Question 12 Marks
Find the difference: $6\frac{2}{3}-3\frac{3}{4}$
Answer$6\frac{2}{3}-3\frac{3}{4}$
$=\frac{20}{3}-\frac{15}{4}$
$L.C.M$ of $3$ and $4 = (2 \times 2 \times 3) = 12$
$=\frac{(80-45)}{12}$
$=\frac{35}{12}$
$=2\frac{11}{12}$
$\Big(\frac{12}{3}=4,4\times20=80\Big)$ and $\Big(\frac{12}{4}=3,3\times15=45\Big)$
View full question & answer→Question 22 Marks
Represent $2\frac{3}{5}$ on the number line.
AnswerLet $OA = AB = BC = 1$ unit
$\therefore$ $OB = 2$ units and $OC = 3$ units Divide $BC$ into $5$ equal parts and take $3$ parts out to reach point $P$ Clearly, point $P$ represents the number $2\frac{3}{5}$.
View full question & answer→Question 32 Marks
Represent the following fractions on the number line:
$\frac{4}{7}$
AnswerDraw a $0$ to $1$ on a number line. Label point $1$ as $A$ and mark the starting point as $0.$
Divide the number line from $0$ to $1$ into $7$ equal parts and take out $4$ parts from it to reach point $P.$
View full question & answer→Question 42 Marks
Compare the fractions given below:
$\frac{5}{8},\frac{7}{12}$
Answer $\frac{5}{8},\frac{7}{12}$
By cross multiplying:
$5\times12=60$
and $8\times7=56$
Clearly, $60>56$
$\therefore\frac{5}{8}>\frac{7}{12}$
View full question & answer→Question 52 Marks
Convert the following into a mixed fraction:$\frac{62}{7}$
AnswerOn dividing $62$ by $7$,
We get, Quotient $= 8$ Remainder $= 6$
Therefore, $\frac{62}{7}=8+\frac{6}{7}$ $=8\frac{6}{7}$
View full question & answer→Question 62 Marks
Represent the following fractions on the number line:
$\frac{1}{4}$
AnswerDraw a $0$ to $1$ on a number line. Label point $1$ as $A$ and mark the starting point as $0$.
Divide the number line from $0$ to $1$ into $4$ equal parts and take out $1$ part from it to reach point $P$.
View full question & answer→Question 72 Marks
Write five fractions equivalent to the following: $\frac{4}{5}$
Answer$\frac{4}{5}$
$\frac{4\times2}{5\times2}=\frac{8}{10}$
$\frac{4\times3}{5\times3}=\frac{12}{15}$
$\frac{4\times4}{5\times4}=\frac{16}{20}$
$\frac{4\times5}{5\times5}=\frac{20}{25}$
$\frac{4\times6}{5\times6}=\frac{24}{30}$
Hence, the five fractions equivalent to $\frac{4}{5}$ are $\frac{8}{10},\frac{12}{15},\frac{16}{20},\frac{20}{25}$ and $\frac{24}{30}$.
View full question & answer→Question 82 Marks
Convert the following into a mixed fraction:$\frac{103}{12}$
AnswerOn dividing $103$ by $12$,
We get, Quotient $= 8$ Remainder $= 7$
Therefore, $\frac{103}{12}=8+\frac{7}{12}$ $=8\frac{7}{12}$
View full question & answer→Question 92 Marks
Define like and unlike fractions and give five examples of each.
AnswerLike fractions: Fractions having the same denominator are called like fractions.
Examples: $\frac{3}{11},\frac{5}{11},\frac{7}{11},\frac{9}{11},\frac{10}{11}$
Unlike fractions: Fractions having different denominators are called unlike fractions.
Examples: $\frac{3}{4},\frac{4}{5},\frac{6}{7},\frac{9}{11},\frac{2}{13}$
View full question & answer→Question 102 Marks
Write five fractions equivalent to the following: $\frac{7}{10}$
Answer$\frac{7}{10}$
$\frac{7\times2}{10\times2}=\frac{14}{20}$
$\frac{7\times3}{10\times3}=\frac{21}{30}$
$\frac{7\times4}{10\times4}=\frac{28}{40}$
$\frac{7\times5}{10\times5}=\frac{35}{50}$
$\frac{7\times6}{10\times6}=\frac{42}{60}$
Hence, the five fractions equivalent to $\frac{7}{10}$ are $\frac{14}{20},\frac{21}{30},\frac{28}{40},\frac{35}{40}$ and $\frac{42}{60}$.
View full question & answer→Question 112 Marks
Find the sum: $\frac{2}{9}+\frac{5}{6}$
Answer$L.C.M.$ of $9$ and $6 = (2 × 3 × 3) = 18$
$\begin{array}{c|c}3&9,6\\\hline3&3,2\\\hline2&1,2\\\hline&1,1\end{array}$
Now, we know: $\frac{2}{9}=\frac{2\times2}{9\times2}=\frac{4}{18}$
$\frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}$
Therefore, $\frac{2}{9}+\frac{5}{6}$ $=\frac{4}{18}+\frac{15}{18}$ $=\frac{(4+15)}{18}$ $=\frac{19}{18}$ $=1\frac{1}{18}$
View full question & answer→Question 122 Marks
Convert the following into a mixed fraction:$\frac{117}{20}$
AnswerOn dividing $117$ by $20$,
We get, Quotient $= 5$ Remainder $= 7$
Therefore, $\frac{117}{20}=5+\frac{17}{20}$ $=5\frac{17}{20}$
View full question & answer→Question 132 Marks
Write five fractions equivalent to the following: $\frac{5}{12}$
Answer$\frac{5}{12}$
$\frac{5\times2}{12\times2}=\frac{10}{24}$
$\frac{5\times3}{12\times3}=\frac{15}{36}$
$\frac{5\times4}{12\times4}=\frac{20}{48}$
$\frac{5\times5}{12\times5}=\frac{25}{60}$
$\frac{5\times6}{12\times6}=\frac{30}{72}$
Hence, the five fractions equivalent to $\frac{5}{12}$ are $\frac{10}{24},\frac{15}{36},\frac{20}{48},\frac{25}{60}$ and $\frac{30}{72}$.
View full question & answer→Question 142 Marks
Compare the fractions given below:
$\frac{2}{3},\frac{4}{9}$
Answer $\frac{2}{3},\frac{4}{9}$
By cross multiplying:
$2\times9=18$
and $4\times3=12$
Clearly, $18>12$
$\therefore\frac{2}{3}>\frac{4}{9}$
View full question & answer→Question 152 Marks
Find the sum: $\frac{5}{8}+\frac{1}{8}$
AnswerThe given fractions are like fractions We know,
Sum of like fractions $=\frac{\text{Sum of the numerators}}{\text{Common denominator}}$
Thus, we have $\frac{5}{8}+\frac{1}{8}$ $=\frac{(5+1)}{8}$ $=\frac{6}{8}$ $=\frac{3}{4}$
View full question & answer→Question 162 Marks
Compare the fractions given below: $\frac{6}{13},\frac{3}{4}$
Answer$\frac{6}{13},\frac{3}{4}$ By cross multiplying:
$6\times4=24$ and $13\times3=39$
Clearly, $24>39$
$\therefore\frac{6}{13}<\frac{3}{4}$
View full question & answer→Question 172 Marks
Find the equivalent fraction of $\frac{5}{9}$ having: Numerator $35$
AnswerLet, $\frac{5}{9}=\frac{35}{\Box}$ Clearly, $35 = 5 \times 7$
So, we multiply the denominator by $7$
$\therefore\frac{5}{9}=\frac{5\times7}{9\times7}=\frac{35}{63}$
$\frac{5}{9}=\frac{35}{63}$
Hence, the required fraction is $\frac{35}{63}$.
View full question & answer→Question 182 Marks
Find the difference: $7-5\frac{2}{3}$
Answer$3\frac{5}{8}-2\frac{5}{12}$
$=\frac{7}{1}-\frac{17}{3}$
$L.C.M$ of $1$ and $3 = 3$ $=\frac{(21-17)}{3}$
$=\frac{4}{3}$
$=1\frac{1}{3}$
$\Big(\frac{3}{1}=3,3\times7=21\Big)$ and $\Big(\frac{3}{3}=1,1\times17=17\Big)$
View full question & answer→Question 192 Marks
Compare the fractions given below: $\frac{4}{5},\frac{5}{7}$
Answer$\frac{4}{5},\frac{5}{7}$
By cross multiplying: $5\times5=25$ and $4\times7=28$
Clearly, $28>25$
$\therefore\frac{4}{5}>\frac{5}{7}$
View full question & answer→Question 202 Marks
Find the difference: $10-6\frac{3}{8}$
Answer$10-6\frac{3}{8}$ $=\frac{10}{1}-\frac{51}{8}$
$L.C.M$ of $1$ and $8 = 8$ $=\frac{(80-51)}{8}$
$=\frac{29}{8}$ $=3\frac{5}{8}$
$\Big(\frac{8}{1}=8,8\times10=80\Big)$ and $\Big(\frac{8}{8}=1,1\times51=51\Big)$
View full question & answer→Question 212 Marks
Convert the following into a mixed fraction:$\frac{95}{13}$
AnswerOn dividing $95$ by $13$,
We get, Quotient $= 7$ Remainder $= 4 $
Therefore, $\frac{95}{13}=7+\frac{4}{13}$ $=7\frac{4}{13}$
View full question & answer→Question 222 Marks
Write five fractions equivalent to the following: $\frac{7}{9}$
Answer$\frac{7}{9}$
$\frac{7\times2}{9\times2}=\frac{14}{18}$
$\frac{7\times3}{9\times3}=\frac{21}{27}$
$\frac{7\times4}{9\times4}=\frac{28}{36}$
$\frac{7\times5}{9\times5}=\frac{35}{45}$
$\frac{7\times6}{9\times6}=\frac{42}{54}$
Hence, the five fractions equivalent to $\frac{7}{9}$ are $\frac{14}{18},\frac{21}{27},\frac{28}{36},\frac{35}{45}$ and $\frac{42}{54}$.
View full question & answer→Question 232 Marks
Convert the following into a mixed fraction:$\frac{87}{16}$
AnswerOn dividing $87$ by $16$,
We get, Quotient $= 5$ Remainder $= 7$
Therefore, $\frac{87}{16}=5+\frac{7}{16}$ $=5\frac{7}{16}$
View full question & answer→Question 242 Marks
Find the equivalent fraction of $\frac{24}{30}$ having numerator $4.$
AnswerLet, $\frac{24}{30}=\frac{4}{\Box}$ Clearly, $4 = 24 ÷ 6$
So, we divide the denominator by $6$
$\therefore\frac{24}{30}=\frac{24\div6}{30\div6}=\frac{4}{5}$
$\frac{24}{30}=\frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$.
View full question & answer→Question 252 Marks
Find the equivalent fraction of $\frac{56}{70}$ with Numerator $4$
AnswerLet $\frac{56}{70}=\frac{4}{\Box}$
Clearly, $4 = 56 ÷ 14$
So, we divide the denominator by $14$
$\therefore\frac{56}{70}=\frac{56\div14}{70\div14}=\frac{4}{5}$
$\frac{56}{70}=\frac{4}{5}$
Hence, the required fraction is $\frac{4}{5}$.
View full question & answer→Question 262 Marks
Find the equivalent fraction of $\frac{5}{8}$ with denominator $56.$
Answer$56 = 8 \times 7 $
So, we need to multiply the numerator by $7$
$\therefore\frac{5}{8}=\frac{5\times7}{8\times7}=\frac{35}{56}$
Hence, the required fraction is $\frac{35}{56}$.
View full question & answer→Question 272 Marks
How many natural numbers are there from $2$ to $10$? What fraction of them are prime numbers?
AnswerThere are total $9$ natural numbers from $2$ to $10$.
They are $2, 3, 4, 5, 6, 7, 8, 9, 10$. Out of these natural numbers, $2, 3, 5, 7$ are the prime numbers.
$\therefore$ The required fraction $=\frac{4}{9}$
View full question & answer→Question 282 Marks
Write five fractions equivalent to the following: $\frac{6}{11}$
Answer$\frac{6}{11}$
$\frac{6\times2}{11\times2}=\frac{12}{22}$
$\frac{6\times3}{11\times3}=\frac{18}{33}$
$\frac{6\times4}{11\times4}=\frac{24}{44}$
$\frac{6\times5}{11\times5}=\frac{30}{55}$
$\frac{6\times6}{11\times6}=\frac{36}{66}$
Hence, the five fractions equivalent to $\frac{6}{11}$ are $\frac{12}{22},\frac{18}{33},\frac{24}{44},\frac{30}{55}$ and $\frac{36}{66}$.
View full question & answer→Question 292 Marks
Write five fractions equivalent to the following: $\frac{2}{3}$
Answer$\frac{2}{3}$
$\frac{2\times2}{3\times2}=\frac{4}{6}$
$\frac{2\times3}{3\times3}=\frac{6}{9}$
$\frac{2\times4}{3\times4}=\frac{8}{12}$
$\frac{2\times5}{3\times5}=\frac{10}{15}$
$\frac{2\times6}{3\times6}=\frac{12}{18}$
Hence, the five fractions equivalent to $\frac{2}{3}$ are $\frac{4}{6},\frac{6}{9},\frac{8}{12},\frac{10}{15}$ and $\frac{12}{18}$.
View full question & answer→Question 302 Marks
Find the difference: $\frac{5}{8}-\frac{1}{8}$
AnswerDifference of like fractions = Difference of numerator ÷ Common denominator
$\frac{5}{8}-\frac{1}{8}$ $=\frac{(5-1)}{8}$
$=\frac{4}{8}$
$=\frac{1}{2}$
View full question & answer→Question 312 Marks
Which of the following are the pairs of equivalent fractions?
$i.\ \frac{5}{6}$ and $\frac{20}{24}$
$ii.\ \frac{3}{8}$ and $\frac{15}{40}$
$iii.\ \frac{4}{7}$ and $\frac{16}{21}$
$iv.\ \frac{2}{9}$ and $\frac{14}{63}$
$v.\ \frac{1}{3}$ and $\frac{9}{24}$
$vi.\ \frac{2}{3}$ and $\frac{33}{22}$
AnswerThe pairs of equivalent fractions are as follows:
$i.\ \frac{5}{6}\ \text{and}\ \frac{20}{24}$
$\Big(\frac{20}{24}=\frac{5\times4}{6\times4}\Big)$
$ii.\ \frac{3}{8}\ \text{and}\ \frac{15}{40}$
$\Big(\frac{15}{40}=\frac{3\times5}{8\times5}\Big)$
$iv.\ \frac{2}{9}\ \text{and}\ \frac{14}{63}$
$\Big(\frac{14}{63}=\frac{2\times7}{9\times7}\Big)$
View full question & answer→Question 322 Marks
Find the equivalent fraction of $\frac{5}{9}$ having: Denominator $54$
AnswerLet, $\frac{5}{9}=\frac{\Box}{54}$ Clearly, $54 = 9 \times 6$
So, we multiply the numerator by $6$
$\therefore\frac{5}{9}=\frac{5\times6}{9\times6}=\frac{30}{54}$
$\frac{5}{9}=\frac{30}{54}$
Hence, the required fraction is $\frac{30}{54}$.
View full question & answer→Question 332 Marks
Compare the fractions given below: $\frac{5}{6},\frac{9}{11}$
Answer$\frac{5}{6},\frac{9}{11}$
By cross multiplying: $5\times11=55$ and $9\times6=54$
Clearly, $55>54$
$\therefore\frac{5}{6}>\frac{9}{11}$
View full question & answer→Question 342 Marks
Determine: $\frac{2}{3}$ of $36$ pens
Answer$\frac{2}{3}$ of $36$ pens $=\frac{2}{3}\times36$ $=2\times12$ $=24$
View full question & answer→Question 352 Marks
Find the equivalent fraction of $\frac{36}{48}$ having: Denominator $4$
AnswerLet, $\frac{36}{48}=\frac{\Box}{4}$
Clearly, $4 = 48 ÷ 12$
So, we multiply the numerator by $12$
$\therefore\frac{36}{48}=\frac{36\div12}{48\div12}=\frac{3}{4}$
$\frac{36}{48}=\frac{3}{4}$
Hence, the required fraction is $\frac{24}{40}$.
View full question & answer→Question 362 Marks
Compare the fractions given below: $\frac{3}{8},\frac{5}{6}$
Answer$\frac{3}{8},\frac{5}{6}$
By cross multiplying: $3\times6=18$ and $5\times8=40$ Clearly, $18>40$
$\therefore\frac{3}{8}>\frac{5}{6}$
View full question & answer→Question 372 Marks
Write five fractions equivalent to the following: $\frac{5}{8}$
Answer$\frac{5}{8}$
$\frac{5\times2}{8\times2}=\frac{10}{16}$
$\frac{5\times3}{8\times3}=\frac{15}{24}$
$\frac{5\times4}{8\times4}=\frac{20}{32}$
$\frac{5\times5}{8\times5}=\frac{25}{40}$
$\frac{5\times6}{8\times6}=\frac{30}{48}$
Hence, the five fractions equivalent to $\frac{5}{8}$ are $\frac{10}{16},\frac{15}{24},\frac{20}{32},\frac{25}{40}$ and $\frac{30}{48}$.
View full question & answer→Question 382 Marks
Find the equivalent fraction of $\frac{3}{5}$ having: Numerator 24
AnswerLet, $\frac{3}{5}=\frac{24}{\Box}$ Clearly, $24 = 3 \times 8$
So, we multiply the denominator by $8$
$\therefore\frac{3}{5}=\frac{3\times8}{5\times8}=\frac{24}{40}$ $\frac{3}{5}=\frac{24}{40}$
Hence, the required fraction is $\frac{24}{40}$.
View full question & answer→Question 392 Marks
Find the equivalent fraction of $\frac{36}{48}$ with: Numerator $9$
AnswerLet, $\frac{36}{48}=\frac{9}{\Box}$ Clearly, $9 = 36 ÷ 4$
So, we divide the denominator by $4$
$\therefore\frac{36}{48}=\frac{36\div4}{48\div4}=\frac{9}{12}$
$\frac{36}{48}=\frac{9}{12}$
Hence, the required fraction is $\frac{9}{12}$.
View full question & answer→Question 402 Marks
Find the difference: $\frac{7}{12}-\frac{5}{12}$
AnswerDifference of like fractions = Difference of numerator ÷ Common denominator
$\frac{7}{12}-\frac{5}{12}$
$=\frac{(7-5)}{12}$
$=\frac{2}{12}$
$=\frac{1}{6}$
View full question & answer→Question 412 Marks
Draw number lines and locate the following points: $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{5}{8},\frac{7}{8}$
AnswerDraw $0$ to $1$ on a number line. Divide the segment into $8$ equal parts, each part corresponds to $\frac{1}{8}$.
Show the consecutive parts as $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{5}{8},\frac{7}{8}$ and $\frac{8}{8}$.
Highlight the required ones only.
View full question & answer→Question 422 Marks
Find the difference:
$\frac{1}{2}-\frac{3}{8}$
Answer$L.C.M$ of $2$ and $8 = (2 \times 2 \times 2) = 8$
Now, we have:
$\frac{1}{2}=\frac{1\times4}{2\times4}=\frac{4}{8}$
Therefore,
$\frac{1}{2}-\frac{3}{8}$
$=\frac{4}{8}-\frac{3}{8}$
$=\frac{(4-3)}{8}$
$=\frac{1}{8}$
View full question & answer→Question 432 Marks
What fraction of an hour is $35$ minutes?
AnswerAn hour has $60$ minutes
$\therefore$ Fraction for $35$ minutes $=\frac{35}{60}=\frac{7}{12}$
Hence, $\frac{7}{12}$ part of an hour is equal to $35$ minutes.
View full question & answer→Question 442 Marks
Represent the following fractions on the number line: $\frac{2}{5}$
AnswerDraw a $0$ to $1$ on a number line. Label point $1$ as $A$ and mark the starting point as $0$. Divide the number line from $0$ to $1$ into $5$ equal parts and take out $2$ parts from it to reach point $P$.
View full question & answer→Question 452 Marks
Determine:
$\frac{2}{3}$ of 15 pens
Answer $\frac{2}{3}$ of 15 pens
$=\frac{2}{3}\times15$
$=2\times5$
$=10$
View full question & answer→Question 462 Marks
Compare the fractions given below: $\frac{7}{11},\frac{6}{7}$
Answer$\frac{7}{11},\frac{6}{7}$
By cross multiplying: $7\times7=49$ and $11\times6=66$
Clearly, $49<66$
$\therefore\frac{7}{11}>\frac{6}{7}$
View full question & answer→Question 472 Marks
Compare the fractions given below: $\frac{3}{4},\frac{5}{6}$
Answer$\frac{3}{4},\frac{5}{6}$ By cross multiplying: $3\times6=18$ and $4\times5=20$ Clearly, $18<20$
$\therefore\frac{3}{4}<\frac{5}{6}$
View full question & answer→Question 482 Marks
Write five fractions equivalent to the following: $\frac{3}{7}$
Answer$\frac{3}{7}$
$\frac{3\times2}{7\times2}=\frac{6}{14}$
$\frac{3\times3}{7\times3}=\frac{9}{21}$
$\frac{3\times4}{7\times4}=\frac{12}{28}$
$\frac{3\times5}{7\times5}=\frac{15}{35}$
$\frac{3\times6}{7\times6}=\frac{18}{42}$
Hence, the five fractions equivalent to $\frac{3}{7}$ are $\frac{6}{14},\frac{9}{21},\frac{12}{28},\frac{15}{35}$ and $\frac{18}{42}$.
View full question & answer→Question 492 Marks
Find the difference: $2\frac{3}{10}-1\frac{7}{15}$
Answer$2\frac{3}{10}-1\frac{7}{15}$ $=\frac{23}{10}-\frac{22}{15}$
$L.C.M$ of $10$ and $15 = (2 \times 3 \times 5) = 30$
$=\frac{(69-44)}{30}$ $=\frac{25}{30}$
$=\frac{5}{6}$ $\Big(\frac{30}{10}=3,3\times23=69\Big)$ and $\Big(\frac{30}{15}=2,2\times22=44\Big)$
View full question & answer→Question 502 Marks
Determine: $\frac{3}{4}$ of $16$ cups
Answer$\frac{3}{4}$ of $16$ cups $=\frac{3}{4}\times16$ $=3\times4$ $=12$
View full question & answer→Question 512 Marks
Find the equivalent fraction of $\frac{6}{11}$ having:
Denominator $77$
AnswerLet, $\frac{6}{11}=\frac{\Box}{77}$
Clearly, $77 = 11 \times 7$
So, we multiply the numerator by $7$
$\therefore\frac{6}{11}=\frac{6\times7}{11\times7}=\frac{42}{77}$
$\frac{6}{11}=\frac{42}{77}$
Hence, the required fraction is $\frac{42}{77}$.
View full question & answer→Question 522 Marks
Find the sum: $\frac{4}{15}+\frac{17}{20}$
AnswerWe have, $L.C.M.$ of $15$ and $20 = (3 \times 5 \times 2 \times 2) = 60$
$\begin{array}{c|c}5&15,20\\\hline3&3,4\\\hline2&1,4\\\hline2&1,2\\\hline&1,1\end{array} $
Therefore, $\frac{4}{15}+\frac{17}{20}$ $=\frac{(16+51)}{60}$
$\Big(\frac{60}{15}=4,4\times4=16\Big)$ and $\Big(\frac{60}{20}=3,17\times3=51\Big)$
$=\frac{67}{60}$
$=1\frac{7}{60}$
View full question & answer→Question 532 Marks
Find the sum: $1\frac{3}{5}+2\frac{4}{5}$
AnswerThe given fractions are like fractions We know,
Sum of like fractions $=\frac{\text{Sum of the numerators}}{\text{Common denominator}}$
Thus, we have $1\frac{3}{5}+2\frac{4}{5}$
$=\frac{8}{5}+\frac{14}{5}$
$=\frac{(8+14)}{5}$
$=\frac{22}{5}$
$=4\frac{2}{5}$
View full question & answer→Question 542 Marks
Draw number lines and locate the following points: $\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{8}{5}$
AnswerDraw $0$ to $2$ on a number line. Divide the segment between $0$ and $1$ into $5$ equal parts, where each part is equal to $\frac{1}{5}$. Show $\frac{2}{5},\frac{3}{5},\frac{4}{5}$ and $\frac{8}{5}$ $3$ parts away from $1$ towards $2$. $\Big(1 <\frac{8}{5} < 2\Big)$
View full question & answer→Question 552 Marks
Find the difference: $4\frac{3}{7}-2\frac{4}{7}$
AnswerDifference of like fractions = Difference of numerator ÷ Common denominator
$4\frac{3}{7}-2\frac{4}{7}$ $=\frac{31}{7}-\frac{18}{7}$
$=\frac{(31-18)}{7}$ $=\frac{13}{7}$
View full question & answer→Question 562 Marks
Find the equivalent fraction of $\frac{6}{11}$ having:
Numerator 60
AnswerLet, $\frac{6}{11}=\frac{60}{\Box}$
Clearly, $60 = 6 \times 10$
So, we multiply the denominator by $10$
$\therefore\frac{6}{11}=\frac{6\times10}{11\times10}=\frac{60}{110}$
$\frac{6}{11}=\frac{60}{110}$
Hence, the required fraction is $\frac{60}{110}$.
View full question & answer→Question 572 Marks
Find the difference: $3\frac{5}{8}-2\frac{5}{12}$
Answer$3\frac{5}{8}-2\frac{5}{12}$ $=\frac{29}{8}-\frac{29}{12}$
$L.C.M$ of $8$ and $12 = (2 \times 2 \times 2 \times 3) = 24$ $=\frac{(87-58)}{24}$ $=\frac{29}{24}$
$=1\frac{5}{24}$ $\Big(\frac{24}{8}=3,3\times29=87\Big)$ and $\Big(\frac{24}{12}=2,2\times29=58\Big)$
View full question & answer→Question 582 Marks
Find the equivalent fraction of $\frac{3}{5}$ having: Denominator $30$
AnswerLet, $\frac{3}{5}=\frac{\Box}{30}$ Clearly, $30 = 5 \times 6$
So, we multiply the numerator by $6$
$\therefore\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}$
$\frac{3}{5}=\frac{18}{30}$
Hence, the required fraction is $\frac{18}{30}$.
View full question & answer→Question 592 Marks
Convert the following into a mixed fraction:$\frac{101}{8}$
AnswerOn dividing $101$ by $8$,
We get, Quotient $= 12$ Remainder $= 5$
Therefore, $\frac{101}{8}=12+\frac{5}{8}$ $=12\frac{5}{8}$
View full question & answer→Question 602 Marks
Determine: $\frac{3}{4}$ of $28$ rackets
Answer$\frac{3}{4}$ of $28$ rackets $=\frac{3}{4}\times28$ $=3\times7$ $=21$
View full question & answer→Question 612 Marks
Represent the following fractions on the number line:
$\frac{3}{8}$
AnswerDraw a $0$ to $1$ on a number line. Label point $1$ as $A$ and mark the starting point as $0.$
Divide the number line from $0$ to $1$ into $8$ equal parts and take out $3$ parts from it to reach point $P.$
View full question & answer→Question 622 Marks
Determine:
$\frac{3}{4}$ of $32$ books
Answer$\frac{3}{4}$ of $32$ books
$=\frac{3}{4}\times32$
$=3\times8$
$=24$
View full question & answer→Question 632 Marks
Find the sum: $\frac{7}{12}+\frac{9}{16}$
Answer$L.C.M.$ of $12$ and $16 = (2 \times 2 \times 2 \times 2 \times 3) = 48$
$\begin{array}{c|c}2&12,16\\\hline2&6,8\\\hline2&3,4\\\hline2&3,2\\\hline3&3,1\\\hline&1,1\end{array}$
Now, we know: $\frac{7}{12}=\frac{7\times4}{12\times4}=\frac{28}{48}$
$\frac{9}{16}=\frac{9\times3}{16\times3}=\frac{27}{48}$
Therefore, $\frac{7}{12}+\frac{9}{16}$
$=\frac{28}{48}+\frac{27}{48}$
$=\frac{(28+27)}{48}$
$=\frac{55}{48}$
$=1\frac{7}{48}$
View full question & answer→Question 642 Marks
Find the sum:
$\frac{4}{9}+\frac{8}{9}$
Answer The given fractions are like fractions
We know,
Sum of like fractions $=\frac{\text{Sum of the numerators}}{\text{Common denominator}}$
Thus, we have
$\frac{4}{9}+\frac{8}{9}$
$=\frac{(4+8)}{9}$
$=\frac{12}{9}$
$=\frac{4}{3}$
$=1\frac{1}{3}$
View full question & answer→Question 652 Marks
Find the equivalent fraction of $\frac{56}{70}$ with Denominator $10$
AnswerLet $\frac{56}{70}=\frac{\Box}{10}$ Clearly, $10 = 70 ÷ 7$
So, we divide the numerator by $7$
$\therefore\frac{56}{70}=\frac{56\div7}{70\div7}=\frac{8}{10}$
$\frac{56}{70}=\frac{8}{10}$
Hence, the required fraction is $\frac{8}{10}$.
View full question & answer→Question 662 Marks
Convert the following into a mixed fraction:$\frac{17}{5}$
AnswerOn dividing $17$ by $5$,
We get, Quotient = $3$ Remainder = $2$
Therefore, $\frac{17}{5}=3+\frac{2}{5}$
$=3\frac{2}{5}$
View full question & answer→Question 672 Marks
Determine: $\frac{2}{3}$ of $27$ pens
Answer$\frac{2}{3}$ of $27$ pens $=\frac{2}{3}\times27$ $=2\times9$ $=18$
View full question & answer→Question 682 Marks
Represent the following fractions on the number line: $\frac{5}{9}$
AnswerDraw a $0$ to $1$ on a number line.
Label point $1$ as $A$ and mark the starting point as $0$.
Divide the number line from $0$ to $1$ into $9$ equal parts and take out $5$ parts from it to reach point $P.$ 
View full question & answer→Question 692 Marks
Draw number lines and locate the following points: $\frac{1}{4},\frac{1}{2},\frac{3}{4},\frac{4}{4}$
AnswerDraw a number line. Mark $0$ as the starting point and $1$ as the ending point.
Then, divide $0$ to $1$ in four equal parts, where each part is equal to $\frac{1}{4}$.
Show the consecutive parts as $\frac{1}{4},\frac{1}{2},\frac{3}{4}$ and at $1$ show $\frac{4}{4}$ $= 1.$ 
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