Question 12 Marks
A picture was marked at Rs. 90 . It was sold at $\frac{3}{4}$ of its marked price. What was the sale price?
AnswerMarked price $=$ Rs. 90
Sale price $=\frac{3}{4}$ of Rs. $90=\frac{3}{4} \times 90$
$=$ Rs. $\frac{270}{4}=$ Rs. 67 $1 / 2=$ Rs. 67.50
View full question & answer→Question 22 Marks
Geeta had 30 problems for homework. She worked out $\frac{2}{5}$ of them. How many problems were still left to be worked out by her?
AnswerNo.of problems of Geeta $=30$
No.of problems worked out $=\frac{2}{3}$ of 30
$ =\frac{2}{3} \times 30=20 $
No. of problems left out $=30-20=10$
View full question & answer→Question 32 Marks
After going $\frac{3}{4}$ of my journey, I find that I have covered $16 \mathrm{~km}$. How much Journey is still left?
Answer
$\begin{aligned} & \frac{3}{4} \text { of journey }=16 \mathrm{~km} . \\ & \therefore \text { Total journey }=16 \mathrm{~km} \times \frac{4}{3}=\frac{64}{3} \mathrm{~km} \\ & \therefore \text { Journey left }=\frac{64}{3}-\frac{16}{1} \\ & =\frac{64-48}{3}=\frac{16}{3} \mathrm{~km}=5 \frac{1}{3}\end{aligned}$
View full question & answer→Question 42 Marks
Subtract $\frac{2}{7}-\frac{5}{21}$ from the sum of $\frac{3}{4}, \frac{5}{7}$ and $\frac{7}{12}$
Answer$\left(\frac{3}{4}+\frac{5}{7}+\frac{7}{12}\right)-\left(\frac{2}{7}-\frac{5}{21}\right)$
$\left(\frac{63+60+49}{84}\right)-\left(\frac{6-5}{21}\right)$
$\frac{172}{84}-\frac{1}{21}=\frac{172-4}{84}=\frac{168}{84}=2$
View full question & answer→Question 52 Marks
A line $A B$ is of length $6 \mathrm{~cm}$. Another line $C D$ is of length $15 \mathrm{~cm}$. What fraction is: $\frac{1}{5}$ of $C D$ to that of $A B$ ?
AnswerLength of line $A B=6 \mathrm{~cm}$
and length of line $C D=15 \mathrm{~cm}$
$\frac{1}{5}$ of $A B=\frac{1}{5} \times 15=3 \mathrm{~cm}$
$\therefore \frac{1}{5}$ of $C D$ to that of $A B=\frac{3}{6}=\frac{1}{2}$
View full question & answer→Question 62 Marks
A line $A B$ is of length $6 \mathrm{~cm}$. Another line $C D$ is of length $15 \mathrm{~cm}$. What fraction is: $\frac{1}{2}$ the length of $A B$ to that of $\frac{1}{3}$ of $C D$ ?
Answer
$\begin{aligned} & \text { Length of line } A B=6 \mathrm{~cm} \\ & \text { and length of line } C D=15 \mathrm{~cm} \\ & \frac{1}{2} \text { of } A B=\frac{1}{2} \times 6=3 \mathrm{~cm} \\ & \frac{1}{3} \text { of } C D=\frac{1}{3} \times 15=5 \mathrm{~cm} \\ & \therefore \frac{1}{2} \text { of } A B \text { to } \frac{1}{3} \text { of } C D=\frac{3}{5}\end{aligned}$
View full question & answer→Question 72 Marks
A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is: The length of AB to that of CD?
AnswerLength of line $A B=6 \mathrm{~cm}$
and length of line $C D=15 \mathrm{~cm}$
Length of line $A B$ to length of $C D=\frac{6}{15}=\frac{2}{5}$
View full question & answer→Question 82 Marks
A rope is $25 \frac{1}{2} \mathrm{~m}$ long. How many pieces, $1 \frac{1}{2}$ each of length can be cut out from it?
Answer
$\begin{aligned} & \text { Total length of the rope }=25 \frac{1}{2} \mathrm{~m}=\frac{51}{2} \mathrm{~m} \\ & \text { Length of each piece }=1 \frac{1}{2} \mathrm{~m}=\frac{3}{2} \mathrm{~m} \\ & \therefore \text { No. of pieces }=\frac{51}{2} \div \frac{3}{2}=\frac{51}{2} \times \frac{2}{3}=17 \text { pieces }\end{aligned}$
View full question & answer→Question 92 Marks
Simplify and reduce to a simple fraction:
$\frac{1}{2} \text { of } \frac{3}{4} \times \frac{1}{2} \div \frac{2}{3}$
Answer$ \frac{1}{2} \text { of } \frac{3}{4} \times \frac{1}{2} \div \frac{2}{3} $
Using BODMAS,
$ \begin{aligned} & =\frac{3}{8} \times \frac{1}{2} \div \frac{2}{3} \\ & =\frac{3}{8} \times \frac{1}{2} \times \frac{3}{2}=\frac{9}{32} \end{aligned} $
View full question & answer→Question 102 Marks
Simplify and reduce to a simple fraction:
$\frac{4}{5} \text { of } \frac{7}{15} \div \frac{8}{9}$
Answer$ \frac{4}{5} \text { of } \frac{7}{15} \div \frac{8}{9} $
Using BODMAS,
$=\frac{28}{75} \div \frac{8}{9}=\frac{28}{75} \times \frac{9}{8} $
$ =\frac{7 \times 3}{25 \times 2}=\frac{21}{50}$
View full question & answer→Question 112 Marks
Simplify and reduce to a simple fraction:
$\frac{4}{5} \div \frac{7}{15} \times \frac{8}{9}$
Answer
$\begin{aligned} & \frac{4}{5} \div \frac{7}{15} \times \frac{8}{9} \\ & =\frac{4}{5} \times \frac{15}{7} \times \frac{8}{9} \\ & =\frac{32}{21}=1 \frac{11}{21}\end{aligned}$
View full question & answer→Question 122 Marks
Simplify and reduce to a simple fraction:
$\frac{4}{5} \div \frac{7}{15} \text { of } \frac{8}{9}$
Answer$ \frac{4}{5} \div \frac{7}{15} \text { of } \frac{8}{9} $
Using BODMAS, we get
$ \begin{aligned} & =\frac{4}{5} \div \frac{56}{135} \\ & =\frac{4}{5} \times \frac{135}{56}=\frac{27}{14}=1 \frac{13}{14} \end{aligned} $
View full question & answer→Question 132 Marks
Simplify and reduce to a simple fraction:
$2 \frac{1}{4} \div \frac{1}{7} \times \frac{1}{3}$
Answer
$\begin{aligned} & 2 \frac{1}{4} \div \frac{1}{7} \times \frac{1}{3} \\ & \left.=\frac{9}{4} \div \frac{1}{7} \times \frac{1}{3}=\frac{9}{4} \times \frac{7}{1} \times \frac{1}{3} \text { [Removing } \div\right] \\ & =\frac{21}{4}=5 \frac{1}{4}\end{aligned}$
View full question & answer→Question 142 Marks
Find the value of $\frac{5}{11}$ of $\frac{4}{5}$ of $22 \mathrm{~kg}$
Answer
$\begin{aligned} & \frac{5}{11} \text { of } \frac{4}{5} \text { of } 22 \mathrm{~kg} \\ & =\left(\frac{5}{11} \times \frac{4}{5} \times \frac{22}{1}\right) \mathrm{kg} \\ & =(4 \times 2)=8 \mathrm{~kg}\end{aligned}$
View full question & answer→Question 152 Marks
Find the value of $\frac{4}{7}$ of $2 \frac{1}{3} \mathrm{~kg}$
Answer
$\begin{aligned} & \frac{4}{7} \text { of } 2 \frac{1}{3} \mathrm{~kg} \\ & =\left(\frac{4}{7} \times \frac{7}{3}\right) \mathrm{kg} \\ & =\frac{4}{3} \mathrm{~kg}=1 \frac{1}{3} \mathrm{~kg}\end{aligned}$
View full question & answer→Question 162 Marks
Find the value of $\frac{3}{5}$ of 1 hour
Answer
$\begin{aligned} & \frac{3}{5} \text { of } 1 \text { hour } \\ & =\left(\frac{3}{5} \times 60\right) \text { minutes } \\ & =3 \times 12=36 \text { minutes }\end{aligned}$
View full question & answer→Question 172 Marks
Subtract: $-\frac{4}{7}$ from $-\frac{6}{11}$
Answer
$\begin{aligned} & -\frac{4}{7} \text { from }-\frac{6}{11} \\ & =-\frac{6}{11}-\left(-\frac{4}{7}\right)=-\frac{6}{11}+\frac{4}{7} \\ & =\frac{-6 \times 7}{11 \times 7}-\frac{4 \times 11}{7 \times 11} \\ & (\text { LCM of } 7 \text { and } 11=77) \\ & =-\frac{42}{77}+\frac{44}{77}=-\frac{42+44}{77}=\frac{2}{77}\end{aligned}$
View full question & answer→Question 182 Marks
Subtract: $\frac{2}{9}$ from $\frac{4}{5}$
Answer
$\begin{aligned} & \frac{2}{9} \text { from } \frac{4}{5} \\ & =\frac{4}{5}-\frac{2}{9}=\frac{4 \times 9}{5 \times 9}-\frac{2 \times 5}{9 \times 5} \\ & (\mathrm{LCM} \text { of } 5 \text { and } 9=45) \\ & =\frac{36}{45}-\frac{10}{45}=\frac{36-10}{45}=\frac{26}{45}\end{aligned}$
View full question & answer→Question 192 Marks
Subtract: $-\frac{3}{7}$ from $\frac{3}{7}$
Answer
$\begin{aligned} & -\frac{3}{7} \text { from } \frac{3}{7} \\ & =\frac{3}{7}-\left(-\frac{3}{7}\right)=\frac{3}{7}+\frac{3}{7} \\ & =\frac{3+3}{7}=\frac{6}{7}\end{aligned}$
View full question & answer→Question 202 Marks
Subtract: $-\frac{2}{5}$ from $\frac{2}{5}$
Answer
$\begin{aligned} & -\frac{2}{5} \text { from } \frac{2}{5} \\ & =\frac{2}{5}-\left(-\frac{2}{5}\right)=\frac{2}{5}+\frac{2}{5} \\ & =\frac{2+2}{5}=\frac{4}{5}\end{aligned}$
View full question & answer→Question 212 Marks
Subtract: $\frac{1}{8}$ from $\frac{5}{8}$
Answer
$\begin{aligned} & \frac{1}{8} \text { from } \frac{5}{8} \\ & =\frac{5}{8}-\frac{1}{8} \\ & =\frac{5-1}{8}=\frac{4}{8}=\frac{1}{2}\end{aligned}$
View full question & answer→Question 222 Marks
Subtract: 2 from $\frac{2}{3}$
Answer
$\begin{aligned} & 2 \text { from } \frac{2}{3} \\ & =\frac{2}{3}-\frac{2}{1} \\ & =\frac{2}{3}-\frac{2 \times 3}{3}=\frac{2}{3}-\frac{6}{3} \\ & =\frac{2-6}{3}=-\frac{4}{3}=-1 \frac{1}{3}\end{aligned}$
View full question & answer→Question 232 Marks
Simplify: $3 \frac{3}{4} \times 1 \frac{1}{5} \times \frac{20}{21}$
Answer
$\begin{aligned} & 3 \frac{3}{4} \times 1 \frac{1}{5} \times \frac{20}{21} \\ & =\frac{15}{4} \times \frac{6}{5} \times \frac{20}{21} \\ & =\frac{15 \times 6 \times 20}{4 \times 5 \times 21}=\frac{1800}{420}=\frac{1800 \div 60}{420 \div 60} \quad(\mathrm{HCF} \text { of } 1800 \text { and } 420=60) \\ & =\frac{30}{7}=4 \frac{2}{7}\end{aligned}$
View full question & answer→Question 242 Marks
Simplify: $-\frac{5}{8} \div \frac{3}{4}$
Answer
$\begin{aligned} & -\frac{5}{8} \div \frac{3}{4} \\ & =-\frac{5}{8} \times \frac{4}{3} \\ & =-\frac{5 \times 4}{8 \times 3}=-\frac{20}{24}=-\frac{20 \div 4}{24 \div 4}=-\frac{5}{6}\end{aligned}$
View full question & answer→Question 252 Marks
Simplify: $\frac{1}{3} \div \frac{1}{4}$
Answer
$\begin{aligned} & \frac{1}{3} \div \frac{1}{4} \\ & =\frac{1}{3} \times \frac{4}{1} \\ & =\frac{1 \times 4}{3 \times 1}=\frac{4}{3}=1 \frac{1}{3}\end{aligned}$
View full question & answer→Question 262 Marks
Simplify: $1 \div \frac{3}{5}$
Answer
$\begin{aligned} & 1 \div \frac{3}{5} \\ & =1 \times \frac{5}{3} \\ & =\frac{1 \times 5}{3}=\frac{5}{3}=1 \frac{2}{3}\end{aligned}$
View full question & answer→Question 272 Marks
Simplify: $3 \div \frac{2}{5}$
Answer
$\begin{aligned} & 3 \div \frac{2}{5} \\ & =\frac{3}{1} \times \frac{5}{2} \\ & =\frac{3 \times 5}{1 \times 2}=\frac{15}{2}=7 \frac{1}{2}\end{aligned}$
View full question & answer→Question 282 Marks
Simplify: $2 \div \frac{1}{3}$
Answer
$\begin{aligned} & 2 \div \frac{1}{3} \\ & =\frac{2}{1} \times \frac{3}{1} \\ & =\frac{2 \times 3}{1 \times 1}=\frac{6}{1}=6\end{aligned}$
View full question & answer→Question 292 Marks
Simplify: $36 \times 3 \frac{1}{4}$
Answer
$\begin{aligned} & 36 \times 3 \frac{1}{4} \\ & =\frac{36}{1} \times \frac{13}{4} \\ & =\frac{36 \times 13}{4 \times 1}=\frac{468}{4}=117\end{aligned}$
View full question & answer→Question 302 Marks
Simplify: $45 \times 2 \frac{1}{3}$
Answer
$\begin{aligned} & 45 \times 2 \frac{1}{3} \\ & =\frac{45}{1} \times \frac{7}{3} \\ & =\frac{45 \times 7}{1 \times 3}=\frac{315}{3}=105\end{aligned}$
View full question & answer→Question 312 Marks
Simplify: $\frac{9}{12} \times \frac{4}{7}$
Answer
$\begin{aligned} & \frac{9}{12} \times \frac{4}{7} \\ & =\frac{9 \times 4}{12 \times 7}=\frac{36}{84} \\ & =\frac{36 \div 12}{84 \div 12}=\frac{3}{7} \quad(\mathrm{HCF} \text { of } 36 \text { and } 84=12)\end{aligned}$
View full question & answer→Question 322 Marks
Simplify: $\frac{3}{4} \times 6$
Answer
$\begin{aligned} & \frac{3}{4} \times 6 \\ & =\frac{3}{4} \times \frac{6}{1}=\frac{3 \times 6}{4 \times 1}=\frac{18}{4} \\ & =\frac{18 \div 2}{4 \div 2}=\frac{9}{2}=4 \frac{1}{2}\end{aligned}$
View full question & answer→Question 332 Marks
By what number should $5 \frac{5}{6}$ be multiplied 1 to get $3 \frac{1}{3}$ ?
Answer
$\begin{aligned} & \text { Required number }=3 \frac{1}{3} \div 5 \frac{5}{6} \\ & =\frac{10}{3} \div \frac{35}{6} \Rightarrow \frac{10}{3} \times \frac{6}{35}=\frac{4}{7} \\ & \therefore \text { Required number }=\frac{4}{7}\end{aligned}$
View full question & answer→Question 342 Marks
The product of two numbers is $20 \frac{5}{7}$. If one of these numbers is $6 \frac{2}{3}$, find the other.
AnswerThe product of two numbers is $20 \frac{5}{7}=\frac{145}{7}$
one number $=6 \frac{2}{3}=\frac{20}{3}$
$\therefore$ Second number $=\frac{145}{7} \div \frac{20}{3}$
$=\frac{145}{7} \times \frac{3}{20}=\frac{87}{28}=3 \frac{3}{28}$
View full question & answer→Question 352 Marks
A rod of length $2 \frac{2}{5}$ meter is divided into five equal parts. Find the length of each part so obtained.
AnswerTotal length of rod $=2 \frac{2}{5} \mathrm{~m}$
Length of rod to be divided into 5 equal parts
$\therefore$ Length of each part of rod $=2 \frac{2}{5} \div 5$
$=\frac{12}{5} \times \frac{1}{5}=\frac{12}{25}$ meter
View full question & answer→Question 362 Marks
Out of $24 \mathrm{~kg}$ of wheat, $\frac{5}{6}$ th of wheat is consumed. Find, how much wheat is still left?
AnswerTotal wheat available $=24 \mathrm{~kg}$
Wheat consumed $=\frac{5}{6}$ "th" of $24 \mathrm{~kg}$
$ =\frac{5}{6} \times 24=20 \mathrm{~kg} $
$\therefore$ Remaining wheat $=24-20 \mathrm{~kg}=4 \mathrm{~kg}$
View full question & answer→Question 372 Marks
Each of 40 identical boxes weighs $4 \frac{4}{5} \mathrm{~kg}$ Find the total weight of all the boxes.
AnswerWeight of one box $=4 \frac{4}{5} \mathrm{~kg}=\frac{24}{5} \mathrm{~kg}$
Weight of 40 boxes $=40 \times \frac{24}{5}$
$ =8 \times 24=192 \mathrm{~kg} $
View full question & answer→Question 382 Marks
Reduce to a single fraction:
$1 \frac{1}{3}+2 \frac{1}{4}$
Answer$ 1 \frac{1}{3}+2 \frac{1}{4}=\frac{4}{3}+\frac{9}{4} $
$=\frac{4 \times 4}{3 \times 4}+\frac{9 \times 3}{4 \times 3}=\frac{16}{12}+\frac{27}{12}($ LCM of 3 and $4=12)$
$ =\frac{16+27}{12}=\frac{43}{12}=3 \frac{7}{12} $
View full question & answer→Question 392 Marks
Reduce to a single fraction:
$\frac{2}{3}-\frac{1}{6}$
Answer
$\begin{aligned} & \frac{2}{3}-\frac{1}{6} \\ & =\frac{2 \times 2}{3 \times 2}-\frac{1}{6}=\frac{4}{6}-\frac{1}{6} \quad(\text { LCM of } 3 \text { and } 6=6) \\ & =\frac{4-1}{6}=\frac{3}{6}=\frac{1}{2}\end{aligned}$
View full question & answer→Question 402 Marks
Reduce to a single fraction:
$\frac{1}{2}+\frac{2}{3}$
Answer
$\begin{aligned} & \frac{1}{2}+\frac{2}{3} \\ & =\frac{1 \times 3}{2 \times 3}+\frac{2 \times 2}{3 \times 2} \quad(\text { LCM of } 2 \text { and } 3=6) \\ & =\frac{3}{6}+\frac{4}{6}=\frac{3+4}{6}=\frac{7}{6}=1 \frac{1}{6}\end{aligned}$
View full question & answer→Question 412 Marks
Insert one fraction between:
$\frac{3}{7} \text { and } \frac{4}{9}$
AnswerFraction between $\frac{3}{7}$ and $\frac{4}{9}$
$=\frac{3+4}{7+9}=\frac{7}{16}$
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