Question 12 Marks
Insert one rational number between $(i) 7$ and $8 (ii) 3.5$ and $5 \frac{1}{2}$ and $ 2$
Answer
View full question & answer→The rational number between $\frac{1}{2}$ and $2 .=\frac{1+2}{2 \times 2}=\frac{3}{4}=1.25$
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Question 22 Marks
Insert one rational number between $(i)\ 0.7$ and $8 \ (ii) \ 3.5$ and $5\ (iii) \ 4.2$ and $3.6$
Answer
View full question & answer→The rational number between $4.2$ and $3.6 = \frac{4.2+3.6}{2}=\frac{7.8}{2}=3.9$
Question 32 Marks
Insert one rational number between $(i)\ 0 .7$ and $8 \ (ii) \ 3.5$ and $5.\ (iii)\ 2$ and $3.2$
Answer
View full question & answer→The rational number between $ 2$ and $3.2 =\frac{2+3.2}{2}=\frac{5.2}{2}=2.6$
Question 42 Marks
Insert one rational number between $(i)\ 0.7$ and $8\ (ii) \ 3.5 $and $5\ (iii)\ 3.5$ and $5$
Answer
View full question & answer→The rational number between $3.5 $ and $5 = \frac{3.5+5}{2}=\frac{8.5}{2}=4.25$
Question 52 Marks
Insert one rational number between $ (i)\ 0.7$ and$ \ 8 \ (ii) \ 3.5 \ $and$\ 5\ (iii)\ 2$ and $3.2$
Answer
View full question & answer→The rational number between $7$ and $8=\frac{7+8}{2}=\frac{15}{2}=7.5$
Question 62 Marks
Draw a number line and mark $\frac{2}{3}, \frac{-8}{3}, \frac{7}{3}, \frac{-2}{3} \text { and }-2$
Answer
View full question & answer→Draw a number line as shown below:
Question 72 Marks
Draw a number line and mark $\frac{3}{4}, \frac{7}{4}, \frac{-3}{4}$ and $\frac{-7}{4}$ on it.
Answer
View full question & answer→Draw a number line as shown below:
Question 82 Marks
If $3 \frac{1}{2}$ litres of milk costs $₹ 49 , $ find the cost of one litre of milk?
Answer
View full question & answer→Given, cost of $3 \frac{1}{2}$ or $\frac{7}{2}$ litres $= \text {₹} 49$
$\therefore$ Value of one litre milk $=\text {₹} 49 \div \frac{7}{2}$
$=\text {₹} 49 \times \frac{2}{7}$
$ =\text {₹} 7 \times 2=\text {₹} 14$
$\therefore$ Value of one litre milk $=\text {₹} 49 \div \frac{7}{2}$
$=\text {₹} 49 \times \frac{2}{7}$
$ =\text {₹} 7 \times 2=\text {₹} 14$
Question 92 Marks
By what number should $\frac{-8}{13}$ be multiplied to get $16$ ?
Answer
View full question & answer→$ \therefore \text { Required number }$
$ =16 \div\left(\frac{-8}{13}\right)$
$ =16 \times\left(\frac{13}{-8}\right)$
$ =(-2) \times 13=-26$
$ =16 \div\left(\frac{-8}{13}\right)$
$ =16 \times\left(\frac{13}{-8}\right)$
$ =(-2) \times 13=-26$
Question 102 Marks
Divide : $-\frac{3}{4} \text { by }-\frac{9}{16}$
Answer
View full question & answer→$ =-\frac{3}{4} \div-\frac{9}{16}$
$ =-\frac{3}{4} \times-\frac{16}{9}=\frac{(-1) \times 4}{1 \times(-3)}$
$ =\frac{-4}{-3}=\frac{4}{3}=1 \frac{1}{3}$
$ =-\frac{3}{4} \times-\frac{16}{9}=\frac{(-1) \times 4}{1 \times(-3)}$
$ =\frac{-4}{-3}=\frac{4}{3}=1 \frac{1}{3}$
Question 112 Marks
Divide : $\frac{-5}{8} \text { by } \frac{1}{4}$
Answer
View full question & answer→$ =\frac{-5}{8} \div \frac{1}{4}$
$ =\frac{-5}{8} \times \frac{4}{1}$
$ =\frac{-5 \times 1}{2 \times 1}=\frac{-5}{2}$
$ =\frac{-5}{8} \times \frac{4}{1}$
$ =\frac{-5 \times 1}{2 \times 1}=\frac{-5}{2}$
Question 122 Marks
Divide : $0 \text { by } \frac{7}{-9}$
Answer
View full question & answer→$ =0 \div \frac{7}{-9}$
$ =0 \times \frac{-9}{7}=0$
$ =0 \times \frac{-9}{7}=0$
Question 132 Marks
Divide : $-2 \text { by }\left(-\frac{1}{2}\right)$
Answer
View full question & answer→$ =-2 \div\left(-\frac{1}{2}\right)$
$ =-2 \times \frac{2}{-1}=4$
$ =-2 \times \frac{2}{-1}=4$
Question 142 Marks
Evaluate : $\frac{-7}{11} \div\left(\frac{-3}{44}\right)$
Answer
View full question & answer→$ =\frac{-7}{11} \times\left(\frac{44}{-3}\right)$
$ =\frac{(-7) \times 4}{1 \times(-3)}$
$=\frac{28}{3}$
$=9 \frac{1}{3}$
$ =\frac{(-7) \times 4}{1 \times(-3)}$
$=\frac{28}{3}$
$=9 \frac{1}{3}$
Question 152 Marks
Evaluate : $-5 \div\left(-\frac{10}{11}\right)$
Answer
View full question & answer→$ =-5 \div \frac{11}{-10}$
$ =\frac{1 \times 11}{1 \times 2}$
$=\frac{11}{2}$
$=5 \frac{1}{2}$
$ =\frac{1 \times 11}{1 \times 2}$
$=\frac{11}{2}$
$=5 \frac{1}{2}$
Question 162 Marks
Evaluate : $\frac{3}{4} \div\left(-\frac{5}{12}\right)$
Answer
View full question & answer→$ =\frac{3}{4} \times\left(-\frac{12}{5}\right)$
$ =\frac{3 \times 3}{1 \times(-5)}$
$=-\frac{9}{5}$
$ =\frac{3 \times 3}{1 \times(-5)}$
$=-\frac{9}{5}$
Question 172 Marks
Evaluate : $\frac{8}{-5} \div \frac{24}{25}$
Answer
View full question & answer→$ =\frac{8}{-5} \times \frac{24}{25}$
$ =\frac{2 \times 5}{(-1) \times 6}$
$=\frac{1 \times 5}{(-1) \times 30}$
$=\frac{-5}{3}$
$ =\frac{2 \times 5}{(-1) \times 6}$
$=\frac{1 \times 5}{(-1) \times 30}$
$=\frac{-5}{3}$
Question 182 Marks
Evaluate:$-\frac{21}{16} \div\left(\frac{-7}{8}\right)$+
Answer
View full question & answer→$ =-\frac{21}{16} \times \frac{8}{-7}$
$ =\frac{3 \times 1}{2 \times 1}=\frac{3}{2}=1 \frac{1}{2}$
$ =\frac{3 \times 1}{2 \times 1}=\frac{3}{2}=1 \frac{1}{2}$
Question 192 Marks
Evaluate : $-\frac{5}{12} \div \frac{1}{16}$
Answer
View full question & answer→$ =-\frac{5}{12} \times \frac{16}{1}$
$ =\frac{-5 \times 4}{3 \times 1}$
$=\frac{-20}{3}$
$=5 \frac{5}{3}$
$ =\frac{-5 \times 4}{3 \times 1}$
$=\frac{-20}{3}$
$=5 \frac{5}{3}$
Question 202 Marks
Find the reciprocal $($multiplicative inverse$) \ $of : $\frac{-3}{5} \times \frac{-1}{13}$
Answer
View full question & answer→$ \frac{-3}{5} \times \frac{-1}{13}$
$=\frac{(-3) \times(-1)}{5 \times 13}$
$ =\frac{3}{65}$
$=\frac{65}{3}$
$=21 \frac{2}{3}$
$=\frac{(-3) \times(-1)}{5 \times 13}$
$ =\frac{3}{65}$
$=\frac{65}{3}$
$=21 \frac{2}{3}$
Question 212 Marks
Find the reciprocal $($multiplicative inverse$)$ of: $\frac{-8}{3} \times \frac{13}{-7}$
Answer
View full question & answer→$ \frac{-8}{3} \times \frac{13}{-7}$
$=\frac{(-8) \times 13}{3 \times(-7)}$
$ =\frac{-104}{-21}$
$=\frac{21}{104}$
$=\frac{(-8) \times 13}{3 \times(-7)}$
$ =\frac{-104}{-21}$
$=\frac{21}{104}$
Question 222 Marks
Find the reciprocal $($multiplicative inverse$) $ of : $\frac{3}{5} \times \frac{2}{3}$
Answer
View full question & answer→$ \frac{3}{5} \times \frac{2}{3}$
$=\frac{3 \times 2}{5 \times 3}$
$ =\frac{1 \times 2}{5 \times 1}$
$=\frac{2}{5}$
$=\frac{5}{2}$
$=\frac{3 \times 2}{5 \times 3}$
$ =\frac{1 \times 2}{5 \times 1}$
$=\frac{2}{5}$
$=\frac{5}{2}$
Question 232 Marks
For the pair of rational numbers, given below, verify that the multiplication is commutative. $3$ and $\frac{-8}{9}$
Answer
View full question & answer→$=\frac{3}{1} \times \frac{-8}{9}=\frac{1 \times(-8)}{1 \times 3}=\frac{-8}{3}
$ And, $\frac{-8}{9} \times \frac{3}{1}=\frac{(-8) \times 1}{3 \times 1}=\frac{-8}{3}$
$\therefore 3 \times \frac{-8}{9}=\frac{-8}{9} \times 3$
$ And, $\frac{-8}{9} \times \frac{3}{1}=\frac{(-8) \times 1}{3 \times 1}=\frac{-8}{3}$
$\therefore 3 \times \frac{-8}{9}=\frac{-8}{9} \times 3$
Question 242 Marks
For the pair of rational numbers, given below, verify that the multiplication is commutative. $\frac{-1}{5} \text { and } \frac{2}{9}$
Answer
View full question & answer→$=\frac{-1}{5} \times \frac{2}{9}=\frac{(-1) \times 2}{5 \times 9}=\frac{-2}{45}
$And, $\frac{2}{9} \times\left(\frac{-1}{5}\right)=\frac{2 \times(-1)}{9 \times 5}=\frac{-2}{45}$
$\therefore \frac{-1}{5} \times \frac{2}{9}=\frac{2}{9} \times \frac{-1}{5}$
$And, $\frac{2}{9} \times\left(\frac{-1}{5}\right)=\frac{2 \times(-1)}{9 \times 5}=\frac{-2}{45}$
$\therefore \frac{-1}{5} \times \frac{2}{9}=\frac{2}{9} \times \frac{-1}{5}$
Question 252 Marks
Evaluate: $\left(\frac{2}{-3} \times \frac{5}{4}\right)+\left(\frac{5}{9} \times \frac{3}{-10}\right)$
Answer
View full question & answer→$ =\left(\frac{2 \times 5}{(-3) \times 4}\right)+\left(\frac{5 \times 3}{9 \times(-10)}\right)$
$ =\left(\frac{1 \times 5}{(-3) \times 2}\right)+\left(\frac{1 \times 1}{3 \times(-2)}\right)$
$ =\frac{-5}{6}+\frac{-1}{6}$
$ =\frac{-5-1}{6}$
$=\frac{-6}{6}$
$=-1$
$ =\left(\frac{1 \times 5}{(-3) \times 2}\right)+\left(\frac{1 \times 1}{3 \times(-2)}\right)$
$ =\frac{-5}{6}+\frac{-1}{6}$
$ =\frac{-5-1}{6}$
$=\frac{-6}{6}$
$=-1$
Question 262 Marks
Evaluate : $\frac{-14}{5} \times \frac{-6}{7}$
Answer
View full question & answer→$ \frac{-14}{5} \times \frac{-6}{7}$
$ =\frac{(-14) \times(-6)}{5 \times 7}=\frac{(-2) \times(-6)}{5 \times 1}$
$ =\frac{12}{5}=2 \frac{2}{5}$
$ =\frac{(-14) \times(-6)}{5 \times 7}=\frac{(-2) \times(-6)}{5 \times 1}$
$ =\frac{12}{5}=2 \frac{2}{5}$
Question 272 Marks
Subtract : $\frac{4}{9} \text { from } \frac{-5}{9}$
Answer
View full question & answer→$ \frac{4}{9} \text { from } \frac{-5}{9}$
$ =\frac{-5}{9}-\frac{4}{9}$
$ =\frac{-5-4}{9}=\frac{-9}{9}=-1$
$ =\frac{-5}{9}-\frac{4}{9}$
$ =\frac{-5-4}{9}=\frac{-9}{9}=-1$
Question 282 Marks
Subtract : $\frac{-8}{11} \text { from } \frac{4}{11} \text { c }$
Answer
View full question & answer→$\frac{-8}{11}$ from $\frac{4}{11}$
$=\frac{4}{11}-\left(\frac{-8}{11}\right)$
$=\frac{4+8}{11}=\frac{12}{11}=1 \frac{1}{11}$
$=\frac{4}{11}-\left(\frac{-8}{11}\right)$
$=\frac{4+8}{11}=\frac{12}{11}=1 \frac{1}{11}$
Question 292 Marks
Subtract : $\frac{5}{8}$ from $\frac{-3}{8}$
Answer
View full question & answer→$ \frac{5}{8} \text { from } \frac{-3}{8}$
$ =\frac{-3}{8}-\frac{5}{8}$
$ =\frac{-3 \times 1}{8}-\frac{5 \times 1}{8 \times 1}$
$ =\frac{-3-5}{8}=\frac{-8}{8}=-1$
$ =\frac{-3}{8}-\frac{5}{8}$
$ =\frac{-3 \times 1}{8}-\frac{5 \times 1}{8 \times 1}$
$ =\frac{-3-5}{8}=\frac{-8}{8}=-1$
Question 302 Marks
Evaluate : $\frac{-2}{7}-\frac{3}{-14}$
Answer
View full question & answer→$\text{(LCM}$ of $7$ and $14=14 )$
$=\frac{-2 \times 2}{7 \times 2}-\frac{-3 \times 1}{14 \times 1}$
$\text{ LCM}$ of $7$ and $14=14$
$=\frac{-4+3}{14}=\frac{-1}{14}$
$=\frac{-2 \times 2}{7 \times 2}-\frac{-3 \times 1}{14 \times 1}$
$\text{ LCM}$ of $7$ and $14=14$
$=\frac{-4+3}{14}=\frac{-1}{14}$
Question 312 Marks
Evaluate : $\frac{-4}{9}-\frac{2}{-3}$
Answer
$=\frac{-4 \times 1}{9 \times 1}-\frac{-2 \times 3}{3 \times 3}$
$(\text{LCM}$ of $3$ and $9=9)$
$\frac{-4+6}{9}=\frac{2}{9}$
View full question & answer→| $3$ | $9, 3$ |
| $5$ | $3, 1$ |
| $1, 1$ |
$(\text{LCM}$ of $3$ and $9=9)$
$\frac{-4+6}{9}=\frac{2}{9}$
Question 322 Marks
Evaluate : $\frac{2}{3}-\frac{4}{5}$
Answer
View full question & answer→$\frac{2}{3}-\frac{4}{5}$
$\text{LCM}$ of $3$ and $5=15$
$=\frac{2 \times 5}{3 \times 5}-\frac{4 \times 3}{5 \times 3}\ (\text{LCM}$ of $3$ and $5=15 )$
$=\frac{10-12}{15}=\frac{-2}{15}$
| $3$ | $3, 5$ |
| $5$ | $1, 5$ |
| $1,1$ |
$=\frac{2 \times 5}{3 \times 5}-\frac{4 \times 3}{5 \times 3}\ (\text{LCM}$ of $3$ and $5=15 )$
$=\frac{10-12}{15}=\frac{-2}{15}$
Question 332 Marks
Evaluate : $\frac{4}{-9}+1$
Answer
View full question & answer→$\frac{-4}{9}+\frac{1}{1}$
$(\text{LCM}$ of $ 9$ and $1=9 )$
$=\frac{-4 \times 1}{9 \times 1}+\frac{1 \times 9}{1 \times 9}$
$ =\frac{-4+9}{9}=\frac{5}{9}$
$(\text{LCM}$ of $ 9$ and $1=9 )$
$=\frac{-4 \times 1}{9 \times 1}+\frac{1 \times 9}{1 \times 9}$
$ =\frac{-4+9}{9}=\frac{5}{9}$
Question 342 Marks
Evaluate : $2+\frac{-3}{5}$
Answer
View full question & answer→$\frac{2}{1}-\frac{3}{5}$
$(\text{ LCM}$ of $1 $ and $5=5 )$
$=\frac{2 \times 5}{1 \times 5}-\frac{3 \times 1}{5 \times 1}$
$ =\frac{10-3}{5}=\frac{7}{5}=1 \frac{2}{5}$
$(\text{ LCM}$ of $1 $ and $5=5 )$
$=\frac{2 \times 5}{1 \times 5}-\frac{3 \times 1}{5 \times 1}$
$ =\frac{10-3}{5}=\frac{7}{5}=1 \frac{2}{5}$
Question 352 Marks
Evaluate : $4+\frac{3}{-5}$
Answer
View full question & answer→$ \frac{4}{1}+\frac{3}{-5}$
$ =\frac{4}{1}-\frac{3}{5}$
$ =\frac{4 \times 5}{1 \times 5}-\frac{3 \times 1}{5 \times 1}(\text { LCM of } 1 \text { and } 5=5)$
$ =\frac{20-3}{5}=\frac{17}{5}=3 \frac{2}{5}$
$ =\frac{4}{1}-\frac{3}{5}$
$ =\frac{4 \times 5}{1 \times 5}-\frac{3 \times 1}{5 \times 1}(\text { LCM of } 1 \text { and } 5=5)$
$ =\frac{20-3}{5}=\frac{17}{5}=3 \frac{2}{5}$
Question 362 Marks
Add, the pair of rational numbers, given below, and show that their addition $($sum$)$ is also a rational number $(-2) \text { and } \frac{2}{5}$
Answer
View full question & answer→$\frac{-2}{1}+\frac{2}{5}(\text { LCM of } 1 \text { and } 5=5)$
$ =\frac{-2 \times 5}{1 \times 5}+\frac{2 \times 1}{5 \times 1}$
$ =\frac{-10+2}{5}=\frac{-8}{5}$
Which is a rational number
$ =\frac{-2 \times 5}{1 \times 5}+\frac{2 \times 1}{5 \times 1}$
$ =\frac{-10+2}{5}=\frac{-8}{5}$
Which is a rational number
Question 372 Marks
Add, the pair of rational numbers, given below, and show that their addition $($sum$) $ is also a rational number
$\frac{6}{11} \text { and } \frac{-9}{11}$
$\frac{6}{11} \text { and } \frac{-9}{11}$
Answer
View full question & answer→$\frac{6}{11}+\left(\frac{-9}{11}\right)$
$($Denominators are same $\therefore \text{LCM} =11 )$
$\frac{6-9}{11}=\frac{-3}{11}$
Which is a rational number
$($Denominators are same $\therefore \text{LCM} =11 )$
$\frac{6-9}{11}=\frac{-3}{11}$
Which is a rational number
Question 382 Marks
Add, the pair of rational numbers, given below, and show that their addition$ ($sum$)$ is also a rational number
$\frac{-8}{13} \text { and } \frac{-4}{13}$
$\frac{-8}{13} \text { and } \frac{-4}{13}$
Answer
View full question & answer→$\frac{-8}{13}+\frac{-4}{13}$
$(\text {LCM}$ of $13$ and $13=13)$
$=\frac{-8-4}{13}=\frac{-12}{13}$
Which is rational number
$(\text {LCM}$ of $13$ and $13=13)$
$=\frac{-8-4}{13}=\frac{-12}{13}$
Which is rational number