# Ncert Solutions For Class 8 Maths Ex 1.1

## Ncert Solutions For Class 8 Maths Chapter 1 Ex 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$\ therefore  \, 0.3\,  is\,   not\,  the\,  multiplicative\,  inverse\,  of\,   3\frac{1}{3}$