Rational Numbers : Exercise 1.2 (Mathematics NCERT Class 8th)

Q.1 Represent these numbers on the number line.
(i)${7 \over 4}$
(ii) ${{ - 5} \over 6}$
Sol. (i) ${7 \over 4}$

(ii) ${{ - 5} \over 6}$

Q.2 Represent ${{ - 2} \over {11}},{{ - 5} \over {11}},{{ - 9} \over {11}}$ on the number line.
Sol.

Q.3 Write five rational numbers which are smaller than 2.
Sol. There can be infinite rational numbers smaller than 2.
The random five rational numbers smaller than 2 are:$1,{1 \over 2},{1 \over 3},0, - {1 \over 2}$.

Q.4 Find ten rational numbers between ${{ - 2} \over 5}$and ${1 \over 2}$.
Sol. The five rational numbers between ${{ - 2} \over 5}$and ${1 \over 2}$are ${{ - 3} \over {10}},{{ - 2} \over {10}},{{ - 1} \over {10}},0,{1 \over {10}}$

Q.5 Find five rational numbers between
(i) ${{\rm{2}} \over {\rm{3}}}{\rm{ and }}{{\rm{4}} \over {\rm{5}}}$
(ii) ${{ - 3} \over 2}{\rm{ and }}{5 \over 3}$
(iii) ${1 \over 4}{\rm{ and }}{1 \over 2}$
Sol. (i) ${{\rm{2}} \over {\rm{3}}}{\rm{ and }}{{\rm{4}} \over {\rm{5}}}$
The given numbers can be written as ${{2 \times 15} \over {3 \times 15}} = {{30} \over {45}}$ and ${{4 \times 9} \over {5 \times 9}} = {{36} \over {45}}$
Hence, five rational numbers between ${{\rm{2}} \over {\rm{3}}}{\rm{ and }}{{\rm{4}} \over {\rm{5}}}$are ${{31} \over {45}},{{32} \over {45}},{{33} \over {45}},{{34} \over {45}},{{35} \over {45}}$

(ii) ${{ - 3} \over 2}{\rm{ and }}{5 \over 3}$
The given numbers can be written as ${{ - 3 \times 3} \over {2 \times 3}} = {{ - 9} \over 6}$ and ${{5 \times 2} \over {3 \times 2}} = {{10} \over 6}$
Hence, five rational numbers between ${{ - 3} \over 2}{\rm{ and }}{5 \over 3}$are${{ - 8} \over 6},{{ - 7} \over 6}, - 1,{{ - 5} \over 6},{{ - 4} \over 6}$

(iii) ${1 \over 4}{\rm{ and }}{1 \over 2}$
The given numbers can be written as ${{1 \times 8} \over {4 \times 8}} = {8 \over {32}}$and ${{1 \times 16} \over {2 \times 16}} = {{16} \over {32}}$
Hence, five rational numbers between ${1 \over 4}{\rm{ and }}{1 \over 2}$are ${9 \over {32}},{{10} \over {32}},{{11} \over {32}},{{12} \over {32}},{{13} \over {32}}$

Q.6 Write five rational numbers greater than – 2
Sol. There can be infinite rational numbers greater than -2.
The random five rational numbers greater than -2 are: -1, 0, 1, ½ and 2.

Q.7 Find ten rational numbers between${3 \over 5}{\rm{ and }}{3 \over 4}$.
Sol. The given numbers can be written as ${{3 \times 20} \over {5 \times 20}} = {{60} \over {100}}$ and ${{3 \times 25} \over {4 \times 25}} = {{75} \over {100}}$
Hence, ten rational numbers between ${3 \over 5}{\rm{ and }}{3 \over 4}$are${{61} \over {100}},{{62} \over {100}},{{63} \over {100}},{{64} \over {100}},{{65} \over {100}},$${{66} \over {100}},{{67} \over {100}},{{68} \over {100}},{{69} \over {100}},{{70} \over {100}}$