Question 512 Marks
Express $\frac{-48}{60}$ as a rational number with denominator $5.$
Answer$60 = 5 \times 12$
$\therefore\frac{-48}{60}=\frac{-48\div12}{60\div12} ($Dividing the numerator and denominator by $12)$
$=\frac{-4}{5}$
View full question & answer→Question 522 Marks
Simplify: $\frac{-16}{35}\div\frac{-15}{14}$
Answer$\frac{-16}{35}\div\frac{-15}{14}$
$\frac{-16}{35}\times\frac{14}{-15}$
$=\frac{-16\times14}{35\times(-15)}$
$=\frac{-224}{-525}=\frac{224}{525}$
$=\frac{224\div7}{525\div7}$
$=\frac{32}{75}$
View full question & answer→Question 532 Marks
Find a rational number between $2$ and $3.$
AnswerRational number between $2$ and $3$
$=\frac{1}{2}(2+3)$
$=\frac{1}{2}\times5$
$=\frac{5}{2}$
View full question & answer→Question 542 Marks
One litre of petrol costs $\text{Rs.}\ 63\frac{3}{4}$. What is the cost of $34$ litres of petrol$?$
AnswerCost of $1$ litre of petrol $=\text{Rs.}\ 63\frac{3}{4}$
$=\text{Rs.}\ \frac{255}{4}$
Cost of $34$ litres of petrol $=\frac{255}{4}\times34$
$=\frac{255\times17}{2}$
$= \frac{4335}{2}$
$=\text{Rs.}\ 2167\frac{1}{2}$
View full question & answer→Question 552 Marks
Express the following rational numbers in standard form. $\frac{-36}{-63}$
Answer$\frac{-36}{-63}$
$H.C.F$ of $36$ and $63 = 9$
Dividing the numerator and denominator by $-9,$
then $\frac{-36}{-63}=\frac{36\div(-9)}{-63\div(-9)}$
$=\frac{4}{7}$
View full question & answer→Question 562 Marks
Find the additive inverse of the following:$\frac{15}{-4}$
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 $\frac{15}{-4}$ or $\frac{-15}{4}$ will be $\frac{15}{4}$
View full question & answer→Question 572 Marks
Find a rational number between $\frac{-1}{3}$ and $\frac{1}{2}$.
AnswerRational number between $\frac{-1}{3}$ and $\frac{1}{2}$ $=\frac{1}{2}\Big[\frac{-1}{3}+\frac{1}{2}\Big]$ $=\frac{1}{2}\Big[\frac{-2+3}{6}\Big]$ $=\frac{1}{2}\times\frac{1}{6}$ $=\frac{1}{12}$
View full question & answer→Question 582 Marks
Find the following products: $\frac{7}{24}\times(-48)$
Answer$\frac{7}{24}\times(-48)$ $=\frac{7\times(-48)}{24}$ $=7\times(-2)$ $=-14$
View full question & answer→Question 592 Marks
Find the additive inverse of the following: $0$
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 $0$ will be $0.$
$\Big(\therefore$ zero has no additive inverse$\Big)$
View full question & answer→Question 602 Marks
Subtract: $\frac{-18}{11}\ \text{from}\ 1$
Answer$\frac{-18}{11}\ \text{from}\ 1$ or $\frac{1}{1}-\frac{-18}{11}$ $=\frac{11-(-18)}{11}$ $=\frac{11+18}{11}$ $=\frac{29}{11}$
View full question & answer→Question 612 Marks
Subtract: $\frac{-8}{9}\ \text{from}\ \frac{-3}{5}$
Answer$\frac{-8}{9}\ \text{from}\ \frac{-3}{5}$ or $\frac{-3}{5}-\frac{-8}{9}$ $=\frac{-27-(-40)}{45}$ $=\frac{-27+40}{45}$ $=\frac{13}{45}$
View full question & answer→Question 622 Marks
Express the following rational numbers in standard form. $\frac{24}{-64}$
Answer$\frac{24}{-64}$
$H.C.F$ of $24$ and$ 64 = 8$ Dividing the numerator and denominator by $8,$
then $\frac{24}{-64}=\frac{24\div8}{-64\div8}$
$=\frac{3}{-8}$
View full question & answer→Question 632 Marks
Evaluate: $(-6)^{-1}$
Answer$(-6)^{-1}$ $=\frac{1}{-6}$ $=\frac{1\times-1}{-6\times-1}$ $=\frac{-1}{6}$
View full question & answer→Question 642 Marks
Express $\frac{-3}{5}$ as a rational number with denominator. $-30$
Answer$-30 = 5 \times (-6)$
$\therefore\frac{-3}{5}=\frac{-3(-6)}{5(-6)} [$Multiplying numerator and denominator by $(-6)]$
$=\frac{18}{-30}$
View full question & answer→Question 652 Marks
Which of the following statements are true and which are false? The rational numbers $\frac{-18}{-13}$ lies to the left of $0$ on the number line.
Answer$\frac{-18}{-13}=\frac{18}{13}$ which is positive and positive number lie on the right of $O.$
View full question & answer→Question 662 Marks
Simplify: $\frac{4}{9}\div\frac{-5}{12}$
Answer$\frac{4}{9}\div\frac{-5}{12}$
$=\frac{4}{9}\times\frac{12}{-5}$
$=\frac{4\times12}{9\times(-5)}$
$=\frac{48}{-45}=\frac{-48}{45}$
$=\frac{-48\div3}{45\div3}$
$=\frac{-16}{15}$
View full question & answer→Question 672 Marks
Find the following products: $\frac{-7}{6}\times24$
Answer$\frac{-7}{6}\times24$ $=\frac{-7\times24}{6}$ $=-7\times4$ $=-28$
View full question & answer→Question 682 Marks
Find the following products: $\frac{25}{-9}\times\frac{3}{-10}$
Answer$\frac{25}{-9}\times\frac{3}{-10}$ $=\frac{25\times3}{(-9)\times(-10)}$ $=\frac{75}{90}$ $=\frac{75\div15}{90\div15}$ $=\frac{5}{6}$
View full question & answer→Question 692 Marks
Find the following products: $\frac{-12}{5}\times\frac{10}{-3}$
Answer$\frac{-12}{5}\times\frac{10}{-3}$ $=\frac{-12\times10}{5\times(-3)}$ $=\frac{-120}{-15}$ $=\frac{-120\div15}{-15\div15}$ $=\frac{-8}{-1}=\frac{8}{1}=8$
View full question & answer→Question 702 Marks
Express $\frac{-3}{5}$ as a rational number with denominator. $20$
Answer$20 = 5 \times 4$
$\frac{-3}{5}=\frac{-3\times4}{5\times4} ($Multiplying numerator and denominator by $4)$
$=\frac{-12}{20}$
View full question & answer→Question 712 Marks
What number should be added to $-1$ so as to get $\frac{5}{7}?$
AnswerSum of two numbers $=\frac{5}{7}$ One number = $-1$
$\therefore$ Second number $=\frac{5}{7}-(-1)$
$=\frac{5}{7}+\frac{1}{1}$
$=\frac{5+7}{7}$
$=\frac{12}{7}$
$\therefore$ Second number $=\frac{12}{7}$
View full question & answer→Question 722 Marks
Represent the following numbers on the number line. $1\frac{3}{4}$
Answer$1\frac{3}{4}$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off units $OA.$ Units $OA, AB, BC$ to the right side of $O.$
Now, divide $AB$ into $4$ equal parts and take $3$ equal parts such that $\text{AP}=\frac{3}{4}$
Then,
$\text{OP}=1+\frac{3}{4}=1\frac{3}{4}$ as shown on the number line given below,
View full question & answer→Question 732 Marks
Subtract: $\frac{-9}{7}\ \text{from}\ -1$
Answer$\frac{-9}{7}\ \text{from}\ -1$ or $\frac{-1}{1}-\frac{-9}{7}$ $=\frac{-7-(-9)}{7}$ $=\frac{-7+9}{7}$ $=\frac{2}{7}$
View full question & answer→Question 742 Marks
Find the additive inverse of the following:
$\frac{1}{3}$
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 $\frac{1}{3}$ will be $\frac{-1}{3}$
View full question & answer→Question 752 Marks
Evaluate: $\Big(\frac{-5}{8}\Big)^{-1}$
Answer$\Big(\frac{-5}{8}\Big)^{-1}$ $=\frac{8}{-5}$ $=\frac{8\times-1}{-5\times-1}$ $=\frac{-8}{5}$
View full question & answer→Question 762 Marks
Subtract: $-7\ \text{from}\ \frac{-4}{7}$
Answer$-7\ \text{from}\ \frac{-4}{7}$ or $\frac{-4}{7}-\Big(\frac{-7}{1}\Big)$ $=\frac{-4-(-49)}{7}$ $=\frac{-4+49}{7}$ $=\frac{-4+49}{7}$ $=\frac{45}{7}$
View full question & answer→Question 772 Marks
Find the additive inverse of the following: $-18$
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 $-18$ will be $18$
View full question & answer→Question 782 Marks
Find the additive inverse of the following: $\frac{23}{9}$
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 $\frac{23}{9}$ will be $\frac{-23}{9}$
View full question & answer→Question 792 Marks
Find a rational number between $\frac{1}{4}$ and $\frac{1}{3}$.
AnswerRational number between $\frac{1}{4}$ and $\frac{1}{3}$ $=\frac{1}{2}\Big[\frac{1}{4}+\frac{1}{3}\Big]$ $=\frac{1}{2}\Big[\frac{3+4}{12}\Big]$ $=\frac{1}{2}\times\frac{7}{12}$ $=\frac{7}{24}$
View full question & answer→Question 802 Marks
Find the following products: $\frac{-13}{5}\times(-10)$
Answer$\frac{-13}{5}\times(-10)$ $=\frac{-13\times(-10)}{5}$ $=-13\times(-2)$ $=26$
View full question & answer→Question 812 Marks
Find the additive inverse of the following:$\frac{-3}{11}$
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 $\frac{-3}{11}$ will be $\frac{3}{11}$
View full question & answer→Question 822 Marks
Verify the following: $\frac{-12}{5}+\frac{2}{7}=\frac{2}{7}+\frac{-12}{5}$
Answer$\text{L.H.S. }=\frac{-12}{5}+\frac{2}{7}$
$=\frac{-84+10}{35}$
$=\frac{-74}{35}$
$\text{R.H.S. }=\frac{2}{7}+\frac{-12}{5}$
$=\frac{10-84}{35}$
$=\frac{-74}{35}$
$\text{L.H.S. }=\text{R.H.S. }$
$\therefore\frac{-12}{5}+\frac{2}{7}=\frac{2}{7}+\frac{-12}{5}$
View full question & answer→Question 832 Marks
Which of the two rational numbers is greater in the given pair? $\frac{3}{8}\ \text{or}\ 0$
Answer$\frac{3}{8}\text{ or }0$ We know that every positive rational number is greater than $0.$
$\therefore\frac{3}{8}$ is greater.
View full question & answer→Question 842 Marks
Find the following products: $\frac{-13}{15}\times\frac{-25}{26}$
Answer$\frac{-13}{15}\times\frac{-25}{26}$ $=\frac{-13\times(-25)}{15\times26}$ $=\frac{325}{390}$ $=\frac{325\div65}{390\div65}$ $=\frac{5}{6}$
View full question & answer→Question 852 Marks
An aeroplane covers $1020\ km$ in an hour. How much distance will it cover in $4\frac{1}{6}$ hours$?$
AnswerDistance covered in $1$ hours $= 1020\ km$
Distance covered in $4\frac{1}{6}$ hours$=1020\times4\frac{1}{6}$
$=1020\times\frac{25}{6}\text{km}$
$=\frac{25500}{6}\text{km}$
$=4250\text{km}$
View full question & answer→Question 862 Marks
Express the following rational numbers in standard form. $\frac{-12}{30}$
Answer$\frac{-12}{30}$
$H.C.F$ of $12$ and $30 = 6$
Dividing the numerator and denominator by $6,$ and $\frac{-12}{30}$
$=\frac{-12\div6}{30\div6}$
$=\frac{-2}{5}$
View full question & answer→Question 872 Marks
Find the multiplicative inverse of: $\frac{11}{4}$
AnswerMultiplicative inverse of a rational number $\frac{\text{a}}{\text{b}}=\frac{\text{b}}{\text{a}}$ Therefore, Negative inverse of $\frac{11}{4}=\frac{4}{11}$
View full question & answer→Question 882 Marks
Represent the following numbers on the number line.
$4\frac{2}{3}$
Answer$4\frac{2}{3}$
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 $EF$ into $3$ equal parts and take $2$ equal parts.
Then,
$\text{EP}=\frac{2}{3}$
$\therefore\text{OP}=\text{OE}+\text{EP}$
$=4+\frac{2}{3}=4\frac{2}{3}$ as shown on the number line given below,
View full question & answer→Question 892 Marks
Represent the following numbers on the number line. $8$
Answer$8$
Draw a line and take a point $O$ on it.
Let it represent $0.$
From $O,$ set off units $OA, AB, BC, CD, DE, EF, FG$ and $GH$ on the right side of $O.$
Then,
$OH = 8$
View full question & answer→Question 902 Marks
Simplify: $\frac{-1}{10}\div\frac{-8}{5}$
Answer$\frac{-1}{10}\div\frac{-8}{5}$
$\frac{-1}{10}\times\frac{5}{-8}$
$=\frac{-1\times5}{10\times(-8)}$
$=\frac{-5}{-80}=\frac{5}{80}$
$=\frac{5\div5}{80\div5}$
$=\frac{1}{16}$
View full question & answer→Question 912 Marks
Verify the following:
$\frac{3}{7}\times\frac{-5}{9}=\frac{-5}{9}\times\frac{3}{7}$
Answer $\text{L.H.S.}=\frac{3}{7}\times\frac{-5}{9}$
$=\frac{3\times(-5)}{7\times9}$
$=\frac{-15}{63}$
$\text{R.H.S.}=\frac{-5}{9}\times\frac{3}{7}$
$=\frac{-5\times3}{9\times7}$
$=\frac{-15}{63}$
$\text{L.H.S.}=\text{R.H.S.}$
$\therefore\frac{3}{7}\times\frac{-5}{9}=\frac{-5}{9}\times\frac{3}{7}$
View full question & answer→