S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2A

Exercise 2A

---

Q1 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 1

Find the value of

(a) $\frac{1}{5}$ of 1 hour 10 minutes

Sol :

$\begin{aligned} 1 \mathrm{~h} 10 \mathrm{~m} &=\{(1 \times 60)+10\} \mathrm{m} \\ &=70~m \\ \frac{1}{5} \text { of } 70 &=\frac{1}{5} \times 70 \mathrm{~m} \\ &=14~m \end{aligned}$

(b) $\frac{1}{5}$ of a non-leap year

Sol :

$\begin{aligned} \frac{1}{5} \text { of } 365 \text{days} &=\left(\frac{1}{5} \times 365\right) \text{days} \\ &=73 \end{aligned}$

---

Q2 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 2

Express $\frac{1}{2}$ as quarters, sixths, eighths, 12 ths, 16 ths and 24 ths.

Sol :

Quarters $=\frac{1}{2} \times \frac{2}{2}=\frac{2}{4}$

Sixths $=\frac{1}{2} \times \frac{3}{3}=\frac{3}{6}$

Eights $=\frac{1}{2} \times \frac{4}{4}=\frac{4}{8}$

12 ths $=\frac{1}{2} \times \frac{6}{6}=\frac{6}{12}$

16 ths $=\frac{1}{2} \times \frac{8}{8}=\frac{8}{16}$

24 ths $=\frac{1}{2} \times \frac{12}{12}=\frac{12}{24}$

---

Q3 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 3

Express $\frac{3}{8}$ as fraction with

(a) numerator 15

(b) denominator 72

Sol :

(a) $\frac{3}{8} \times \frac{5}{5}=\frac{15}{40}$

(b) $\frac{3}{8} \times \frac{9}{9}=\frac{27}{72}$

---

Q4 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 4

Reduce each of the following fractions to its lowest terms.

(a) $\frac{18}{48}$

(b) $\frac{105}{120}$

(c) $\frac{210}{315}$

Sol :

(a) $=\frac{18\div 2}{48 \div 2}=\frac{9\div 3}{24\div 3}=\frac{3}{8}$

(b) $=\frac{105\div 5}{120\div 5}=\frac{21\div3}{24\div 3}=\frac{7}{8}$

(c) $=\frac{210\div5}{315\div5}=\frac{42\div3 }{63\div3}=\frac{14\div7}{21\div7}=\frac{2}{3}$

---

Q5 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 5

Express each of the following mixed number as improper fraction

(a) $9 \frac{7}{10}$

$=\frac{(9 \times 10)+7}{10}$

$=\frac{97}{10}$

(b) $3 \frac{15}{22}$

$=\frac{(3 \times 22)+15}{22}$

$=\frac{81}{22}$

(c) $18 \frac{11}{30}$

$=\frac{(18 \times 30)+11}{30}$

$=\frac{551}{30}$

---

Q6 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 6

Express each of the following as mixed number

(a) $\frac{19}{5}=3 \frac{4}{5}$

(b) $\frac{77}{24}=3 \frac{5}{24}$

(c) $\frac{659}{50}=13 \frac{9}{50}$

---

Q7 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 7

In each of the following write down the largest value and smallest value

(a) $\frac{2}{11}, \frac{8}{11}, \frac{5}{11}, \frac{9}{11}$

Sol :

Largest value$=\frac{9}{11}$

Smallest value$=\frac{2}{11}$

(b) $\frac{2}{3}, \frac{2}{7}, \frac{2}{5}, \frac{2}{9}$

Sol :

LCM of 3,7,5,9=315

$\frac{2 \times 105}{3 \times 105}=\frac{210}{315}$

$\frac{2 \times 45}{7 \times 45}=\frac{90}{315}$

$\frac{2 \times 63}{5 \times 63}=\frac{126}{315}$

$\frac{2 \times 35}{9 \times 35}=\frac{70}{315}$

Largest value $=\frac{2}{3}$ 

Smallest value $=\frac{2}{9}$

(c) $\frac{9}{16}, \frac{3}{5}, \frac{11}{20}, \frac{23}{40}$

Sol :

LCM of 16,5,20,40 is 80

$\frac{9 \times 5}{16 \times 5}=\frac{45}{80}$

$\frac{3 \times 16}{5 \times 16}=\frac{48}{80}$

$\frac{11 \times 4}{20 \times 4}=\frac{44}{80}$

$\frac{23 \times 2}{40 \times 2}=\frac{46}{80}$

Largest value $=\frac{3}{5}$

Smallest value $=\frac{11}{20}$

(d)  $\frac{5}{6}, \frac{13}{15}, \frac{23}{30}, \frac{14}{18}$

Sol :

LCM of 6, 15, 30, 18 is 90

$\frac{5 \times 15}{6 \times 15}=\frac{75}{90}$

$\frac{13 \times 6}{15 \times 6}=\frac{78}{90}$

$\frac{23 \times 3}{30 \times 3}=\frac{69}{90}$

$\frac{14 \times 5}{18 \times 5}=\frac{70}{90}$

$\begin{aligned} \text { Largest } \text { value } &=\frac{13}{15} \\ \text { Smallest value}  &=\frac{23}{30} \end{aligned}$

---

Q8 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 8

Insert <  = or >

(a) $\frac{4}{9} \square \frac{5}{12}$

Sol :

LCM of 9, 12 is 36

$\frac{4 \times 4}{9 \times 4}=\frac{16}{36}$

$\frac{5 \times 3}{12 \times 3}=\frac{15}{36}$

∴$\frac{4}{9}>\frac{5}{12}$

(b) $\frac{7}{24} \square \frac{11}{36}$

Sol :

LCM of 24,36 is 72

$\begin{aligned}&\frac{7 \times 3}{24 \times 3}=\frac{21}{72} \\&\frac{11 \times 2}{36 \times 2}=\frac{22}{72}\end{aligned}$

∴$\frac{7}{24}<\frac{11}{36}$

(c) $\frac{4}{5} \square \frac{12}{15}$

Sol :

LCM of 5, 15 is 15

$\frac{4 \times 3}{5 \times 3}=\frac{12}{15}$

$\frac{12 \times 1}{15 \times 1}=\frac{12}{15}$

∴$\frac{4}{5}=\frac{12}{15}$

---

Q9 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 9

Arrange in descending order

(a) $\frac{3}{10}, \frac{2}{5}, \frac{1}{3}$

Sol :

(a) LCM of 10, 5, 3 is 30

$\frac{3 \times 3}{10 \times 3}=\frac{9}{30}$

$\frac{2 \times 6}{5 \times 6}=\frac{12}{30}$

$\frac{1 \times 10}{3 \times 10}=\frac{10}{30}$

∴$\frac{2}{5}, \frac{1}{3}, \frac{3}{10}$

(b) $\frac{7}{12}, \frac{5}{9}, \frac{9}{16}$

Sol :

LCM of 12, 9, 16 is 144

$\frac{7 \times 12}{12 \times 12}=\frac{84}{144}$

$\frac{5 \times 16}{9 \times 16}=\frac{80}{144}$

$\frac{9 \times 9}{16 \times 9}=\frac{81}{144}$

∴$\frac{7}{12},\frac{9}{16}, \frac{5}{9}$

---

Q10 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 10

Arrange in ascending order

(a) $\frac{11}{15} , \frac{3}{4}, \frac{13}{20}$

Sol :

LCM of 15, 4, 20 is 60

$\frac{11 \times 4}{15 \times 4}=\frac{44}{60}$

$\frac{3 \times 15}{4 \times 15}=\frac{45}{60}$

$\frac{13 \times 3}{20 \times 3}=\frac{39}{60}$

$\frac{39}{60}<\frac{44}{60} <\frac{45}{60}$

∴$\frac{13}{20}< \frac{11}{15}< \frac{3}{4}$

(b) $\frac{5}{12}, \frac{7}{18}, \frac{11}{27}$

Sol :

LCM of 12, 8, 27 is 108

$\frac{5 \times 9}{12 \times 9}=\frac{45}{108}$

$\frac{7 \times 6}{18 \times 6}=\frac{42}{108}$

$\frac{11 \times 4}{27 \times 4}=\frac{44}{108}$

∴$\frac{7}{18}, \frac{11}{27}, \frac{5}{12}$

---

Q11 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 11

Simplify the following, expressing your answer in the simplest form

(a) $\frac{17}{24}+\frac{1}{24}$

Sol :

$\begin{aligned} =& \frac{17}{24}+\frac{1}{24} \\=& \frac{17+1}{24} \\=& \frac{18}{24} \\=& \frac{3}{4} \end{aligned}$

(b) $\frac{14}{15}+\frac{11}{15}+1 \frac{1}{15}$

Sol :

$\frac{14}{15}+\frac{11}{15}+1 \frac{1}{15}$

$=\frac{14}{15}+\frac{11}{15}+\frac{16}{15}$

$=\frac{14+11+16}{15}$

$=\frac{41}{15}=2 \frac{11}{15}$

(c) $\frac{5}{6}-\frac{1}{6}$

Sol :

$=\frac{5}{6}-\frac{1}{6}$

$=\frac{5-1}{6}$

$=\frac{4}{6}=\frac{2}{3}$

(d) $12 \frac{6}{7}-9 \frac{1}{7}$

Sol :

$\begin{aligned} =& 12 \frac{6}{7}-9 \frac{1}{7} \\=& \frac{90}{7}-\frac{64}{7} \\=& \frac{90-64}{7} \\=& \frac{26}{7} \\=& 3 \frac{5}{7} \end{aligned}$

(e) $18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19}$

Sol :

$18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19}$

$\begin{aligned}&=(18+23-15)+\frac{12}{19}+\frac{18}{19}-\frac{14}{19} \\&=26+\frac{12+18-14}{19} \\&=26+\frac{16}{19} \\&=\frac{494+16}{19} \\&=\frac{510}{19} \\&=26 \frac{16}{19}\end{aligned}$

---

Q12 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 12

(a) $\frac{15}{1}+4 \frac{1}{4}$

Sol :

$\begin{aligned}=& 15+4 \frac{1}{4} \\=& 15+\frac{17}{4} \\=& \frac{60+17}{4} \\=& \frac{77}{4} \\=& 19 \frac{1}{4}\end{aligned}$

(b) $\frac{27}{1}-3 \frac{1}{5}$

Sol :

$\begin{aligned}=&27-3 \frac{1}{5} \\=&27-\frac{16}{5} \\=&\frac{135-16}{5} \\=&\frac{119}{5} \\=&23 \frac{4}{5}\end{aligned}$

(c) $61-2 \frac{7}{8}$

Sol :

$\begin{aligned}&=61-2 \frac{7}{8} \\&=61-\frac{23}{8} \\&=\frac{488-23}{8} \\&=\frac{465}{8} \\&=58 \frac{1}{8}\end{aligned}$

---

Q13 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 13

(a) $1 \frac{2}{5}+3 \frac{1}{4}+\frac{7}{10}$

$\begin{aligned}&=\frac{7}{5}+\frac{13}{4}+\frac{7}{10} \\&=\frac{28+65+14}{20} \\&=\frac{107}{20} \\&=5 \frac{7}{20}\end{aligned}$

(b) $7 \frac{6}{15}+4 \frac{11}{12}+3 \frac{7}{30}$

$=\frac{111}{15}+\frac{59}{12}+\frac{27}{30}$

$=\frac{444+295+194}{60}$

$=\frac{933}{60}=15\frac{11}{20}$

---

Q14 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 14

(a) $5 \frac{2}{3}-5 \frac{1}{6}+2 \frac{5}{6}$

$=\frac{17}{3}-\frac{31}{6}+\frac{17}{6}$

$=\frac{34-31+17}{6}$

$=\frac{20}{6}$

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

(b) $3 \frac{5}{24}-1 \frac{7}{36}+\frac{11}{16}$

$=\frac{77}{24}-\frac{43}{36}+\frac{11}{16}$

$=\frac{462-172+99}{144}$

$=\frac{389}{144}$

$=2 \frac{101}{144}$

---

Q15 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 15

(a) $6 \frac{1}{5}-\left(4 \frac{3}{10}-1 \frac{1}{2}\right)$

$=\frac{31}{5}-\left(\frac{43}{10}-\frac{3}{2}\right)$

$=\frac{31}{5}-\frac{43-15}{10}$

$=\frac{31}{5}-\frac{28}{10}$

$=\frac{62-28}{10}=\frac{34}{10}$

$=3 \frac{2}{5}$

(b) $3 \frac{5}{9}-\left(2 \frac{1}{3}-1 \frac{5}{12}\right)+1 \frac{5}{6}$

$=\frac{32}{9}-\left(\frac{7}{3}-\frac{17}{12}\right)+\frac{11}{6}$

$=\frac{32}{9}-\frac{28-17}{12}+\frac{11}{6}$

$=\frac{32}{9}-\frac{11}{12}+\frac{11}{6}$

$=\frac{128-33+66}{36}$

$=\frac{161}{36}$

$=4 \frac{17}{36}$

---

Q16 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 16

If in a mushroom $\frac{19}{20}$ is water, what fraction of it is solid matter?

Sol :

The fraction of mushroom in solid matter

$\begin{aligned}&=1-\frac{19}{20} \\&=\frac{20-19}{20} \\&=\frac{1}{20}\end{aligned}$

---

Q17 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 17

During a campaign an army loses $\frac{1}{10}$ of its member in battle and $\frac{1}{5}$ by sickness what fraction survive?

Sol :

The fraction of campaign survives 

$\begin{aligned}&=1-\left(\frac{1}{10}+\frac{1}{5}\right) \\&=1-\frac{3}{10} \\&=\frac{10-3}{10} \\&=\frac{7}{10}\end{aligned}$

---

Q18 | Ex-2A | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

OPEN IN YOUTUBE

Question 18

In a certain magazine $\frac{11}{27}$ consists of advertisements and $\frac{1}{3}$ of illustrations, what fraction is readable matter

Sol :

The fraction in readable matter

$\begin{aligned}&=1-\left(\frac{11}{27}+\frac{1}{3}\right) \\&=1-\frac{11+9}{27} \\&=1-\frac{20}{27} \\&=\frac{27-20}{27} \\&=\frac{7}{27}\end{aligned}$