Question 12 Marks
Subtract as indicated:
$\frac{29}{7}$ from $\frac{45}{7}$
AnswerThe denominators are same.
Therefore, $\frac{45}{7}-\frac{29}{7}=\frac{16}{7}=2 \frac{2}{7}$
View full question & answer→Question 22 Marks
Subtract as indicated:
$\frac{18}{5}$ from $\frac{23}{3}$
AnswerThe denominators of the given fractions are 3 and 5.
The LCM of 3 and 5 is 15.
Then, $\frac{23}{3}=\frac{23 \times 5}{3 \times 5}=\frac{115}{15}, \frac{18}{5}=\frac{18 \times 3}{5 \times 3}=\frac{54}{15}$
Therefore, $\frac{23}{3}-\frac{18}{5}=\frac{115}{15}-\frac{54}{15}=\frac{61}{15}=4 \frac{1}{15}$
View full question & answer→Question 32 Marks
Subtract as indicated:
$\frac{13}{4}$ from $\frac{10}{3}$
AnswerThe denominators of the given fractions are 3 and 4. The LCM of 3 and 4 is 12.
Then $\frac{13}{4}=\frac{13 \times 3}{4 \times 3}=\frac{39}{12}, \frac{10}{3}=\frac{10 \times 4}{3 \times 4}=\frac{40}{12}$
Therefore, $\frac{10}{3}-\frac{13}{4}=\frac{40}{12}-\frac{39}{12}=\frac{1}{12}$
View full question & answer→Question 42 Marks
subtraction using Brahmagupta’s method:
$\frac{2}{3}-\frac{1}{2}$
AnswerGiven $\frac{2}{3}-\frac{1}{2}$
Here LCM of 3 and 2 is 6. Fractional unit for both fractions should be $\frac{1}{6}$
$\begin{aligned} \therefore \quad & \frac{2 \times 2}{3 \times 2}-\frac{1 \times 3}{2 \times 3} \\ & =\frac{4}{6}-\frac{3}{6} \\ & =\frac{4-3}{6} \\ & =\frac{1}{6}\end{aligned}$
View full question & answer→Question 52 Marks
subtraction using Brahmagupta’s method:
$\frac{5}{6}-\frac{4}{9}$
AnswerGiven $\frac{5}{6}-\frac{4}{9}$
Hence LCM of 6 and 9 is 18. Fractional unit for both fractions should be $\frac{1}{18}$ then
$\begin{array}{l}\frac{5 \times 3}{6 \times 3}-\frac{4 \times 2}{9 \times 2} \\ =\frac{15}{18}-\frac{8}{18} \\ =\frac{15-8}{18} \\ =\frac{7}{18}\end{array}$
View full question & answer→Question 62 Marks
subtraction using Brahmagupta’s method:
$\frac{2}{5}-\frac{4}{15}$
AnswerGiven $\frac{2}{5}-\frac{4}{15}$
Here LCM of 5 and 15 is 15. Fractional unit for both fractions should be $\frac{1}{15}$
$\begin{array}{l}\text { then } \frac{2 \times 3}{5 \times 3}-\frac{4 \times 1}{15 \times 1} \\ =\frac{6}{15}-\frac{4}{15} \\ =\frac{6-4}{15} \\ =\frac{2}{15}\end{array}$
View full question & answer→Question 72 Marks
subtraction using Brahmagupta’s method:
$\frac{8}{15}-\frac{3}{15}$
AnswerGiven $\frac{8}{15}-\frac{3}{15}$
Fractional unit for both fractions is $\frac{1}{15}$ then $\frac{2 \times 3}{5 \times 3}-\frac{4 \times 1}{15 \times 1}$
$\begin{array}{l}\frac{8}{15}-\frac{3}{15}=\frac{8-3}{15} \\ =\frac{5}{15}=\frac{1}{3}\end{array}$
View full question & answer→Question 82 Marks
$\frac{10}{27}-\frac{1}{27} \frac{10}{27}-\frac{1}{27}$
Answer$\begin{array}{l}\text { Here } \frac{10}{27}-\frac{1}{27} \\ =\frac{10-1}{27} \\ =\frac{9}{27}=\frac{1}{3}\end{array}$
View full question & answer→Question 92 Marks
$\frac{7}{9}-\frac{5}{9}$
AnswerGiven $\frac{7}{9}-\frac{5}{9}$
As fractional unit is same i.e., $\frac{1}{9}$ we shall simply subtract numerators keeping fractional unit as $\frac{1}{9}$
$\begin{array}{l}\frac{7}{9}-\frac{5}{9} \\ =\frac{7-5}{9}=\frac{2}{9}\end{array}$
View full question & answer→Question 102 Marks
$\frac{5}{8}-\frac{3}{8}$
AnswerGiven $\frac{5}{8}-\frac{3}{8}$
As fractional unit is same i.e., $\frac{1}{8}$ we shall simply subtract numerators keeping fractional unit as $\frac{1}{8}$
Then $\frac{5}{8}-\frac{3}{8}=\frac{5-3}{8}$
$=\frac{2}{8}=\frac{1}{4}$
View full question & answer→Question 112 Marks
Add the fractions using Brahmagupta’s method:
$\frac{9}{2}+\frac{5}{4}+\frac{7}{6}$
Answer
$\begin{array}{l}\frac{54}{12}+\frac{15}{12}+\frac{14}{12}=\frac{83}{12} \\ =\frac{11}{12}\end{array}$
View full question & answer→Question 122 Marks
Add the fractions using Brahmagupta’s method:
$\frac{2}{3}+\frac{4}{5}+\frac{3}{7}$
Answer
$\begin{array}{l}\frac{70}{105}+\frac{84}{105}+\frac{45}{105}=\frac{199}{105} \\ =1 \frac{94}{105}\end{array}$
View full question & answer→Question 132 Marks
Add the fractions using Brahmagupta’s method:
$\frac{3}{4}+\frac{1}{3}+\frac{1}{5}$
Answer
$\begin{array}{l}\frac{45}{60}+\frac{20}{60}+\frac{12}{60}=\frac{77}{60} \\ =1 \frac{17}{60}\end{array}$
View full question & answer→Question 142 Marks
Add the fractions using Brahmagupta’s method:
$\frac{8}{3}+\frac{2}{7}$
Answer$\begin{array}{l}\frac{56}{21}+\frac{6}{21}=\frac{62}{21} \\ =2 \frac{20}{21}\end{array}$
View full question & answer→Question 152 Marks
Add the fractions using Brahmagupta’s method:
$\frac{9}{2}+\frac{5}{4}$
Answer
$\begin{array}{l}\frac{18}{4}+\frac{5}{4}=\frac{23}{4} \\ =5 \frac{3}{4}\end{array}$
View full question & answer→Question 162 Marks
Add the fractions using Brahmagupta’s method:
$\frac{3}{5}+\frac{5}{8}$
Answer
$\begin{array}{l}\frac{24}{40}+\frac{25}{40}=\frac{49}{40} \\ =\frac{9}{40}\end{array}$
View full question & answer→Question 172 Marks
Add the fractions using Brahmagupta’s method:
$\frac{4}{5}+\frac{2}{3}$
Answer
$\begin{array}{l}\frac{12}{15}+\frac{10}{15}=\frac{22}{15} \\ =1 \frac{7}{15}\end{array}$
View full question & answer→Question 182 Marks
Add the fractions using Brahmagupta’s method:
$\frac{2}{3}+\frac{4}{5}$
Answer
$\begin{array}{l}\frac{10}{15}+\frac{12}{15}=\frac{22}{15} \\ =1 \frac{7}{15}\end{array}$
View full question & answer→Question 192 Marks
Add the fractions using Brahmagupta’s method:
$\frac{3}{4}+\frac{1}{3}+\frac{1}{5}$
Answer
$\begin{array}{l}\frac{45}{60}+\frac{20}{60}+\frac{12}{60} \\ =\frac{77}{60} \\ =1 \frac{17}{60}\end{array}$
View full question & answer→Question 202 Marks
Add the fractions using Brahmagupta’s method:
$\frac{2}{3}+\frac{2}{7}$
Answer
$\begin{array}{l}\frac{2}{3}+\frac{2}{7}=\frac{2}{3} \times \frac{7}{7}+\frac{2}{7} \times \frac{3}{3} \\ =\frac{14}{21}+\frac{6}{21}=\frac{20}{21}\end{array}$
View full question & answer→Question 212 Marks
Add the fractions using Brahmagupta’s method:
$\frac{2}{3}+\frac{5}{6}$
Answer
$\begin{array}{l}\frac{2}{3}+\frac{5}{6}=\frac{2}{3} \times \frac{2}{2}+\frac{5}{6} \\ \frac{4}{6}+\frac{5}{6}=\frac{9}{6}=\frac{3}{2} \\ =1 \frac{1}{2}\end{array}$
View full question & answer→Question 222 Marks
Add the fractions using Brahmagupta’s method:
$\frac{3}{4}+\frac{1}{3}$
Answer
$\begin{array}{l}\frac{3}{4}+\frac{1}{3}=\frac{3}{4} \times \frac{3}{3}+\frac{1}{3} \times \frac{4}{4} \\ =\frac{9}{12}+\frac{4}{12}=\frac{9+4}{12} \\ =\frac{13}{12} \\ =1 \frac{1}{12}\end{array}$
View full question & answer→Question 232 Marks
Add the fractions using Brahmagupta’s method:
$\frac{2}{7}+\frac{5}{7}+\frac{6}{7}$
Answer
$\begin{array}{l}\frac{2}{7}+\frac{5}{7}+\frac{6}{7} \\ =\frac{2+5+6}{7}=\frac{13}{7} \\ =1 \frac{6}{7}\end{array}$
View full question & answer→Question 242 Marks
Compare the fractions and justify your answer:
$\frac{9}{4}, \frac{5}{2}$
AnswerGiven, fractions are $\frac{9}{4}, \frac{5}{2}$
LCM of 4 and 2 is 4
$\begin{array}{l}\frac{9}{4} \times \frac{1}{1}=\frac{9}{4} \\ \frac{5}{2} \times \frac{2}{2}=\frac{10}{4}\end{array}$
Clearly $\frac{9}{4}<\frac{10}{4}$ So, $\frac{9}{4}<\frac{5}{2}$
View full question & answer→Question 252 Marks
Compare the fractions and justify your answer:
$\frac{12}{5}, \frac{8}{5}$
AnswerGiven fractions are $\frac{12}{5}$ and $\frac{8}{5}$
Clearly $\frac{12}{5}>\frac{8}{5}$
As denominators are same, so $\frac{12}{5}>\frac{8}{5}$
View full question & answer→Question 262 Marks
Compare the fractions and justify your answer:
$\frac{7}{10}, \frac{9}{14}$
AnswerGiven fractions are $\frac{7}{10}$ and $\frac{9}{14}$
LCM of 10 and 14 is 70.
$\begin{array}{l}\frac{7}{10}=\frac{7}{10} \times \frac{7}{7}=\frac{49}{70} \\ \frac{9}{14}=\frac{9}{14} \times \frac{5}{5}=\frac{45}{70}\end{array}$
Clearly, $\frac{49}{70}>\frac{45}{70}$ So, $\frac{7}{10}>\frac{9}{14}$
View full question & answer→Question 272 Marks
Compare the fractions and justify your answer:
$\frac{4}{9}, \frac{3}{7}$
AnswerGiven, fractions are $\frac{4}{9}$ and $\frac{3}{7}$
LCM of 9 and 7 is 63.
$\begin{array}{l}\frac{4}{9}=\frac{4}{9} \times \frac{7}{7}=\frac{28}{63} \\ \frac{3}{7}=\frac{3}{7} \times \frac{9}{9}=\frac{27}{63}\end{array}$
Clearly, $\frac{28}{63}>\frac{27}{63}$ So, $\frac{4}{9}>\frac{3}{7}$
View full question & answer→Question 282 Marks
Compare the fractions and justify your answer:
$\frac{8}{3}, \frac{5}{2}$
AnswerGiven, fractions are $\frac{4}{9}$ and $\frac{3}{7}$
LCM of 3 and 2 is 6
$\frac{8}{3}=\frac{8}{3} \times \frac{2}{2}=\frac{16}{6}$ and $\frac{5}{2}=\frac{5}{2} \times \frac{3}{3}=\frac{15}{6}$
Clearly, $\frac{16}{6}>\frac{15}{6}$ So, $\frac{8}{3}>\frac{5}{2}$
View full question & answer→Question 292 Marks
Compare the fractions and justify your answer:
$\frac{9}{4}, \frac{5}{2}$
AnswerGiven, fractions are $\frac{9}{4}, \frac{5}{2}$
LCM of 4 and 2 is 4
$\begin{array}{l}\frac{9}{4} \times \frac{1}{1}=\frac{9}{4} \\ \frac{5}{2} \times \frac{2}{2}=\frac{10}{4}\end{array}$
Clearly $\frac{9}{4}<\frac{10}{4}$ So, $\frac{9}{4}<\frac{5}{2}$
View full question & answer→Question 302 Marks
Compare the fractions and justify your answer:
$\frac{12}{5}, \frac{8}{5}$
AnswerGiven fractions are $\frac{12}{5}$ and $\frac{8}{5}$
Clearly $\frac{12}{5}>\frac{8}{5}$
As denominators are same, so $\frac{12}{5}>\frac{8}{5}$
View full question & answer→Question 312 Marks
Compare the fractions and justify your answer:
$\frac{7}{10}, \frac{9}{14}$
AnswerGiven fractions are $\frac{7}{10}$ and $\frac{9}{14}$
LCM of 10 and 14 is 70.
$\begin{array}{l}\frac{7}{10}=\frac{7}{10} \times \frac{7}{7}=\frac{49}{70} \\ \frac{9}{14}=\frac{9}{14} \times \frac{5}{5}=\frac{45}{70}\end{array}$
Clearly, $\frac{49}{70}>\frac{45}{70}$ So, $\frac{7}{10}>\frac{9}{14}$
View full question & answer→Question 322 Marks
Compare the fractions and justify your answer:
$\frac{4}{9}, \frac{3}{7}$
AnswerGiven fractions are $\frac{4}{9}$ and $\frac{3}{7}$
LCM of 9 and 7 is 63.
$\begin{array}{l}\frac{4}{9}=\frac{4}{9} \times \frac{7}{7}=\frac{28}{63} \\ \frac{3}{7}=\frac{3}{7} \times \frac{9}{9}=\frac{27}{63}\end{array}$
Clearly, $\frac{28}{63}>\frac{27}{63}$ So, $\frac{4}{9}>\frac{3}{7}$
View full question & answer→Question 332 Marks
Compare the fractions and justify your answer:
$\frac{8}{3}, \frac{5}{2}$
AnswerGiven fractions are $\frac{8}{3}$ and $\frac{5}{2}$
LCM of 3 and 2 is 6
$\frac{8}{3}=\frac{8}{3} \times \frac{2}{2}=\frac{16}{6}$ and $\frac{5}{2}=\frac{5}{2} \times \frac{3}{3}=\frac{15}{6}$
Clearly, $\frac{16}{6}>\frac{15}{6}$ So, $\frac{8}{3}>\frac{5}{2}$
View full question & answer→Question 342 Marks
How many whole units are there in $\frac{4}{3}$ and in $\frac{7}{3} ?$
Answer
$\frac{4}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=1+\frac{1}{3}$
So, there are 1 whole unit in $\frac{4}{3}$.
$\frac{7}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=2+\frac{1}{3}$
So, there are 2 whole units in $\frac{7}{3}$.
View full question & answer→Question 352 Marks
How many whole units are there in $\frac{7}{2} ?$
Answer
$\frac{7}{2}=\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=3+\frac{1}{2}$
So, there are 3 whole units in $\frac{7}{2}$.
View full question & answer→Question 362 Marks
Write the fraction that gives the lengths of the black lines in the respective boxes.
Question 372 Marks
What is the length of the pink line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is $\frac{1}{2}$. So the pink line is y units long. Write the fraction that gives the length of the black line in the box.
AnswerLength of black line is $\frac{1}{2}$;
Length of black line is $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$
Fraction that gives length of black line $=\frac{3}{2}$
View full question & answer→Question 382 Marks
How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
AnswerThere are an infinite number of fractions between 0 and 1.
Example: $\frac{3}{5}, \frac{4}{5}, \frac{7}{10} \frac{1}{2}$ etc.
View full question & answer→Question 392 Marks
$\frac{4}{6}$ = ________ = ________ = ________ = ________
Answer$\begin{aligned} \frac{4}{6} & =\frac{4 \times 2}{6 \times 2}=\frac{4 \times 3}{6 \times 3}=\frac{4 \times 4}{6 \times 4} \\ & =\frac{8}{12}=\frac{12}{18}=\frac{16}{24}\end{aligned}$
View full question & answer→Question 402 Marks
Write two equivalent fractions for $\frac{2}{6}$.
AnswerFrom the fractional wall we can choose any two fractions that denote the same length as $\frac{2}{6} \cdot \frac{2}{6}=\frac{1}{3}=\frac{3}{9}$
View full question & answer→Question 412 Marks
Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook Solution:Here number line OH is divided into 8 equal parts OA, AB, BC, CD, DE, EF, FG and GH.
Answer
Also, $OA =\frac{1}{8}, OB =\frac{2}{8}, OC =\frac{3}{8}, OH =\frac{8}{8}=1$ View full question & answer→Question 422 Marks
Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the pink lines in the respective boxes or in your notebook.
AnswerHere number line OT = 1 unit is divided into five equal parts OP, PQ, QR, RS and ST.
Hence length of pink line $O Q=O P+P Q=\frac{1}{5}+\frac{1}{5}=\frac{2}{5}$
Now, length of pink line $OS = OP + PQ + QR + RS =\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{4}{5}$
Hence, $OQ =\frac{2}{5} OS =\frac{4}{5}$
View full question & answer→Question 432 Marks
Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the pink line in the box or in your notebook.
AnswerHere number line OR is divided into three equal parts OP, PQ and QR.
Hence length of pink line $= OP + PQ =\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$
View full question & answer→