August 9, 2024

# Class 8 Maths Chapter 1 (Rational numbers) Exercise 1.1

## Class 8 maths chapter 1 exercise 1.2 solutions

NCERT maths class 8 chapter 1  (Exercise 1.2)

1. Represent these numbers on the number line. (i)        (ii)

Sol.  (i) To represent  $\frac{7}{4}$ the number line may be divided into four equal parts as shown  fig 1.  We use the number $\frac{1}{4}$ to name the first point of this division. The second point of division will be labelled $\frac{2}{4}$, the third point $\frac{3}{4}$, and so on . The point A will represent $\frac{7}{4}$ .

(ii)  To represent  $\frac{5}{6}$ the number line may be divided into six equal parts as shown  fig 2.  We use the number $\frac{1}{6}$ to name the first point of this division. The second point of division will be labelled $\frac{2}{6}$, the third point $\frac{3}{6}$, and so on . The point B will represent $\frac{5}{6}$ .

2. Represent  on the number line.

Sol.  Point A is  $-\frac{2}{11}$,  point B is $-\frac{5}{11}$ and point C is $-\frac{9}{11}$ .

3. Write five rational numbers which are smaller than 2.

Sol. Five rational numbers smaller than 2 are  $\frac{1}{2},&space;\frac{1}{4}&space;,&space;\frac{1}{8},&space;\frac{3}{20}&space;\,&space;\,\mathrm{and&space;}&space;\frac{5}{3}.$

4. Find ten rational numbers between  .

Sol.  We first convert $\frac{-2}{5}&space;\,&space;\,&space;\mathrm{and&space;}&space;\,&space;\,&space;\frac{1}{2}$ to rational numbers with the same denominators.

$\frac{-2}{5}=\frac{-2&space;\times&space;6}{5&space;\times&space;6&space;}=\frac{-12}{30}$ and $\frac{1}{2}=\frac{1\times&space;15}{2\times&space;15}=\frac{15}{30}$

Thus we have $\frac{-11}{30},\frac{-10}{30},\frac{-9}{30},\frac{-8}{30},\frac{-7}{30},\frac{-6}{30},\frac{-5}{30},\frac{-4}{30},\frac{-3}{30},&space;..............\,&space;\,&space;\mathrm{and}\,&space;\,\frac{12}{30},\frac{13}{30},&space;\frac{14}{30}$  between $\frac{-2}{5}&space;\,&space;\,&space;\mathrm{and&space;}&space;\,&space;\,&space;\frac{1}{2}$ .

You can take any ten of these. In fact , you get countless rational numbers between any two given rational numbers.

5. Find five rational numbers between (i)      (ii)           (iii)

Sol. (i) $\frac{-2}{3}$ can be written as $\frac{-2}{3}=\frac{-2\times&space;10}{3\times&space;10}=\frac{-20}{30}$  and $\frac{4}{5}$  as $\frac{4}{5}=\frac{4\times&space;6}{5\times&space;6}=\frac{24}{30}$ .

Thus we have $\frac{-19}{30},\frac{-18}{30},\frac{-17}{30},\frac{-16}{30},\frac{-15}{30},\frac{-14}{30},............,\frac{23}{30}$  between $\frac{-2}{3}$   and $\frac{4}{5}$ .

You can take any five of these.

(ii) $\frac{-3}{2}$ can be written as $\frac{-3}{2}=\frac{-3\times&space;3}{2\times&space;3}=\frac{-9}{6}$  and $\frac{5}{3}$  as $\frac{5}{3}=\frac{5\times&space;2}{3\times&space;2}=\frac{10}{6}$ .

Thus we have $\frac{-8}{6},\frac{-7}{6},\frac{-6}{6},\frac{-5}{6},\frac{-4}{6},\frac{-3}{6},............,\frac{9}{6}$  between $\frac{-3}{2}$   and $\frac{5}{3}$ .

You can take any five of these.

(iii) $\frac{1}{4}$ can be written as $\frac{1}{4}=\frac{1\times&space;6}{4\times&space;6}=\frac{6}{24}$  and $\frac{1}{2}$  as $\frac{1}{2}=\frac{1\times&space;12}{2\times&space;12}=\frac{12}{24}$ .

Thus we have $\frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24}&space;\,&space;\,&space;\mathrm{and}\,&space;\,&space;\frac{11}{24}$ are five rational numbers   between $\frac{1}{4}$   and $\frac{1}{2}$ .

6. Write five rational numbers greater than –2.

Sol. The five rational numbers greater than -2  are $\frac{-1}{2},&space;0,&space;\frac{1}{2},\frac{3}{2}&space;\,&space;\mathrm{and}\,&space;\,&space;\frac{1}{4}$  .

7. Find ten rational numbers between  .

Sol. We first convert $\frac{3}{5}&space;\,&space;\,&space;\mathrm{and&space;}&space;\,&space;\,&space;\frac{3}{4}$ to rational numbers with the same denominators.

$\frac{3}{5}=\frac{3&space;\times&space;20}{5&space;\times&space;20&space;}=\frac{60}{100}$ and $\frac{3}{4}=\frac{3\times&space;25}{4\times&space;25}=\frac{75}{100}$

Thus we have $\frac{61}{100},\frac{62}{100},\frac{63}{100},\frac{64}{100},\frac{65}{100},\frac{66}{100},\frac{67}{100},\frac{68}{100},\frac{69}{100},&space;..............\,&space;\,&space;\mathrm{and}\,&space;\,\frac{72}{100},\frac{73}{100},&space;\frac{74}{100}$  between $\frac{3}{5}&space;\,&space;\,&space;\mathrm{and&space;}&space;\,&space;\,&space;\frac{3}{4}$.

You can take any ten of these. In fact , you get countless rational numbers between any two given rational numbers.

#### Bina singh

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