Class 8 maths chapter 1 exercise 1.2 solutions

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)\frac{7}{4}

        (ii)\frac{5}{6}

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} .

Class 8 maths chapter 1 exercise 1.2 solutions
Fig .1

(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} .

Fig. 2

2. Represent  \frac{-2}{11}, \, \frac{-5}{11}, \, \frac{-9}{11} on the number line.

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

 

                              fig 3

 

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

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

4. Find ten rational numbers between  \frac{-2}{5}\, \, \mathrm{and}\, \, \frac{1}{2}.

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

\frac{-2}{5}=\frac{-2 \times 6}{5 \times 6 }=\frac{-12}{30} and \frac{1}{2}=\frac{1\times 15}{2\times 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}, ..............\, \, \mathrm{and}\, \,\frac{12}{30},\frac{13}{30}, \frac{14}{30}  between \frac{-2}{5} \, \, \mathrm{and } \, \, \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)  \frac{-2}{3}\, \, \mathrm{and}\, \, \frac{4}{5}     (ii)\frac{-3}{2}\, \, \mathrm{and}\, \, \frac{5}{3}           (iii) \frac{1}{4}\, \, \mathrm{and}\, \, \frac{1}{2}

 

Sol. (i) \frac{-2}{3} can be written as \frac{-2}{3}=\frac{-2\times 10}{3\times 10}=\frac{-20}{30}  and \frac{4}{5}  as \frac{4}{5}=\frac{4\times 6}{5\times 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 3}{2\times 3}=\frac{-9}{6}  and \frac{5}{3}  as \frac{5}{3}=\frac{5\times 2}{3\times 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 6}{4\times 6}=\frac{6}{24}  and \frac{1}{2}  as \frac{1}{2}=\frac{1\times 12}{2\times 12}=\frac{12}{24} .

Thus we have \frac{7}{24},\frac{8}{24},\frac{9}{24},\frac{10}{24} \, \, \mathrm{and}\, \, \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}, 0, \frac{1}{2},\frac{3}{2} \, \mathrm{and}\, \, \frac{1}{4}  .

7. Find ten rational numbers between  \frac{3}{5}\, \, \mathrm{and}\, \, \frac{3}{4}.

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

\frac{3}{5}=\frac{3 \times 20}{5 \times 20 }=\frac{60}{100} and \frac{3}{4}=\frac{3\times 25}{4\times 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}, ..............\, \, \mathrm{and}\, \,\frac{72}{100},\frac{73}{100}, \frac{74}{100}  between \frac{3}{5} \, \, \mathrm{and } \, \, \frac{3}{4}.

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

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