \frac{(5\times 6)}{2\times 1}}$

= $({\displaystyle \frac{30}{2}})$

=15

(vii) 11 × $({\displaystyle \frac{4}{7}})$ 

Solution:-

= $({\displaystyle \frac{11}{1}})\times ({\displaystyle \frac{4}{7}})$ 

= ${\displaystyle \frac{(11\times 4)}{1\times 7}}$

= $({\displaystyle \frac{44}{7}})$

(viii) 20 × $({\displaystyle \frac{4}{5}})$

Solution:-

= $({\displaystyle \frac{20}{1}})\times ({\displaystyle \frac{4}{5}})$ 

= ${\displaystyle \frac{(20\times 4)}{1\times 5}}$

= $({\displaystyle \frac{80}{5}})$

= 16

(ix) 13 × $({\displaystyle \frac{1}{3}})$

Solution:-

= $({\displaystyle \frac{13}{1}})\times ({\displaystyle \frac{1}{3}})$ 

= ${\displaystyle \frac{(13\times 1)}{1\times 3}}$

= $({\displaystyle \frac{13}{3}})$

(x) 15 × $({\displaystyle \frac{3}{5}})$

Solution:-

= $({\displaystyle \frac{15}{1}})\times ({\displaystyle \frac{3}{5}})$ 

= ${\displaystyle \frac{(15\times 3)}{1\times 5}}$

= $({\displaystyle \frac{45}{5}})$

= 9

Question 4. 

Shade:

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

Solution:-

(i) We may observe that there are 12 circles in the given box. So, we have to shade ${\displaystyle \frac{1}{2}}$ of the circles in the box. ∴ 12 × ${\displaystyle \frac{1}{2}}$ = ${\displaystyle \frac{12}{2}}$=6 So we have to shade any 6 circles in the box. (ii) We may observe that there are 9 triangles in the given box. So, we have to shade ${\displaystyle \frac{2}{3}}$ of the triangles in the box. ∴ 9 × ${\displaystyle \frac{2}{3}}$ = ${\displaystyle \frac{18}{3}}$= 6 So we have to shade any 6 triangles in the box. (iii) We may observe that there are 15 squares in the given box. So, we have to shade ${\displaystyle \frac{3}{5}}$ of the squares in the box. ∴ 15 × ${\displaystyle \frac{3}{5}}$ = ${\displaystyle \frac{45}{5}}$ = 9 So we have to shade any 9 squares in the box.

Question 5. 

Find:

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

Solution:-

(i) 24

= ${\displaystyle \frac{1}{2}}$ × 24

= ${\displaystyle \frac{24}{2}}$

= 12

(ii) 46

= ${\displaystyle \frac{1}{2}}$ × 46

= ${\displaystyle \frac{46}{2}}$

= 23

(b) ${\displaystyle \frac{2}{3}}$ of (i) 18 (ii) 27

Solution:-

(i) 18

= ${\displaystyle \frac{2}{3}}$ × 18

= 2 × 6

= 12

(ii) 27

= ${\displaystyle \frac{2}{3}}$ × 27

= 2 × 9

= 18

(c) ${\displaystyle \frac{3}{4}}$ of (i) 16 (ii) 36

Solution:-

(i) 16

= ${\displaystyle \frac{3}{4}}$ × 16

= 3 × 4

= 12

(ii) 36

= ${\displaystyle \frac{3}{4}}$ × 36

= 3 × 9

= 27

(d) ${\displaystyle \frac{4}{5}}$ of (i) 20 (ii) 35

Solution:-

(i) 20

= ${\displaystyle \frac{4}{5}}$ × 20

= 4 × 4

= 16

(ii) 35

= ${\displaystyle \frac{4}{5}}$ × 35

= 4 × 7

= 28

Question 6. 

Multiply and express as a mixed fraction:

(a) 3 × 5${\displaystyle \frac{1}{5}}$

Solution:-

= 3 × ${\displaystyle \frac{26}{5}}$

= ${\displaystyle \frac{78}{5}}$

$15{\displaystyle \frac{3}{5}}$

(b) 5 × 6 ${\displaystyle \frac{3}{4}}$

Solution:-

= 6 ${\displaystyle \frac{3}{4}}$ = ${\displaystyle \frac{27}{4}}$

= 5 × ${\displaystyle \frac{27}{4}}$

= ${\displaystyle \frac{135}{4}}$

= 33 ${\displaystyle \frac{3}{4}}$

(c) 7 × 2 ${\displaystyle \frac{1}{4}}$

Solution:-

= 2 ${\displaystyle \frac{1}{4}}$ = ${\displaystyle \frac{9}{4}}$

= 7 × ${\displaystyle \frac{9}{4}}$

= ${\displaystyle \frac{63}{4}}$

= 15 ${\displaystyle \frac{3}{4}}$

(d) 4 × $6{\displaystyle \frac{1}{3}}$

Solution:-

= 4 × ${\displaystyle \frac{19}{3}}$

= ${\displaystyle \frac{76}{3}}$

=$25{\displaystyle \frac{1}{3}}$

(e) 3 ${\displaystyle \frac{1}{4}}$ × 6

Solution:-

= 3 ${\displaystyle \frac{1}{4}}$ = ${\displaystyle \frac{13}{4}}$

= (${\displaystyle \frac{13}{4}}$) × 6

= (${\displaystyle \frac{13}{2}}$) × 3

= ${\displaystyle \frac{39}{2}}$

= $19{\displaystyle \frac{1}{2}}$

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

Solution:-

=$3{\displaystyle \frac{2}{5}}$ × 8

= (${\displaystyle \frac{17}{5}}$) × 8

= ${\displaystyle \frac{136}{5}}$

$27{\displaystyle \frac{1}{5}}$

Question 7. 

Find:

(a) ${\displaystyle \frac{1}{2}}$ of (i) 2 ${\displaystyle \frac{3}{4}}$ (ii) 4${\displaystyle \frac{2}{9}}$

Solution:-

(i) 2 ${\displaystyle \frac{3}{4}}$

First convert the given mixed fraction into improper fraction.

= 2 ${\displaystyle \frac{3}{4}}$ = ${\displaystyle \frac{11}{4}}$

Now,

=${\displaystyle \frac{1}{2}}$ × ${\displaystyle \frac{11}{4}}$

=${\displaystyle \frac{1}{2}}\times {\displaystyle \frac{1}{2}}$

=${\displaystyle \frac{1\times 11}{2\times 4}}$

= ${\displaystyle \frac{11}{8}}$

=$1{\displaystyle \frac{3}{8}}$

(ii)4${\displaystyle \frac{2}{9}}$

First convert the given mixed fraction into improper fraction.

=4${\displaystyle \frac{2}{9}}$= ${\displaystyle \frac{38}{9}}$

Now,

= ${\displaystyle \frac{1}{2}}\times {\displaystyle \frac{38}{9}}$

= ${\displaystyle \frac{1\times 38}{2\times 9}}$

=  ${\displaystyle \frac{38}{18}}$

=  ${\displaystyle \frac{19}{9}}$

= $2{\displaystyle \frac{1}{9}}$

(b)   ${\displaystyle \frac{5}{8}}$ of (i) $3{\displaystyle \frac{5}{6}}$  (ii)   $9{\displaystyle \frac{2}{3}}$

Solution:-

(i)

=${\displaystyle \frac{5}{8}}$ × $3{\displaystyle \frac{5}{6}}$ 

=${\displaystyle \frac{5}{8}}$ × ${\displaystyle \frac{23}{6}}$ 

= ${\displaystyle \frac{5\times 23}{8\times 6}}$

= ${\displaystyle \frac{115}{8\times 48}}$

=$2{\displaystyle \frac{19}{48}}$

(ii)$9{\displaystyle \frac{2}{3}}$

=${\displaystyle \frac{5}{8}}\times$ ${\displaystyle \frac{29}{3}}$

=${\displaystyle \frac{5\times 28}{8\times 3}}$

=${\displaystyle \frac{145}{24}}$

=$6{\displaystyle \frac{1}{24}}$

Question 8. 

Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 liters water. Vidya consumed $({\displaystyle \frac{2}{5}})$ 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?

Solution:-

(i) From the question, it is given that,

Amount of water in the water bottle = 5 liters

Amount of water consumed by Vidya = $({\displaystyle \frac{2}{5}})$ of 5 liters

= $({\displaystyle \frac{2}{5}})$ × 5

= 2 liters

So, the total amount of water drank by Vidya is 2 liters

(ii) From the question, it is given that,

Amount of water in the water bottle = 5 liters

Then,

Amount of water consumed by Pratap = (1 – water consumed by Vidya)

= (1 – $({\displaystyle \frac{2}{5}})$)

= $({\displaystyle \frac{5-2}{5}})$

= $({\displaystyle \frac{3}{5}})$

∴ Total amount of water consumed by Pratap = $({\displaystyle \frac{3}{5}})$ of 5 liters

= $({\displaystyle \frac{3}{5}})$ × 5

= 3 liters

So, the total amount of water drank by Pratap is 3 liters.