SChand Composite Mathematics Class 7 Chapter 4 Rational Numbers Exercise 4B

  Exercise 4B

---

Q1 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 1

Add the following rational number

(i) $\frac{2}{7} \text{ and } \frac{3}{7}$

Sol :

$=\frac{2+3}{7}=\frac{5}{7}$

(ii) $\frac{-4}{11} \text{ and } \frac{7}{11}$

Sol :

$=\frac{-4+7}{11}=\frac{3}{11}$

(iii) $\frac{-2}{9} \text{ and  } \frac{-4}{9}$

Sol :

$=\frac{-2+(-4)}{9}=\frac{-2-4}{9}$

$=\frac{-6}{9}=\frac{-2}{3}$

(iv) $\frac{-8}{-17} \text{ and } \frac{10}{-17}$

Sol :

$=\frac{8+(-10)}{17}=\frac{8-10}{17}$

$=\frac{-2}{17}$

(v) $\frac{9}{23} \text{ and } \frac{-11}{-23}$

Sol :

$=\frac{9+11}{23}=\frac{20}{23}$

(vi) $\frac{13}{-38} \text{ and } \frac{-21}{38}$

Sol :

$=\frac{-13+(-21)}{38}=\frac{-13-21}{38}$

$=\frac{-34}{38}=\frac{-17}{19}$

---

Q2 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 2

(i) $\frac{5}{6} \text{ and } \frac{-2}{3}$

Sol :

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

$=\frac{5}{6}+\frac{-4}{6}=\frac{5-4}{6}=\frac{1}{6}$

(ii) $\frac{-1}{2} \text{ and } \frac{1}{6}$

Sol :

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

$=\frac{-3}{6}+\frac{1}{6}=\frac{-3+1}{6}$

$=\frac{-2}{6}=\frac{-1}{3}$

(iii) $\frac{1}{8} \text{ and } \frac{3}{4}$

Sol :

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

$=\frac{1}{8}+\frac{6}{8}=\frac{1+6}{8}=\frac{7}{8}$

(iv) $\frac{1}{5} \text{ and  } \frac{4}{-7}$

Sol :

L.C.M of 3 and 7 is 35

$\frac{1 \times 7}{5 \times 7}$

$\frac{4 \times 5}{-7 \times 5}$

$=\frac{7+(-20)}{35}=\frac{7-20}{35}=\frac{-13}{35}$

(v) $\frac{-2}{3} \text{ and } \frac{3}{-4}$

Sol :

$\frac{-2 \times 4}{3 \times 4} \text{ and } \frac{3 \times 3}{-4 \times 3}$

$=\frac{-8}{12}+\frac{-9}{12}=\frac{-8-9}{12}=\frac{-17}{12}$

(vi) $\frac{5}{-12} \text{ and } \frac{7}{-9}$

Sol :

$\frac{5 \times 3}{-12 \times 3} \text{ and } \frac{7 \times 4}{-9 \times 4}$

$=\frac{-15+(-28)}{36}=\frac{-15-28}{36}=\frac{-43}{36}$

(vii) $2\frac{3}{14} \text{ and } \frac{-3}{-7}$

Sol :

$2\frac{3}{14} =\frac{2\times 14 +3}{14}=\frac{31}{14}$

$\frac{-3}{-7}=\frac{3 \times 2}{7 \times 2}$

$=2\frac{3}{14}+ \frac{3}{7}=\frac{31}{14}+\frac{6}{14}$

$=\frac{31+6}{14}=\frac{37}{14}$

---

Q3 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 3

Evaluation :

(i) $\frac{-3}{8}+\frac{1}{8}+\frac{5}{8}$

Sol :

$=\frac{-3+1+5}{8}=\frac{-3+6}{8}=\frac{3}{8}$

(ii) $\frac{-13}{9}+\frac{7}{9}+\frac{2}{-9}$

Sol :

$=\frac{-13+7+(-2)}{9}=\frac{-13+7-2}{9}$

$=\frac{-15+7}{9}=\frac{-8}{9}$

(iii) $\frac{-1}{2}+\frac{2}{3}+\frac{4}{5}$

Sol :

L.C.M of 2, 3, 5 is 30

$\frac{-1 \times 15}{2 \times 15}+\frac{2 \times 10}{3 \times 10}+\frac{4 \times 6}{5 \times 6}$

$=\frac{-15}{30}+\frac{20}{30}+\frac{24}{30}$

$=\frac{-15+20+24}{30}=\frac{29}{30}$

(iv) $8+\left(\frac{-5}{6}\right)+1\frac{1}{5}$

Sol :

$=\frac{8}{1}-\frac{5}{6}+\frac{6}{5}$

L.C.M of 1, 6 , 5 is 30

$=\frac{8 \times 30}{1 \times 30}-\frac{5 \times 5}{6 \times 5}+\frac{6 \times 6}{5 \times 6}$

$=\frac{240}{30}-\frac{25}{30}+\frac{36}{30}$

$=\frac{240-25+36}{30}=\frac{251}{30}=8\frac{11}{30}$

(v) $\frac{-12}{5}+\frac{31}{10}+\frac{11}{-15}+\frac{-7}{-18}$

Sol :

L.C.M of 5, 10 ,15 , 18 is 90

$=\frac{-12 \times 18}{5 \times 18}+\frac{31 \times 9}{10 \times 9}+\frac{11 \times 6}{-15 \times 6}+\frac{-7 \times 5}{-18 \times 5}$

$=\frac{-216}{90}+\frac{279}{90}-\frac{66}{90}+\frac{35}{90}$

$=\frac{-216+279-66+35}{90}=\frac{32}{90}=\frac{16}{45}$

(vi) $\frac{-7}{12}+\frac{13}{-24}+\frac{-29}{-36}+5$

Sol :

L.C.M of 12 , 24 , 36 is 72

$=\frac{-7 \times 6}{12 \times 6}+\frac{13 \times 3}{-24 \times 3}+\frac{-29 \times 2}{-36 \times }+\frac{5 \times 72}{1 \times 72}$

$=\frac{-42}{72}+\frac{39}{-72}+\frac{58}{72}+\frac{360}{72}$

$=\frac{-42-39+58+360}{72}=\frac{337}{72}$

$=4\frac{49}{72}$

---

Q4 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 4

Express each of the following rational numbers as sum of an integer and a rational number

(i) $\frac{33}{8}$

Sol :

$=4\frac{1}{8}$

$=4+\frac{1}{8}$

(ii) $\frac{-25}{8}$

Sol :

$=-\left(3+\frac{1}{8}\right)$

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

(iii) $\frac{-27}{5}$

Sol :

$=-\left(5+\frac{2}{5}\right)$

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

(iv) $\frac{107}{-11}$

Sol :

$=-\left(9+\frac{8}{11}\right)$

$=-9-\frac{8}{11}$

---

Q5 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 5

Subtract the first rational number from the second in each of the following:

(i) $\frac{2}{7} , \frac{5}{7}$

Sol :

$=\frac{5}{7}-\frac{2}{7}=\frac{5-2}{7}=\frac{3}{7}$

(ii) $\frac{-5}{11}, \frac{8}{11}$

Sol :

$=\frac{8}{11}-\left(\frac{-5}{-11}\right)$

$=\frac{8+5}{11}=\frac{13}{11}$

(iii) $\frac{-7}{25} , \frac{-14}{25}$

Sol :

$=\frac{-14}{25}-\left(\frac{-7}{25}\right)$

$=\frac{-14+7}{25}=\frac{-7}{25}$

(iv) $\frac{-12}{-19} , \frac{-7}{19}$

Sol :

 $\frac{-7}{19}-\frac{12}{19}=\frac{-7-12}{19}=\frac{-19}{19}$

=-1

(v) $\frac{5}{6} , \frac{-7}{8}$

Sol :

L.C.M of 6 and 8 is 24

$=\frac{-7 \times 3}{8 \times 3} -\frac{5 \times 4}{6 \times 4}$

$=\frac{-21}{24}-\frac{20}{24}=\frac{-21-20}{24}$

$=\frac{-41}{24}$

(vi) $\frac{-3}{7} , \frac{5}{14}$

Sol :

L.C.M of 7 and 14 is 14

$\frac{-3 \times 2}{7 \times 2}$

$=\frac{5}{14}-\left(\frac{-6}{14}\right)$

$=\frac{5+6}{14}=\frac{11}{14}$

(vii) $\frac{-8}{15} , \frac{17}{-20}$

Sol :

L.C.M of 15 and 20 is 60

$\frac{-8 \times 4}{15 \times 4}=\frac{-32}{60} ,\frac{17 \times 3}{-20 \times 3}\frac{51}{-60}$

$=\frac{51}{-60}-\left(\frac{-32}{60}\right)$

$=\frac{-51+32}{60}=\frac{-19}{60}$

(viii) $\frac{-11}{26} , \frac{17}{-39}$

Sol :

L.C.M of 26 and 39 is 78

$\frac{-11 \times 3}{26 \times 3}, \frac{17 \times 2}{-39 \times 2}$

$=\frac{-34}{78}-\left(\frac{-33}{78}\right)$

$=\frac{-34+33}{78}=\frac{-1}{78}$

---

Q6 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 6

Evaluate each of the following:

(i) $\frac{2}{7}-\frac{12}{-35}$

Sol :

$\frac{2 \times 5}{7 \times 5}-\frac{12}{-35}$

$=\frac{10}{35}+\frac{12}{35}=\frac{10+12}{35}=\frac{22}{35}$

(ii) $\frac{-6}{13}-5-\frac{1}{-26}$

Sol :
$=\frac{-6\times 2}{13 \times 2}-\frac{5 \times 16}{1 \times 16}-\frac{1 \times 1}{-26 \times 1}$

$=\frac{-12}{26}-\frac{130}{26}+\frac{1}{26}$

$=\frac{-12-130+1}{26}=\frac{-141}{26}=-5\frac{11}{26}$

(iii) $\frac{7}{57}-\frac{-9}{19}+\frac{5}{-38}$

Sol :

L.C.M of 57 , 19 , 38 is 114

$=\frac{7 \times 2}{57 \times 2}-\frac{-9 \times 6}{15 \times 6}+\frac{5 \times 3}{-38 \times 3}$

$=\frac{14}{114}+\frac{54}{114}-\frac{15}{114}$

$=\frac{14+54-15}{114}=\frac{53}{114}$

---

Q7 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 7

(i) The sum of two rational numbers is $\frac{8}{7}$. If one of the numbers is $\frac{1}{14}$, find the other.

Sol :

Let x be the other number. 

$x+\frac{1}{14}=\frac{8}{7}$

$x=\frac{8 \times 2}{7 \times 2}=\frac{1}{14}$

$x=\frac{16}{14}-\frac{1}{14}=\frac{16-1}{14}$

$=\frac{15}{14}=1\frac{1}{14}$

(ii) What number should be added to $\frac{-6}{11}$ so as to get $\frac{4}{9}$ ? 

Sol :
$\frac{-6}{11}+x=\frac{4}{9}$

$x=\frac{4 \times 11}{9 \times 11}+\frac{6 \times 9}{11 \times 9}$

$x=\frac{44}{99}+\frac{54}{99}=\frac{44+54}{99}=\frac{98}{99}$

(iii) What number should be subtracted from $\frac{-8}{15}$ so as to get $\frac{-5}{6}$ ?

Sol :

$\frac{-8}{15}-x=\frac{-5}{6}$

$-x=\frac{-5 \times 5}{6 \times 5}+\frac{8 \times 2}{15 \times 2}$

$=\frac{-25}{30}+\frac{16}{30}=\frac{-25+16}{30}=\frac{-9}{30}$

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

---

Q8 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 8

What should be added to $\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\right)$ to get 4 ?

Sol :
$\left(\frac{1 \times 15}{2 \times 15}+\frac{1 \times 10}{3 \times 10}+\frac{1 \times 6}{5 \times 6}\right)+x=4$

$\left(\frac{15}{30}+\frac{10}{30}+\frac{6}{30}\right)+x=4$

$\left(\frac{15+10+6}{30}\right)+x=4$

$x=\frac{4}{1}-\frac{31}{30}$

$x=\frac{120-31}{30}=\frac{89}{30}=2\frac{29}{30}$

---

Q9 | Ex-4B |Class 7 | Rational numbers | S.Chand | Composite Mathematics | Chapter 4 | myhelper

OPEN IN YOUTUBE

Question 9

Simplify : $\frac{-5}{6}-\frac{7}{-8}+\frac{11}{12}-\frac{-1}{6}+0-\frac{-7}{-16}$

Sol :

L.C.M of 6, 8, 12 , 6, 16 is 48

$=\frac{-5}{6}+\frac{7}{8}+\frac{11}{12}+\frac{1}{6}-\frac{7}{16}$

$=\frac{-5\times 8+7\times 6+11\times 4+1\times 8-7\times 3}{48}$

$=\frac{-40+42+44+8-21}{48}$

$=\frac{33}{48}=\frac{11}{16}$