# NCERT Solutions For Class 8 Maths Chapter 1

## NCERT Solutions Class 8 Maths Rational Numbers

NCERT solutions for class 8 maths chapter 1 Rational numbers is provided here. Class 8 is an important phase of a students life, the topic which are taught in class 8 are essential to understand the topics of class 9. To score good marks in class 8 mathematics examination it is advised to solve questions provided at the end of each chapter in the NCERT book. Solving NCERT questions will help you to know about the different types of questions with their difficulty level. Students can download NCERT solutions for class 8 maths chapter 1 pdf from the table below.

### NCERT Solutions Class 8 Maths Chapter 1 Exercises

Exercise – 1.1

1. Using appropriate properties find the value of 23×35+5235×16$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

Sol.   23×35+5235×16$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$23×3535×16+52$\frac{-2}{3}\times \frac{3}{5}-\frac{3}{5}\times \frac{1}{6}+\frac{5}{2}$

=35(23+16)+52$\frac{-3}{5}(\frac{2}{3}+\frac{1}{6})+\frac{5}{2}$

=35(4+16)+52$\frac{-3}{5}(\frac{4+1}{6})+\frac{5}{2}$

=35(56)+52$\frac{-3}{5}(\frac{5}{6})+\frac{5}{2}$

=1530+52$\frac{-15}{30}+\frac{5}{2}$

=12+52$\frac{-1}{2}+\frac{5}{2}$

=42$\frac{4}{2}$

=2$2$

therefore23×35+5235×16$\ therefore\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$ =2

1. Using appropriate properties find the value of 25×3716×32+114×25$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Sol. 25×3716×32+114×25$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

= 25×3712×12+17×15$\frac{-2}{5}\times \frac{3}{7}-\frac{1}{2}\times \frac{1}{2}+\frac{1}{7}\times \frac{1}{5}$

=63514+135$\frac{-6}{35}-\frac{1}{4}+\frac{1}{35}$

=53514$\frac{-5}{35}-\frac{1}{4}$

=1714$\frac{-1}{7}-\frac{1}{4}$

=1128$\frac{-11}{28}$

=25×3716×32+114×25$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

=1128$\frac{-11}{28}$

1. Solving the additive inverse of 28$\frac{2}{8}$

Sol.  Additive inverse of 28is28$\frac{2}{8} is \frac{-2}{8}$

1. Solving the additive inverse of 59$\frac{-5}{9}$

Sol.  Additive inverse of 59is59$\frac{-5}{9} is\frac{5}{9}$

1. Solving the additive inverse of 65$\frac{-6}{-5}$

Sol. 6565$\frac{-6}{-5}\frac{-6}{-5}$

Additive inverse of 65is65$\frac{6}{5} is\frac{-6}{5}$

Additive inverse of 6565$\frac{-6}{-5}\frac{-6}{5}$

1. Solving the additive inverse of 29$\frac{2}{-9}$

Sol.  Additive inverse of 29is29$\frac{2}{-9} is\frac{2}{9}$

1. Verify that –(-x )=x for x=1115$x=\frac{11}{15}$

Sol. x=1115$x = \frac{11}{15}$

x=1115$– x =\frac{-11}{15}$ (x)=(1115)$-(-x)= -(\frac{-11}{15})$

=1115=x$\frac{11}{15}=x$

therefore(x)=x$\ therefore -(-x)=x$

1. Verify that –(-x )=x for x=1317$x=\frac{-13}{17}$

Sol. x=1317$x = \frac{-13}{17}$

x=(1317)=1317$– x =(-\frac{-13}{17})=\frac{13}{17}$ (x)=(1317)$-(-x)= -(\frac{-13}{17})$

=1317=x$\frac{-13}{17}=x$

therefore(x)=x$\ therefore -(-x)=x$

1. Solve that multiplicative inverse of -13

Sol. Given multiplicative inverse -13 is113$\frac{-1}{13}$

1. Solve that multiplicative inverse of 1319$\frac{-13}{19}$

Sol. Given multiplicative inverse 1319is1913$\frac{-13}{19} is\frac{-19}{13}$

1. Solve that multiplicative inverse of 58×37$\frac{-5}{8}\times \frac{-3}{7}$

Sol. Given multiplicative inverse 58×37$\frac{-5}{8}\times \frac{-3}{7}$is 85×73$\frac{8}{5}\times \frac{7}{3}$ or 85×73$\frac{-8}{5}\times \frac{-7}{3}$

1. What is the multiplicative inverse of -1.

Sol.  The multiplicative inverse of -1 is -1.

1. Name the property under multiplicative used in each of the following.

(i) 45×1=1×45=45$\frac{-4}{5}\times 1=1\times \frac{-4}{5}=\frac{-4}{5}$

(ii) 1317×27=27×1317$\frac{-13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{17}$

(iii) 1929×2919=1$\frac{-19}{29}\times \frac{29}{-19}=1$

Sol. (i) ROLE OF 1

(ii) COMMUTATIVITY

(iii) MULTIPLICATIVE  INVERSE

1. Multiply 613$\frac{6}{13}$ by the reciprocal of 76$\frac{-7}{6}$

Sol. Reciprocal of 76$\frac{-7}{6}$ is 67$\frac{6}{-7}$

therefore613×67$\ therefore \frac{6}{13}\times \frac{6}{-7}$

=3691$\frac{-36}{91}$

1. what property allows you to compute 13×(6×43)(13×6)×45$\frac{1}{3}\times (6\times \frac{4}{3})(\frac{1}{3}\times 6)\times \frac{4}{5}$

Sol.  Associativity

1. Is 89$\frac{8}{9}$ the multiplicative inverse of 118$-1\frac{1}{8}$ ? why or why not.

Sol.

118=98$-1\frac{1}{8} = \frac{-9}{8}$

=89×98$\frac{8}{9}\times \frac{-9}{8}$

=11$-1 \neq 1$

therefore89$\ therefore\frac{8}{9}$ is  not the multiplicative inverse of 118$ -1\frac{1}{8}$

1. Is 0.3 the multiplicative inverse of 313$3\frac{1}{3}$ ? why or why not.

Sol.        313=103=3.3$3\frac{1}{3} = \frac{10}{3} =3.3$

3.3×0.3=0.991$ 3.3\times 0.3= 0.99\neq 1$

therefore0.3isnotthemultiplicativeinverseof313$\ therefore  \, 0.3\,  is\,   not\,  the\,  multiplicative\,  inverse\,  of\,   3\frac{1}{3}$

Exercise 1.2:

Question 1:

Solve the following using appropriate properties:

1. ii)25371632+11425$\frac{2}{5}* \frac{-3}{7} – \frac{1}{6} *\frac{3}{2}+\frac{1}{14}*\frac{2}{5}$

1. ii) Use commutativity of rational numbers
25371632+11425$\frac{2}{5}* \frac{-3}{7} – \frac{1}{6} *\frac{3}{2}+\frac{1}{14}*\frac{2}{5}$

Using distributive property

25[37+114]14$\frac{2}{5} * [\frac{-3}{7} + \frac{1}{14}] – \frac{1}{4}$

= 2532+11414$\frac{2}{5} * \frac{-3*2+1}{14} – \frac{1}{4}$

=2551414$\frac{2}{5} * \frac{-5}{14} – \frac{1}{4}$

=4728=1128$\frac{-4-7}{28} = \frac{-11}{28}$

Question 2:

(i) 57$\frac{-5}{-7}$

(ii) 47$\frac{-4}{-7}$

(iii)25$\frac{2}{-5}$

(iv)59$\frac{5}{-9}$

Solution:

(i) 57$\frac{-5}{-7}$

additive inverse = 57$\frac{5}{-7}$

(ii)  47$\frac{-4}{-7}$47$\frac{4}{7}$

Additive inverse = 47$\frac{-4}{7}$

(iii)  25$\frac{2}{-5}$

Additive inverse = 25$\frac{2}{5}$

(iv)  59$\frac{5}{-9}$

Additive inverse = 59$\frac{5}{9}$
Question 3:

(i)  x = 1115$\frac{11}{15}$

(ii) x= 1317$\frac{-13}{17}$

Solution:

x = 1115$\frac{11}{15}$

The additive inverse of  is   x = 1115$\frac{-11}{15}$

This equality

x = 1115+frac1115=0$\frac{11}{15}+frac{-11}{15}= 0$

=(x)=x$-(-x) = x$

x= 1317$\frac{-13}{17}$

The additive inverse of  x= 1317$\frac{-13}{17}$ =  x= 1317$\frac{13}{17}$

This equaliity

x = 1317+frac1317=0$\frac{-13}{17}+frac{13}{17}= 0$

=(x)=x$-(-x) = x$

Question 4:

(i)  -12

(ii) 1913$\frac{-19}{13}$

(iii) 13$\frac{1}{3}$

(iv)  3838$\frac{-3}{8} * \frac{-3}{8}$

(v)  135$-1 * \frac{-3}{5}$

Solutions:

1. The multiplicative inverse of  -12 is 112$\frac{1}{12}$
2. The multiplicative inverse of 1913$\frac{-19}{13}$ is1319$\frac{-13}{19}$
3. The multiplicative inverse of 13$\frac{1}{3}$  is 31$\frac{3}{1}$ = 3
4. The multiplicative inverse of  135$-1 * \frac{-3}{5}$ is 53$\frac{5}{3}$

Question 5:

Find out the multiplication property that is used in the following sums:

(i) 371=137=37$\frac{-3}{7} * 1 = 1 * \frac{-3}{7} = \frac{-3}{7}$

(ii) 141734=341417$\frac{-14}{17}* \frac{-3}{4} = \frac{-3}{4} * \frac{-14}{17}$

(iii) 17373717=1$\frac{-17}{37} * \frac{37}{-17} = 1$

Solutions:

1. This use the multiplicative identity property and the multiplicative identity is 1
2. This uses the commutativity property
3. This uses the multiplicative inverse property

Question 6:

Find the product of  715$\frac{7}{15}$ and the reciprocal of 417$\frac{-4}{17}$

Solution:

Reciprocal of  417$\frac{-4}{17}$1714$\frac{-17}{14}$

7151714=11960$\frac{7}{15}* \frac{-17}{14} = \frac{119}{60}$

Question 7:

1. Which rational number does not have a reciprocal
2. Which rational number is equal to its own reciprocal
3. Which rational number is equal to its own negative

Solution:

1. Zero is the rational number that has no reciprocal
2. One and negative one are rational numbers that are equal to their own reciprocal
3. Zero is a rational number that is also equal to its own negative.

Question 8: Answer or complete the following sentences:

1. Does zero have a reciprocal?
2. The two numbers _____ and _________ are their own reciprocals.
3. What is the reciprocal of -6?
4. What is the reciprocal of ?
5. The product of two rational numbers is always a __________.
6. The reciprocal of a positive rational number is ___________.

Solutions:

1. No it doesn’t
2. 1, -1
3. -1/6
4. X
5. Rational number
6. Positive rational number

Question 9:

Find the multiplicative inverse of the following:

1. -12
2. 1218$\frac{-12}{18}$
3. 27$\frac{2}{7}$
4. -1
5. 3857$\frac{-3}{8} * \frac{-5}{7}$
6. 227$-2 * \frac{-2}{7}$

Solutions:

1. 112$\frac{-1}{12}$
2. 1218$\frac{-12}{18}$
3. 72$\frac{7}{2}$
4. -1
5. 5615$\frac{56}{15}$
6. 72$\frac{7}{2}$

Question 10:

Is 0.3 the multiplicative inverse of   313$3 \frac{1}{3}$? Why or why not?

313=103$3 \frac{1}{3}= \frac{10}{3}$ 0.3313=0.3103=310103=1$0.3*3 \frac{1}{3} = 0.3 * \frac{10}{3} = \frac{3}{10} * \frac{10}{3} = 1$
Therefore, 0.3 is the multiplicative inverse of  313$3 \frac{1}{3}$