Question 512 Marks
Express $\frac{-48}{60}$ as a rational number with denominator 5.
Answer60 = 5 × 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 × (-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.
AnswerFalse.Solution:
$\frac{-18}{-13}=\frac{18}{13}$ 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
Answer20 = 5 × 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:
$\frac{1}{3}$
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 $\frac{1}{3}$ 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 1020km in an hour. How much distance will it cover in $4\frac{1}{6}$ hours?
AnswerDistance covered in 1 hours = 1020km 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
Answer8
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→