Q: Exercise 8.2 asks students to add, subtract, multiply and divide rational numbers in the listed subparts.

1. (i) $-\frac{3}{2}$ (ii) $\frac{34}{15}$ (iii) $\frac{17}{30}$ (iv) $\frac{82}{99}$ (v) $-\frac{26}{57}$ (vi) $-\frac{2}{3}$ (vii) $\frac{34}{15}$. 2. (i) $-\frac{13}{72}$ (ii) $\frac{23}{63}$ (iii) $\frac{1}{195}$ (iv) $-\frac{89}{88}$ (v) $-\frac{73}{9}$. 3. (i) $-\frac{63}{8}$ (ii) $-\frac{27}{10}$ (iii) $-\frac{54}{55}$ (iv) $-\frac{6}{35}$ (v) $\frac{6}{55}$ (vi) 1. 4. (i) $-6$ (ii) $-\frac{3}{10}$ (iii) $\frac{4}{15}$ (iv) $-\frac{1}{6}$ (v) $-\frac{14}{13}$ (vi) $\frac{91}{24}$ (vii) $-\frac{15}{4}$.

Question 1

1. List five rational numbers between: (i) $-1$ and $0$ (ii) $-2$ and $-1$ (iii) $-\frac{4}{5}$ and $-\frac{2}{3}$ (iv) $-\frac{1}{2}$ and $\frac{2}{3}$. 2. Write four more rational numbers in each of the following patterns: (i) $-\frac{3}{5},-\frac{6}{10},-\frac{9}{15},-\frac{12}{20},\ldots$ (ii) $-\frac{1}{4},-\frac{2}{8},-\frac{3}{12},\ldots$ (iii) $\frac{-1}{6},\frac{2}{-12},\frac{3}{-18},\frac{4}{-24},\ldots$ (iv) $\frac{-2}{3},\frac{2}{-3},\frac{4}{-6},\frac{6}{-9},\ldots$. 3. Give four rational numbers equivalent to: (i) $-\frac{2}{7}$ (ii) $\frac{5}{-3}$ (iii) $\frac{4}{9}$. 4. Draw the number line and represent the following rational numbers on it: (i) $\frac{3}{4}$ (ii) $-\frac{5}{8}$ (iii) $-\frac{7}{4}$ (iv) $\frac{7}{8}$. 5. The points P, Q, R, S, T, U, A and B on the number line are such that, $TR=RS=SU$ and $AP=PQ=QB$. In the figure, U, S, R, T divide the interval from $-2$ to $-1$ into three equal parts in that order, and A, P, Q, B divide the interval from 2 to 3 into three equal parts in that order. Name the rational numbers represented by P, Q, R and S. 6. Which of the following pairs represent the same rational number? (i) $-\frac{7}{21}$ and $\frac{3}{9}$ (ii) $-\frac{16}{20}$ and $\frac{20}{-25}$ (iii) $-\frac{2}{-3}$ and $\frac{2}{3}$ (iv) $-\frac{3}{5}$ and $\frac{-12}{20}$ (v) $\frac{8}{-5}$ and $\frac{-24}{15}$ (vi) $\frac{1}{3}$ and $\frac{-1}{9}$ (vii) $\frac{-5}{-9}$ and $\frac{5}{-9}$. 7. Rewrite the following rational numbers in the simplest form: (i) $\frac{-8}{6}$ (ii) $\frac{25}{45}$ (iii) $\frac{-44}{72}$ (iv) $\frac{-8}{10}$. 8. Fill in the boxes with the correct symbol out of >, <, and =. (i) $-\frac{5}{7}\Box\frac{2}{3}$ (ii) $-\frac{4}{5}\Box-\frac{5}{7}$ (iii) $-\frac{7}{8}\Box\frac{14}{-16}$ (iv) $-\frac{8}{5}\Box-\frac{7}{4}$ (v) $\frac{1}{-3}\Box-\frac{1}{4}$ (vi) $\frac{5}{-11}\Box\frac{-5}{11}$ (vii) $0\Box-\frac{7}{6}$. 9. Which is greater in each of the following: (i) $\frac{2}{3},\frac{5}{2}$ (ii) $-\frac{5}{6},\frac{4}{-3}$ (iii) $\frac{-3}{4},\frac{2}{-3}$ (iv) $-\frac{1}{4},\frac{1}{4}$ (v) $-\frac{3}{7},-\frac{2}{5}$. 10. Write the following rational numbers in ascending order: (i) $-\frac{3}{5},-\frac{2}{5},-\frac{1}{5}$ (ii) $-\frac{1}{3},-\frac{2}{9},-\frac{4}{3}$ (iii) $-\frac{3}{7},-\frac{3}{2},-\frac{3}{4}$.

Accepted Answer

1. (i)

-\frac{2}{3},-\frac{1}{2},-\frac{2}{5},-\frac{1}{3},-\frac{2}{7}

(ii)

-\frac{3}{2},-\frac{5}{3},-\frac{8}{5},-\frac{10}{7},-\frac{9}{5}

(iii)

-\frac{35}{45},-\frac{34}{45},-\frac{33}{45},-\frac{32}{45},-\frac{31}{45}

(iv)

-\frac{1}{3},-\frac{1}{4},0,\frac{1}{3},\frac{1}{2}

.
2. (i)

-\frac{15}{25},-\frac{18}{30},-\frac{21}{35},-\frac{24}{40}

(ii)

-\frac{4}{16},-\frac{5}{20},-\frac{6}{24},-\frac{7}{28}

(iii)

-\frac{5}{30},-\frac{6}{36},-\frac{7}{42},-\frac{8}{48}

(iv)

-\frac{8}{12},-\frac{10}{15},-\frac{12}{18},-\frac{14}{21}

.
3. (i)

-\frac{4}{14},-\frac{6}{21},-\frac{8}{28},-\frac{10}{35}

(ii)

-\frac{10}{6},-\frac{15}{9},-\frac{20}{12},-\frac{25}{15}

(iii)

\frac{8}{18},\frac{12}{27},\frac{16}{36},\frac{28}{63}

.
5.

P=\frac{7}{3}

,

Q=\frac{8}{3}

,

R=-\frac{4}{3}

,

S=-\frac{5}{3}

.
6. (ii), (iii), (iv), (v).
7. (i)

-\frac{4}{3}

(ii)

\frac{5}{9}

(iii)

-\frac{11}{18}

(iv)

-\frac{4}{5}

.
8. (i)

$<$

(ii)

$<$

(iii)

$=$

(iv)

$>$

(v)

$<$

(vi)

$=$

(vii)

$>$

.
9. (i)

\frac{5}{2}

(ii)

-\frac{5}{6}

(iii)

-\frac{2}{3}

(iv)

\frac{1}{4}

(v)

-\frac{2}{37}

.
10. (i)

-\frac{3}{5},-\frac{2}{5},-\frac{1}{5}

(ii)

-\frac{4}{3},-\frac{1}{3},-\frac{2}{9}

(iii)

-\frac{3}{2},-\frac{3}{4},-\frac{3}{7}

.

Question 2

Exercise 8.2 asks students to add, subtract, multiply and divide rational numbers in the listed subparts.

Accepted Answer

1. (i)

-\frac{3}{2}

(ii)

\frac{34}{15}

(iii)

\frac{17}{30}

(iv)

\frac{82}{99}

(v)

-\frac{26}{57}

(vi)

-\frac{2}{3}

(vii)

\frac{34}{15}

.
2. (i)

-\frac{13}{72}

(ii)

\frac{23}{63}

(iii)

\frac{1}{195}

(iv)

-\frac{89}{88}

(v)

-\frac{73}{9}

.
3. (i)

-\frac{63}{8}

(ii)

-\frac{27}{10}

(iii)

-\frac{54}{55}

(iv)

-\frac{6}{35}

(v)

\frac{6}{55}

(vi) 1.
4. (i)

$-6$

(ii)

-\frac{3}{10}

(iii)

\frac{4}{15}

(iv)

-\frac{1}{6}

(v)

-\frac{14}{13}

(vi)

\frac{91}{24}

(vii)

-\frac{15}{4}

.