Question 12 Marks
Find the following products: $\frac{5}{-18}\times\frac{-9}{20}$
Answer$\frac{5}{-18}\times\frac{-9}{20}$ $=\frac{5\times(-9)}{-18\times20}$ $=\frac{-45}{-360}$ $=\frac{-45\div45}{-360\div45}$ $=\frac{-1}{-8}=\frac{1}{8}$
View full question & answer→Question 22 Marks
Verify the following: $3+\frac{-7}{12}=\frac{-7}{12}+3$
Answer$\text{L.H.S. }=3+\frac{-7}{12}$
$=\frac{36-7}{12}$
$=\frac{29}{12}$
$\text{R.H.S. }=\frac{-7}{12}+3$
$=\frac{-7+36}{12}$
$=\frac{29}{12}$
$\text{L.H.S. }=\text{R.H.S. }$
$\therefore3+\frac{-7}{12}=\frac{-7}{12}+3$
View full question & answer→Question 32 Marks
What number should be added to $\frac{-5}{8}$ so as to get $\frac{-3}{2}$?
AnswerSum of two numbers $=\frac{-3}{2}$ One number $=\frac{-5}{8}$ $\therefore$ Second number $=\frac{-3}{2}-\Big(\frac{-5}{8}\Big)$ $=\frac{-3}{2}+\frac{5}{8}$ $=\frac{-12+5}{8}$ $=\frac{-7}{8}$ $\therefore$ Second number $=\frac{-7}{8}$
View full question & answer→Question 42 Marks
What number should be subtracted from $\frac{-2}{3}$ to get $\frac{-1}{6}$?
AnswerDifference of two numbers $=\frac{-1}{6}$ One number $=\frac{-2}{3}$ $\therefore$ Second number $=\frac{2}{3}-\Big(\frac{-1}{6}\Big)$ $=\frac{-2}{3}+\frac{1}{6}$ $=\frac{-4+1}{6}$ $=\frac{-3}{6}$ $=\frac{-3\div3}{6\div3}$ $=\frac{-1}{2}$ $\therefore$ Second number $=\frac{-1}{2}$
View full question & answer→Question 52 Marks
Verify the following: $\frac{2}{-7}+\frac{12}{-35}=\frac{12}{-35}+\frac{2}{-7}$
Answer$\text{L.H.S. }=\frac{2}{-7}+\frac{12}{-35}=\frac{-2}{7}+\frac{-12}{35}$
$=\frac{-10-12}{35}$
$=\frac{-22}{35}$
$\text{R.H.S. }=\frac{12}{-35}+\frac{2}{-7}=\frac{-12}{35}+\frac{-2}{7}$
$=\frac{-12-10}{35}$
$=\frac{-22}{35}$
$\text{L.H.S. }=\text{R.H.S. }$
$\therefore\frac{2}{-7}+\frac{12}{-35}=\frac{12}{-35}+\frac{2}{-7}$
View full question & answer→Question 62 Marks
Subtract: $\frac{-32}{13}\ \text{from}\ \frac{-6}{5}$
Answer$\frac{-32}{13}\ \text{from}\ \frac{-6}{5}$ or $\frac{-6}{5}-\frac{-32}{13}$ $=\frac{-78-(-160)}{65}$ $=\frac{-78+160}{65}$ $=\frac{82}{65}$
View full question & answer→Question 72 Marks
Find the following products:
$\frac{3}{5}\times\frac{-7}{8}$
Answer $\frac{3}{5}\times\frac{-7}{8}$
$=\frac{3\times(-7)}{5\times8}$
$=\frac{-21}{40}$
View full question & answer→Question 82 Marks
Simplify: $\frac{-65}{14}\div\frac{13}{7}$
Answer$\frac{-65}{14}\div\frac{13}{7}$
$\frac{-65}{14}\times\frac{7}{13}$
$=\frac{-455}{182}$
$=\frac{-455\div91}{182\div91}$
$=\frac{-5}{2}$
View full question & answer→Question 92 Marks
Express the following rational numbers in standard form.
$\frac{-14}{49}$
Answer$\frac{-14}{49}$
$H.C.F$ of $14$ and $49 = 7$
Dividing the numerator and denominator by $7,$ then
$\frac{-14}{49}=\frac{-14\div7}{49\div7}$
$=\frac{-2}{7}$
View full question & answer→Question 102 Marks
Find the additive inverse of the following:
$\frac{19}{-6}$
Answer We know that additive inverse of $\frac{\text{a}}{\text{b}}$ is $\frac{\text{-a}}{\text{b}}$ and of $\frac{\text{-a}}{\text{b}}$ is $\frac{\text{a}}{\text{b}}$.
Therefore Additive inverse of $\frac{19}{-6}$ or $\frac{-19}{6}$ will be $\frac{19}{6}$
View full question & answer→Question 112 Marks
Subtract: $\frac{-5}{6}\ \text{from}\ \frac{1}{3}$
Answer$\frac{-5}{6}\ \text{from}\ \frac{1}{3}$ or $\frac{1}{3}-\frac{-5}{6}$ $=\frac{2-(-5)}{6}$ $=\frac{2+5}{6}$ $=\frac{7}{6}$
View full question & answer→Question 122 Marks
The cost of $3\frac{1}{2}$ metres of cloth is $\text{Rs}.\ 166\frac{1}{4}$. What is the cost of one metre of cloth?
AnswerCost of $3\frac{1}{2}\text{m}$ cloth $=\text{Rs}.\ 166\frac{1}{4}$ $\therefore$ Cost of 1 metre $=\text{Rs}.\ 166\frac{1}{4}\div3\frac{1}{2}$ $=\text{Rs}.\ \frac{665}{4}\div\frac{7}{2}$ $=\text{Rs}.\ \frac{665}{4}\times\frac{2}{7}$ $=\frac{95\times1}{2}$ $=\text{Rs.}\ 47\frac{1}{2}$
View full question & answer→Question 132 Marks
Find the additive inverse of:$\frac{7}{-10}$
AnswerAdditive inverse of a number $\frac{\text{a}}{\text{b}}$ is the number $-\frac{\text{a}}{\text{b}}$ Such that, $\frac{\text{a}}{\text{b}}+\Big(\frac{-\text{a}}{\text{b}}\Big)=0$ Therefore,$\frac{7}{-10}=\frac{7\times-1}{-10\times-1}$
$=\frac{7}{-10}$
Additive inverse of $\frac{-7}{10}$ is $\frac{7}{10}$
View full question & answer→Question 142 Marks
The sum of two rational numbers is $−2.$ If one of the numbers is $\frac{-14}{5}$, find the other.
AnswerSum of two numbers $= -2$ One number $=\frac{-14}{5}$
$\therefore$ Second number $=-2-\Big(\frac{-14}{5}\Big)$
$=\frac{-2}{1}+\frac{14}{5}$
$=\frac{-10+14}{5}$
$=\frac{4}{5}$
$\therefore$ Second number $=\frac{4}{5}$
View full question & answer→Question 152 Marks
Subtract: $\frac{-13}{9}\ \text{from}\ 0$
Answer$\frac{-13}{9}\ \text{from}\ 0$ or $0-\Big(\frac{-13}{9}\Big)$ $=\frac{-0-(-13)}{9}$ $=\frac{-0+13}{9}$ $=\frac{13}{9}$
View full question & answer→Question 162 Marks
Simplify: $\frac{-12}{7}\div(-18)$
Answer$\frac{-12}{7}\div(-18)$
$\frac{-12}{7}\times\frac{1}{-18}$
$=\frac{-12\times1}{7\times(-18)}$
$=\frac{-12}{-126}=\frac{12}{126}$
$=\frac{12\div6}{126\div6}$
$=\frac{2}{21}$
View full question & answer→Question 172 Marks
Which of the two rational numbers is greater in the given pair? $\frac{-2}{9}\ \text{or}\ 0$
Answer$\frac{-2}{9}\ \text{or}\ 0$ We know that every negative rational number is less than $0.$
$\therefore 0$ is greater.
View full question & answer→Question 182 Marks
Verify whether the given statement is true or false: $\frac{13}{5}\div\frac{26}{10}=\frac{26}{10}\div\frac{13}{5}$
AnswerFalse.
Solution:
$\text{L.H.S.}=\frac{13}{5}\div\frac{26}{10}$
$=\frac{13}{5}\times\frac{10}{26}$
$=\frac{13\times10}{5\times26}$
$=\frac{130}{130}$
$=1$
$\text{R.H.S.}=\frac{26}{10}\div\frac{13}{5}$
$=\frac{26}{10}\times\frac{5}{13}$
$=\frac{26\times5}{10\times13}$
$=\frac{130}{130}$
$=1$
It is true but law is not true.
Hence, False.
View full question & answer→Question 192 Marks
Represent the following numbers on the number line. $2\frac{2}{5}$
Answer$2\frac{2}{5}$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off units $OA, AB, BC, CD$ to the right side of $O.$
Now, divide $BC$ into $5$ equal parts and take 2 equal parts.
Then $\text{BP}=\frac{2}{5}$
$\therefore\text{OP}=\text{OB}+\text{BP}$
$=2+\frac{2}{5}=2\frac{2}{5}$ as shown on the number line given below-
View full question & answer→Question 202 Marks
Simplify: $-8\div\frac{-7}{16}$
Answer$-8\div\frac{-7}{16}$
$-8\times\frac{16}{-7}$
$=\frac{-8\times16}{-7}$
$=\frac{-128}{-7}$
$=\frac{128}{7}$
View full question & answer→Question 212 Marks
Find the area of a square plot of land whose each side measures $8\frac{1}{2}$metres.
AnswerSide of the square plot $=8\frac{1}{2}\text{m}$
$=\frac{17}{2}\text{m}$
$\mathrm{Area = (Side)^2= Side × Side}$
$=\frac{17}{2}\times\frac{17}{2}\text{m}^2$
$=\frac{289}{4}\text{m}^2$
$=72\frac{1}{4}\text{m}^2$
View full question & answer→Question 222 Marks
Represent the following numbers on the number line. $\frac{1}{3}$
Answer$\frac{1}{3}$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off unit $OA, AB$ to right side of $O,$ representing integers $1, 2 $ respectively.
Now, divide $OA$ into $3$ equal parts and take one part $OR$ Which is $\frac{1}{3}$ as shown below on the line,
View full question & answer→Question 232 Marks
Express $\frac{-3}{5}$ as a rational number with denominator. $-40$
Answer$-40 = 5 \times (-8)$
$\therefore\frac{-3}{5}=\frac{-3\times(-8)}{5\times(-8)}$
$[$Multiplying the numerator and denominator by $(-8)]$
$=\frac{24}{-40}$
View full question & answer→Question 242 Marks
The product of two numbers is $-8.$ If one of them is $-12,$ find the other.
AnswerLet the other number be $x$
Thus, we have:
$-12\times\text{x}=-8$
$\Rightarrow\text{x}=(-8)\div(-12)$
$\Rightarrow\text{x}=(-8)\times\frac{1}{-12}$
$\Rightarrow\text{x}=\frac{8}{12}$
$\Rightarrow\text{x}=\frac{2}{3}$
View full question & answer→Question 252 Marks
Represent the following numbers on the number line. $5\frac{5}{7}$
Answer$5\frac{5}{7}$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off units $OA, AB, BC, CD, DE, EF$ to the right side of $O.$
Now, divide $CD$ into $7$ equal parts and take $EP = 5$ equal parts.
Then,
$\therefore\text{OP}=\text{OE}+\text{EP}$
$=5+\frac{5}{7}=5\frac{5}{7}$ as shown on the number line given below,
View full question & answer→Question 262 Marks
What number should be added to $\frac{-3}{5}$ to get $\frac{2}{3}$?
AnswerLet the required number be $x$
Thus, we have: $\text{x}+\frac{(-3)}{5}=\frac{2}{3}$
$\Rightarrow\text{x}-\frac{3}{5}=\frac{2}{3}$
$\Rightarrow\text{x}=\frac{2}{3}+\frac{3}{5}$
$\Rightarrow\text{x}=\frac{2\times5+3\times3}{15}$
$\Rightarrow\text{x}=\frac{10+9}{15}$
$\Rightarrow\text{x}=\frac{19}{15}$
View full question & answer→Question 272 Marks
Find the additive inverse of the following:$\frac{-17}{8}$
AnswerWe know that additive inverse of $\frac{\text{a}}{\text{b}}$ is $\frac{\text{-a}}{\text{b}}$ and of $\frac{\text{-a}}{\text{b}}$ is $\frac{\text{a}}{\text{b}}$. Therefore Additive inverse of $\frac{-17}{8}$ will be $\frac{17}{8}$
View full question & answer→Question 282 Marks
What number should be subtracted to $\frac{-3}{4}$ to get $\frac{-1}{2}$?
AnswerLet the number subtracted be $x$
Thus, we have: $\frac{-3}{4}-\text{x}=\frac{-1}{2}$
$\Rightarrow\frac{-3}{4}+\frac{1}{2}=\text{x}$
$\Rightarrow\text{x}=\frac{2-3}{4}$
$\Rightarrow\text{x}=\frac{-1}{4}$
View full question & answer→Question 292 Marks
Represent the following numbers on the number line. $\frac{2}{7}$
Answer$\frac{2}{7}$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off units $OA, AB$ to the right side of $O.$
Now, divide $OA$ into $7$ equal parts and take two parts.
Let $OP = 2$ parts.
Then,
$\text{OP}=\frac{2}{7}$ as shown on the number line gien below,
View full question & answer→Question 302 Marks
Verify the following: $\frac{-8}{7}\times\frac{13}{9}=\frac{13}{9}\times\frac{-8}{7}$
Answer$\text{L.H.S.}=\frac{-8}{7}\times\frac{13}{9}$
$=\frac{-8\times13}{7\times9}$
$=\frac{-104}{63}$
$\text{R.H.S.}=\frac{13}{9}\times\frac{-8}{7}$
$=\frac{13\times(-8)}{9\times7}$
$=\frac{-104}{63}$
$\text{L.H.S.}=\text{R.H.S.}$
$\therefore\frac{-8}{7}\times\frac{13}{9}=\frac{13}{9}\times\frac{-8}{7}$
View full question & answer→Question 312 Marks
Find the following products: $\frac{-6}{11}\times\frac{-5}{3}$
Answer$\frac{-6}{11}\times\frac{-5}{3}$ $=\frac{-6\times(-5)}{11\times3}$ $=\frac{30}{33}$ $=\frac{30\div3}{33\div3}$ $=\frac{10}{11}$
View full question & answer→Question 322 Marks
Which of the two rational numbers is greater in the given pair? $\frac{-3}{4}\text{ or }\frac{1}{4}$
Answer$\frac{-3}4\text{ or }\frac{1}{4}$ We know that every negative rational number is less than every positive rational number.
$\therefore\frac{1}{4}$ is greater.
View full question & answer→Question 332 Marks
Subtract: $\frac{3}{4}\ \text{from}\ \frac{1}{3}$
Answer$\frac{3}{4}\ \text{from}\ \frac{1}{3}$ or $\frac{1}{3}-\frac{3}{4}$ $=\frac{4-9}{12}$ $=\frac{-5}{12}$
View full question & answer→Question 342 Marks
Find the additive inverse of the following: $\frac{-8}{-7}$
AnswerWe know that additive inverse of $\frac{\text{a}}{\text{b}}$ is $\frac{\text{-a}}{\text{b}}$ and of $\frac{\text{-a}}{\text{b}}$ is $\frac{\text{a}}{\text{b}}$. Therefore Additive inverse of $\frac{-8}{-7}$ or $\frac{8}{7}$ will be $\frac{-8}{7}$
View full question & answer→Question 352 Marks
Find the following products:
$\frac{-2}{3}\times\frac{6}{7}$
Answer $\frac{-2}{3}\times\frac{6}{7}$
$=\frac{-2\times6}{3\times7}$
$=\frac{-12}{21}$
$=\frac{-12\div3}{5\div3}$
$=\frac{-4}{7}$
View full question & answer→Question 362 Marks
Verify whether the given statement is true or false: $-9\div\frac{3}{4}=\frac{3}{4}\div(-9)$
AnswerFalse.
Solution:
$\text{L.H.S.}=-9\div\frac{3}{4}$
$=-9\times\frac{4}{3}$
$=\frac{-36}{3}$
$=-12$
$\text{R.H.S.}=\frac{3}{4}\div(-9)$
$=\frac{3}{4}\times\frac{1}{-9}$
$=\frac{3}{-36}$
$=\frac{1}{-12}$
$=\frac{-1}{12}$
$\text{L.H.S}\neq\text{R.H.S}$
$\therefore$ It is false.
View full question & answer→Question 372 Marks
Find the additive inverse of:$\frac{8}{5}$
AnswerAdditive inverse of a number $\frac{\text{a}}{\text{b}}$ is the number $-\frac{\text{a}}{\text{b}}$ Such that, $\frac{\text{a}}{\text{b}}+\Big(\frac{-\text{a}}{\text{b}}\Big)=0$ Therefore, Additive inverse of $\frac{8}{5}$ is $\frac{-8}{5}$
View full question & answer→Question 382 Marks
Evaluate: $\frac{-3}{5}\times\frac{10}{7}$
Answer$\frac{-3}{5}\times\frac{10}{7}$ $=\frac{-3\times10}{5\times7}$ $=\frac{-30}{35}$ $=\frac{-30\div5}{35\div5}$ $=\frac{-6}{7}$
View full question & answer→Question 392 Marks
Find the following products: $\frac{16}{-21}\times\frac{14}{5}$
Answer$\frac{16}{-21}\times\frac{14}{5}$ $=\frac{16\times14}{-21\times5}$ $=\frac{224}{-105}$ $=\frac{224\div7}{-105\div7}$ $=\frac{32}{-15}=\frac{-32}{15}$
View full question & answer→Question 402 Marks
Verify the following:
$\frac{-12}{5}\times\frac{7}{-36}=\frac{7}{-36}\times\frac{-12}{5}$
Answer $\text{L.H.S}.=\frac{-12}{5}\times\frac{7}{-36}$
$=\frac{-12\times7}{5\times(-36)}$
$=\frac{-84}{-180}=\frac{84}{180}$
$=\frac{84\div12}{180\div12}$
$=\frac{7}{15}$
$\text{R.H.S.}=\frac{7}{-36}\times\frac{-12}{5}$
$=\frac{7\times(-12)}{-36\times5}$
$=\frac{-84}{-180}=\frac{84}{180}$
$=\frac{84\div12}{180\div12}$
$=\frac{7}{15}$
$\text{L.H.S.}=\text{R.H.S.}$
$\therefore\frac{-12}{5}\times\frac{7}{-36}=\frac{7}{-36}\times\frac{-12}{5}$
View full question & answer→Question 412 Marks
Verify the following: $-8\times\frac{-13}{12}=\frac{-13}{12}\times(-8)$
Answer$\text{L.H.S.}=-8\times\frac{-13}{12}$
$=\frac{-8\times(-13)}{12}$
$=\frac{104}{12}$
$=\frac{104\div4}{12\div4}$
$=\frac{26}{3}$
$\text{R.H.S.}=\frac{-13}{12}\times(-8)$
$=\frac{-13\times(-8)}{12}$
$=\frac{104}{12}$
$=\frac{104\div4}{12\div4}$
$=\frac{26}{3}$
$\text{L.H.S.}=\text{R.H.S.}$
$\therefore-8\times\frac{-13}{12}=\frac{-13}{12}\times(-8)$
View full question & answer→Question 422 Marks
Find the following products: $\frac{-9}{2}\times\frac{5}{4}$
Answer$\frac{-9}{2}\times\frac{5}{4}$ $=\frac{-9\times5}{2\times4}$ $=\frac{-45}{8}$
View full question & answer→Question 432 Marks
Find the multiplicative inverse of: $\frac{-3}{4}$
AnswerMultiplicative inverse of a rational number $\frac{\text{a}}{\text{b}}=\frac{\text{b}}{\text{a}}$ Therefore, Negative inverse of $\frac{-3}{4}=\frac{4}{-3}$ $\frac{4}{-3}=\frac{4\times-1}{-3\times-1}$ $=\frac{-4}{3}$
View full question & answer→Question 442 Marks
Find the additive inverse of the following:$\frac{-16}{-5}$
AnswerWe know that additive inverse of $\frac{\text{a}}{\text{b}}$ is $\frac{\text{-a}}{\text{b}}$ and of $\frac{\text{-a}}{\text{b}}$ is $\frac{\text{a}}{\text{b}}$. Therefore Additive inverse of $\frac{-16}{-5}$ or $\frac{16}{5}$ will be $\frac{-16}{5}$
View full question & answer→Question 452 Marks
Represent the following numbers on the number line. $3\frac{1}{2}$
Answer$3\frac{1}{2}$
Draw a line and take a point $O$ on it.
Let it represent $0$.
From $O,$ set off units $OA, AB, BC, CD$ to the right side of $O.$
Now, divide $CD$ into $2$ equal parts and take $1$ parts.
Then,
$\text{CP}=\frac{1}{2}$
$\therefore\text{OP}=\text{OC}+\text{CP}$
$=3+\frac{1}{2}=3\frac{1}{2}$ as shown on the number line given below,
View full question & answer→Question 462 Marks
Verify the following: $\frac{-5}{8}+\frac{-9}{13}=\frac{-9}{13}+\frac{-5}{8}$
Answer$\text{L.H.S. }=\frac{-5}{8}+\frac{-9}{13}$
$=\frac{-65-72}{104}$
$=\frac{-137}{104}$
$\text{R.H.S. }=\frac{-9}{13}+\frac{-5}{8}$
$=\frac{-72-65}{104}$
$=\frac{-137}{104}$
$\text{L.H.S. }=\text{R.H.S. }$
$\therefore\frac{-5}{8}+\frac{-9}{13}=\frac{-9}{13}+\frac{-5}{8}$
View full question & answer→Question 472 Marks
The sum of two rational numbers is $\frac{-1}{2}$. If one of the numbers is $\frac{5}{6}$, find the other.
Answer Sum of two numbers $=\frac{-1}{2}$
One number $=\frac{5}{6}$
$\therefore$ Second number $=\frac{-1}{2}-\Big(\frac{5}{6}\Big)$
$=\frac{-1}{2}-\frac{5}{6}$
$=\frac{-3-5}{6}$
$=\frac{-8}{6}$
$=\frac{-8\div2}{6\div2}$
$=\frac{-4}{3}$
$\therefore$ Second number $=\frac{-4}{3}$
View full question & answer→Question 482 Marks
Express $\frac{-3}{5}$ as a rational number with denominator. $35$
Answer$35 = 5 \times 7$
$\therefore\frac{-3}{5}=\frac{-3\times7}{5\times7} ($Multiplying the numerator and denominator by $7)$
$=\frac{-21}{35}$
View full question & answer→Question 492 Marks
Which of the two rational numbers is greater in the given pair? $\frac{-5}{7}\ \text{or}\ \frac{-4}{7}$
Answer$\frac{-5}{7}\ \text{or}\ \frac{-4}{7}$ Here, denominator is same i.e.,it is $7$ and $(-4) > (-5)$
$\therefore\frac{-4}{7}$ is greater.
View full question & answer→Question 502 Marks
Express $\frac{-42}{98}$ as a rational number with denominator $7.$
Answer$98 = 7 \times 14$
$\therefore\frac{-42}{98}=\frac{-42\div14}{98\div14} ($Dividing the numerator and denominator by $14)$
$=\frac{-3}{7}$
View full question & answer→