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) ${7 \over 4}$
$class 8 math Rational Numbers2 Solution of exercise 1.2$

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

$class 8 math Rational Numbers4 Solution of exercise 1.2$

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

$class 8 math Rational Numbers6 Solution of exercise 1.2$

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 ${{61} \over {100}},{{62} \over {100}},{{63} \over {100}},{{64} \over {100}},{{65} \over {100}},$ ${{66} \over {100}},{{67} \over {100}},{{68} \over {100}},{{69} \over {100}},{{70} \over {100}}$