S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1B

Exercise 1B

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Q1 | Ex-1B | Class 8 | SChand Composite Maths | Rational Numbers | Chapter 1 | myhelper 

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Question 1

Answer True (T) or False (F) :

(i) Subtraction is commutative for rational numbers.

(ii) To subtract $\frac{c}{d}$ from $\frac{a}{b}$. We add the additive inverse of $\frac{a}{b}$ to $\frac{c}{d}$.

(iii) 0 is its own additive inverse.

(iv) The additive inverse of $\frac{-21}{-30}$ is $\frac{-21}{30}$.

(v) While subtracting three or more rational numbers, they can be grouped in any order.

Sol :

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Question 2

Add the following rational numbers :

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

(ii) $-\frac{11}{13}$ and $\frac{9}{13}$

(iii) $\frac{-1}{6}$ and $\frac{3}{10}$

(iv) $\frac{-5}{12}$ and $\frac{-7}{18}$

(v) $\frac{6}{15}$ and $\frac{-7}{25}$

(vi) $\frac{13}{14}$ and $\frac{9}{-7}$

(vii) $3 \frac{3}{4}$ and $4 \frac{1}{3}$

(viii) $2 \frac{5}{7}$ and $\frac{-3}{-14}$

Sol :

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Question 3

Simplify :

(i) $\frac{5}{6}+\frac{7}{18}+\frac{-11}{12}$

(ii) $\frac{7}{15}+\frac{-9}{25}+\frac{-3}{10}$

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

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

Sol :

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Question 4

Verify the following :

(i) $\frac{3}{4}+\frac{-2}{5}=\frac{-2}{5}+\frac{3}{4}$

(ii) $\frac{-3}{4}+\frac{7}{-8}=\frac{7}{-8}+\frac{-3}{4}$

(iii) $-8+\frac{-11}{-12}=\frac{-11}{-12}+(-8)$

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Question 5

Verify that :

(i) $\left(\frac{-5}{8}+\frac{9}{8}\right)+\frac{13}{8}=\frac{-5}{8}+\left(\frac{9}{8}+\frac{13}{8}\right)$

(ii) $-20+\left(\frac{3}{-5}+\frac{-7}{-10}\right)=\left(-20+\frac{3}{-5}\right)+\frac{-7}{-10}$

Sol :

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Question 6

Find the additive inverse of each of the following :

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

(ii) 0

(iii) $\frac{17}{9}$

(iv) $\frac{-15}{-11}$

(v) -23

(vi) $\frac{-16}{13}$

(vii) $\frac{8}{-29}$

Sol :

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Question 7

Arrange and simplify :

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

(ii) $\frac{28}{17}+\frac{35}{17}+\frac{-16}{17}+\frac{-23}{17}$

(iii) $\frac{2}{3}+\frac{-3}{5}+\frac{1}{6}+\frac{-8}{15}$

(iv) $\frac{3}{5}+\frac{5}{3}+\frac{-11}{5}+\frac{-2}{3}$

(v) $\frac{4}{3}+\frac{3}{5}+\frac{-2}{3}+\frac{-11}{5}$

(vi) $\frac{4}{9}+\frac{5}{3}+\frac{-4}{5}+\frac{7}{9}+\frac{-2}{3}+\frac{9}{5}$

Sol :

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Question 8

Verify that -(-x)=x, when x= (a) $\frac{7}{6}$

(b) $\frac{-8}{9}$.

Sol :

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Question 9

Verify that $-(x+y)=(-x)+(-y)$, when

(a) $x=\frac{3}{4}, y=\frac{6}{7}$

(b) $x=\frac{-3}{4}, y=\frac{-6}{7}$.

Sol :

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Question 10

Subtract :

(i) $\frac{1}{5}$ from $\frac{3}{5}$

(ii) $\frac{4}{9}$ from $\frac{-1}{6}$

(iii) $\frac{-4}{15}$ from $\frac{3}{10}$

(iv) $\frac{3}{-4}$ from $\frac{4}{5}$

Sol :

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Question 11

The sum of two rational numbers is $\frac{5}{18}$. If one of the numbers is $\frac{1}{8}$, find the other.

Sol :

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Question 12

What number should be subtracted from $\frac{7}{-8}$ to get $\frac{-13}{12}$ ?

Sol :

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Question 13

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

Sol :

MULTIPLE CHOICE QUESTION (MCQS)

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Question 14

What number should be added to $\frac{-5}{16}$ to get $\frac{7}{24}$ ?

(a) $\frac{-29}{48}$

(b) $\frac{15}{48}$

(c) $\frac{29}{48}$

(d) $\frac{21}{28}$

Sol :

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Question 15

$\frac{-5}{7}+\frac{1}{12}+\frac{3}{4}+\frac{-1}{3}+\frac{10}{7}+-\frac{1}{6}$ equals

(a) 0

(b) 1

(c) $1 \frac{1}{21}$

(d) -1

Sol :