Question 13 Marks
Find the sum:
$3\frac{1}{3}+4\frac{1}{4}+6\frac{1}{6}$
AnswerWe have,
$L.C.M$. of $3, 4$ and $6 = (2 \times 2 \times 3) = 12$
$\begin{array}{c|c}3&3,4,6\\\hline2&1,4,2\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
Therefore,
$3\frac{1}{3}+4\frac{1}{4}+6\frac{1}{6}$
$=\frac{10}{3}+\frac{17}{4}+\frac{37}{6}$
$=\frac{(40+51+74)}{12}$
$\Big(\frac{12}{3}=4,4\times10=40\Big)$
$\Big(\frac{12}{4}=3,3\times17=51\Big)$
and $\Big(\frac{12}{6}=2,2\times37=74\Big)$
$=\frac{165}{12}$
$=\frac{55}{4}$
$=13\frac{3}{4}$
View full question & answer→Question 23 Marks
Convert $\frac{1}{4},\frac{5}{8},\frac{7}{12}$ and $\frac{13}{24}$ into like fractions.
AnswerThe given fractions are $\frac{1}{4},\frac{5}{8},\frac{7}{12}$ and $\frac{13}{24}$
$L.C.M.$ of $4, 8, 12$ and $24 = (4 \times 2 \times 3) = 24$
So, we convert the given fractions into equivalent fractions with $24$ as the denominator.
(But, one of the fractions already has $24$ as its denominator.
So, there is no need to convert it into an equivalent fraction.)
Thus, we have: $\frac{1}{4}=\frac{1\times6}{4\times6}=\frac{6}{24}$,
$\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$,
$\frac{7}{12}=\frac{7\times2}{12\times2}=\frac{14}{24}$
Hence, the required like fractions are $\frac{6}{24},\frac{15}{24},\frac{14}{24}$ and $\frac{13}{24}$.
View full question & answer→Question 33 Marks
Find the sum:
$3\frac{2}{3}+1\frac{5}{6}+2$
AnswerWe have,
$L.C.M.$ of $3$ and $6 = (2 \times 3) = 6$
$\begin{array}{c|c}3&3,6\\\hline2&1,2\\\hline&1,1\end{array}$
Therefore,
$3\frac{2}{3}+1\frac{5}{6}+2$
$=\frac{11}{3}+\frac{11}{6}+\frac{2}{1}$
$=\frac{(22+11+12)}{6}$
$\Big(\frac{6}{3}=2,2\times11=22\Big)$
$\Big(\frac{6}{6}=1,1\times11=11\Big)$
and $\Big(\frac{6}{1}=6,6\times2=12\Big)$
$=\frac{45}{6}$
$=\frac{15}{2}$
$=7\frac{1}{2}$
View full question & answer→Question 43 Marks
Lalita read $30$ pages of a book containing $100$ pages while Sarita read $\frac{2}{5}$ of the book. Who read more?
AnswerLalita read $30$ pages of a book having $100$ pages Sarita read $\frac{2}{5}$ of the same book $\frac{2}{5}$ of $100$ pages = $\frac{2}{5}\times100$
$=\frac{200}{5}=40 = 40$ pages
Hence, Sarita read more pages than Lalita as $40$ is greater than $30.$
View full question & answer→Question 53 Marks
In a school $20$ students out of $25$ passed in $VI A$, while $24$ out of $30$ passed in $VI B$. Which section gave better result?
AnswerFraction of students who passed in $ VI A =\frac{20}{25}$
$=\frac{20\div5}{25\div5}=\frac{4}{5}$
Fraction of students who passed in $VI B =\frac{24}{30}$
$=\frac{24\div6}{30\div6}=\frac{4}{5}$
In both the sections, the fraction of students who passed is the same, so both the sections have the same result.
View full question & answer→Question 63 Marks
Reduce the following fractions into its simplest form: $\frac{150}{60}$
AnswerHere, numerator $= 150$ and denominator $= 60$ Factors of $150$ are $1, 2, 3, 5, 6, 10, 15, 25, 30, 75$ and $150$
Factors of $60$ are $1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30$ and $60$
Common factors of $150$ and $60$ are $1, 2, 3, 5, 6, 10, 15$ and $30 H.C.F$. of $150$ and $60$ is $30.$
$\therefore\frac{150}{60}=\frac{150\div30}{60\div30}=\frac{5}{2}$
Hence, the simplest form of $\frac{150}{60}$ is $\frac{5}{2}$.
View full question & answer→Question 73 Marks
Show that the following fractions is in the simplest form: $\frac{8}{11}$
View full question & answer→Question 83 Marks
Subtract the sum of $3\frac{5}{9}$ and $3\frac{1}{3}$ from the sum of $5\frac{5}{6}$ and $4\frac{1}{9}$.
Answer$\Big(5\frac{5}{6}+4\frac{1}{9}\Big)-\Big(3\frac{5}{9}+3\frac{1}{3}\Big)$$\Big(\frac{35}{6}+\frac{37}{9}\Big)-\Big(\frac{32}{9}+\frac{10}{3}\Big)$
$\begin{array}{c|c}2&6,9,3\\\hline3&3,9,3\\\hline3&1,3,1\\\hline&1,1,1\end{array}$
$L.C.M$. of $3, 6$ and $9 = (2 \times 2 \times 3) = 18$
$=\frac{[105+74]-[64+60]}{18}$
$\Big(\frac{18}{6}=3,3\times35=105\Big)$
and $\Big(\frac{18}{9}=2,2\times37=74\Big)$
$\Big(\frac{18}{9}=2,2\times32=64\Big)$
and $\Big(\frac{18}{3}=6,6\times10=60\Big)$
$=\frac{[179]-[124]}{18}$
$=\frac{55}{18}$
$=3\frac{1}{18}$
View full question & answer→Question 93 Marks
Find the sum: $3\frac{1}{8}+1\frac{5}{12}$
Answer$L.C.M.$ of $8$ and $12 = (2 × 2 × 2 × 3) = 34$
$\begin{array}{c|c}2&8,12\\\hline2&4,6\\\hline2&2,3\\\hline3&1,3\\\hline&1,1\end{array} $
Therefore, $3\frac{1}{8}+1\frac{5}{12}$
$=\frac{25}{8}+\frac{17}{12}$
$=\frac{(75+34)}{24}$
$\Big(\frac{24}{8}=3,3\times25=75\Big)$ and $\Big(\frac{24}{12}=2,2\times17=34\Big)$
$=\frac{109}{24}$
$=4\frac{13}{24}$
View full question & answer→Question 103 Marks
The weight of an empty gas cylinder is $16\frac{4}{5}\text{kg}$ and it contains $14\frac{2}{3}\text{kg}$ of gas. What is the weight of the cylinder filled with gas?
AnswerWeight of the cylinder filled with gas = Weight of the empty cylinder $+$ Weight of the gas inside the cylinder
Thus, we have: $(L.C.M .of 5$ and $3 = (5 \times 3) = 15$
$\Big(16\frac{4}{5}+14\frac{2}{3}\Big)\text{kg}$
$=\Big(\frac{84}{5}+\frac{44}{3}\Big)\text{kg}$
$=\frac{(252+220)}{15}\text{kg}$
$=\frac{472}{15}\text{kg}$
$=31\frac{7}{15}\text{kg}$
Hence, the weight of the cylinder filled with gas is $31\frac{7}{15}\text{kg}$.
View full question & answer→Question 113 Marks
Simplify:$\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$
AnswerWe have:$\frac{5}{8}+\frac{3}{4}-\frac{7}{12}$
$\begin{array}{c|c}2&4,8,12\\\hline2&2,4,6\\\hline2&1,2,3\\\hline3&1,1,3\\\hline&1,1,1\end{array}$
$L.C.M.$ of $4, 8$ and $12 = (2 \times 2 \times 2 \times 3) = 24$
$=\frac{(15+18-14)}{24}$
$\Big(\frac{24}{8}=3,3\times5=15\Big)$
$\Big(\frac{24}{4}=6,6\times3=18\Big)$ and $\Big(\frac{24}{12}=2,2\times7=14\Big)$
$=\frac{(33-14)}{24}$
$=\frac{19}{24}$
View full question & answer→Question 123 Marks
Mrs Soni bought $7\frac{1}{2}$ litres of milk. Out of this milk, $5\frac{3}{4}$ litres was consumed. How much milk is left with her?
AnswerAmount of milk left with Mrs. Soni = Total amount of milk bought by her - Amount of milk consumed
$\therefore$ Amount of milk left with Mrs. Soni $=7\frac{1}{2}-5\frac{3}{4}$
$=\frac{15}{2}-\frac{23}{4}$
$L.C.M.$ of $2$ and $4 = (2 \times 2) = 4$
$=\frac{30-23}{4}$
$\Big(\frac{4}{2}=2,2\times15=30\Big)$ and $\Big(\frac{4}{4}=1,1\times23=23\Big)$
$=\frac{7}{4}$
$=1\frac{3}{4}\ \text{litres}$
Therefore, Milk left with Mrs. Soni $=1\frac{3}{4}\ \text{litres}$
View full question & answer→Question 133 Marks
What should be added to $9\frac{2}{3}$ to get $19?$
AnswerLet x be added to $9\frac{2}{3}$ to get $19$
Therefore, $9\frac{2}{3}+\text{x}=19$ Thus,
we have: $\text{x}=19-9\frac{2}{3}$ $=\frac{19}{1}-\frac{29}{3}$
$L.C.M.$ of $1$ and $3$ is 3$=\frac{(57-29)}{3}$
$\Big(\frac{3}{1}=3,3\times19=57\Big)$
and $\Big(\frac{3}{3}=1,1\times29=29\Big)$
$=\frac{28}{3}$
$=9\frac{1}{3}$
View full question & answer→Question 143 Marks
Show that the following fractions is in the simplest form: $\frac{9}{14}$
AnswerHere, numerator $= 9$ and denominator $= 14$
Factors of $9$ are $1, 3$ and $9$
Factors of $14$ are $1, 2, 7$ and $14$
Common factor of $9$ and $14$ is $1$
Thus, $H.C.F.$ of $9$ and $14$ is $1$
Hence, $\frac{9}{14}$ is the simplest form.
View full question & answer→Question 153 Marks
Sohini bought $4\frac{1}{2}\text{m}$ of cloth for her kurta and $2\frac{2}{3}\text{m}$ of cloth for her pyjamas. Ho much cloth did she purchase in all?
AnswerTotal cloth purchased by Sohini = Cloth for kurta + Cloth for pyjamas
Thus, we have:
$\Big(4\frac{1}{2}+2\frac{2}{3}\Big)\ \text{m}$
$=\Big(\frac{9}{2}+\frac{8}{3}\Big)\ \text{m}$
$(L.C.M.$ of $2$ and $3 = (2 \times 3) = 6)$
$=\Big(\frac{(27+16)}{6}\Big)\ \text{m}$
$\Big(\frac{16}{2}=3,3\times9=27\Big)$
and $\Big(\frac{6}{3}=2,2\times8=16\Big)$
$=\frac{43}{6}\ \text{m}$
$=7\frac{1}{6}\ \text{m}$
$\therefore$ Total length of cloth purchased $=7\frac{1}{6}\ \text{m}$
View full question & answer→Question 163 Marks
Simplify:$5\frac{3}{4}-4\frac{5}{12}+3\frac{1}{6}$
AnswerWe have:$5\frac{3}{4}-4\frac{5}{12}+3\frac{1}{6}$
$\frac{23}{4}-\frac{53}{12}+\frac{19}{6}$
$\begin{array}{c|c}2&4,12,6\\\hline2&2,6,3\\\hline3&1,2,3\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
$L.C.M$. of $4, 12$ and $6 = (2 \times 2 \times 3) = 12$
$=\frac{(69-53+38)}{12}$
$\Big(\frac{12}{4}=3,3\times23=69\Big)$
$\Big(\frac{12}{12}=1,1\times53=53\Big)$ and
$\Big(\frac{12}{6}=2,2\times19=38\Big)$
$=\frac{(107-53)}{12}$
$=\frac{54}{12}$
$=\frac{9}{2}$
$=4\frac{1}{2}$
View full question & answer→Question 173 Marks
Neelam has $25$ pencils. She gives $\frac{4}{5}$ of them to Meena. How many pencils does Meena get? How many pencils are left with Neelam?
AnswerNeelam gives $\frac{4}{5}$ of $25$
pencils to Meena $\Big(\frac{4}{5}\times25\Big) = 20$
Pencils Thus, Meena gets $20$ pencils.
Therefore, Number of pencils left with Neelam $= 25 - 20 = 5$ pencils
Thus, $5$ pencils are left with Neelam
View full question & answer→Question 183 Marks
Rohit bought a pencil for Rs. $3\frac{2}{5}$ and an eraser for Rs. $2\frac{7}{10}$. What is the total cost of both the articles?
AnswerTotal cost of both articles $=$ Cost of pencil $+$ Cost of eraser
Thus, we have: $\text{Rs.}\ 3\frac{2}{5}+\text{Rs.}\ 2\frac{7}{10}$
$=\frac{17}{5}+\frac{27}{10}$
$=\frac{(34+27)}{10}$
$(L.C.M.$ of $5$ and $10 = (5 \times 2) = 10)$
$=\frac{61}{10}$
$=\text{Rs.}\ 6\frac{1}{10}$
Hence, the total cost of both the articles is $\text{Rs.}\ 6\frac{1}{10}$.
View full question & answer→Question 193 Marks
Show that the following fractions is in the simplest form: $\frac{8}{15}$
AnswerHere, numerator $= 8$ and denominator $= 15$
Factors of 8 are $1, 2, 4$ and $8$ Factors of $15$ are $1, 3, 5$ and $15$
Common factor of $8$ and $15$ is $1$
Thus, $H.C.F$. of $8$ and $15$ is $1$
Hence, $\frac{8}{15}$ is the simplest form.
View full question & answer→Question 203 Marks
Reduce the following fractions into its simplest form:
$\frac{48}{60}$
AnswerHere, numerator $= 84$ and denominator $= 98$
Factors of $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 42$ and $84$
Factors of $98$ are $1, 2, 7, 14, 49$ and $98$
Common factors of $84$ and $98$ are $1, 2, 7$ and $14$
$H.C.F.$ of $84$ and $98$ is $14$
$\therefore\frac{48}{60}=\frac{48\div12}{60\div12}=\frac{4}{5}$
Hence, the simplest form of $\frac{48}{60}$ is $\frac{4}{5}$.
View full question & answer→Question 213 Marks
What should be added to $6\frac{7}{15}$ to get $8\frac{1}{5}$?
AnswerLet $x$ be added to $6\frac{7}{15}$ to get $8\frac{1}{5}$
Therefore, $6\frac{7}{15}+\text{x}=8\frac{1}{5}$
Thus, we have: $\text{x}=8\frac{1}{5}-6\frac{7}{15}$
$=\frac{41}{5}-\frac{97}{15}$ $L.C.M$. of $5$ and $15 = (5 \times 3) = 15 =\frac{(123-97)}{15}$
$\Big(\frac{15}{5}=3,3\times41=123\Big)$
and $\Big(\frac{15}{15}=1,1\times97=97\Big)$
$=\frac{26}{15}$
$=1\frac{11}{15}$
View full question & answer→Question 223 Marks
Simplify:$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}$
AnswerWe have:$3+1\frac{1}{5}+\frac{2}{3}-\frac{7}{15}$
$=\frac{3}{1}+\frac{6}{5}+\frac{2}{3}-\frac{7}{15}$
$\begin{array}{c|c}5&5,3,15\\\hline3&1,3,3\ \\\hline&1,1,1\ \end{array}$
$L.C.M$. of $5, 3$ and $15 = (5 \times 3) = 15$
$=\frac{(45+18+10-7)}{15}$
$\Big(\frac{15}{1}=15,15\times3=45\Big)$
$\Big(\frac{15}{5}=3,3\times6=18\Big)$
$\Big(\frac{15}{3}=5,5\times2=10\Big)$ and
$\Big(\frac{15}{15}=1,1\times7=7\Big)$
$=\frac{(73-7)}{15}$
$=\frac{66}{15}$
$=\frac{22}{5}$
$=4\frac{2}{5}$
View full question & answer→Question 233 Marks
Show that the following fractions is in the simplest form:
$\frac{21}{10}$
AnswerHere, numerator $= 21$ and denominator $= 10$
Factors of $21$ are $1, 3, 7$ and $21$
Factors of $10$ are $1, 2, 5$ and $10$
Common factor of $21$ and $10$ is $1$
Thus, $H.C.F.$ of $21$ and $10$ is $1.$
Hence, $\frac{21}{10}$ is the simplest form.
View full question & answer→Question 243 Marks
Rafiq exercised for $\frac{2}{3}$ hour, while Rohit exercise for $\frac{3}{4}$ hour. Who exercised for a longer time?
AnswerTo know who exercised for a longer time,
we have to compare $\frac{2}{3}$ hour with $\frac{3}{4}$
hour On cross multiplying: $4 \times 2 = 8$ and $3 \times 3 = 9$
Clearly, $8 < 9$
$\therefore\frac{2}{3}$
hour $< \frac{3}{4}$ hour
Hence, Rohit exercised for a longer time.
View full question & answer→Question 253 Marks
Convert $\frac{3}{5},\frac{7}{10},\frac{8}{15}$ and $\frac{11}{30}$ into like fractions.
AnswerThe given fractions are $\frac{3}{5},\frac{7}{10},\frac{8}{15}$ and $\frac{11}{30}$
$\begin{array}{c|c}5&5,10,15,30\\\hline2&1,2,3,6\ \ \ \ \ \ \\\hline3&1,1,3,3\ \ \ \ \ \\\hline&1,1,1,1\ \ \ \ \ \end{array}$
$L.C.M$. of $5, 10, 15$ and $30 = (5 \times 2 \times 3) = 30$
So, we convert the given fractions into equivalent fractions with $30$ as the denominator.
(But, one of the fractions already has $30$ as its denominator.
So, there is no need to convert it into an equivalent fraction.)
Thus, we have: $\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}$,
$\frac{7}{10}=\frac{7\times3}{10\times3}=\frac{21}{30}$,
$\frac{8}{15}=\frac{8\times2}{15\times2}=\frac{16}{30}$
Hence, the required like fractions are $\frac{18}{30},\frac{21}{30},\frac{16}{30}$ and $\frac{11}{30}$.
View full question & answer→Question 263 Marks
Find the sum: $2\frac{1}{3}+1\frac{1}{4}+2\frac{5}{6}+3\frac{7}{12}$
AnswerWe have, $L.C.M$. of $3, 4, 6$ and $12 = (2 \times 2 \times 3) = 12$
$\begin{array}{c|c}2&3,4,6,12\\\hline2&3,2,3,6\ \ \\\hline3&3,1,3,3\ \ \\\hline&1,1,1,1\ \ \end{array}$
Therefore, $2\frac{1}{3}+1\frac{1}{4}+2\frac{5}{6}+3\frac{7}{12}$
$=\frac{7}{3}+\frac{5}{4}+\frac{17}{6}+\frac{43}{12}$
$=\frac{(28+15+34+43)}{12}$
$\Big(\frac{12}{3}=4,4\times7=28\Big)$
$\Big(\frac{12}{4}=3,3\times5=15\Big)$
$\Big(\frac{12}{6}=2,2\times17=34\Big)$ and
$\Big(\frac{12}{12}=1,1\times43=43\Big)$
$=\frac{120}{12}$
$=10$
View full question & answer→Question 273 Marks
Simplify:$2+5\frac{7}{10}-3\frac{14}{15}$
AnswerWe have:$2+5\frac{7}{10}-3\frac{14}{15}$
$=\frac{2}{1}+\frac{57}{10}-\frac{59}{15}$
$\begin{array}{c|c}5&4,10,15\\\hline2&1,2,3\ \ \\\hline3&1,1,3\ \ \\\hline&1,1,1\ \ \end{array}$
$L.C.M.$ of $10$ and $15 = (2 \times 5 \times 3) = 30$
$=\frac{(69+171-118)}{30}$
$\Big(\frac{30}{1}=30,30\times2=60\Big)$
$\Big(\frac{30}{10}=3,3\times57=171\Big)$ and $\Big(\frac{30}{15}=2,2\times59=118\Big)$
$=\frac{(231-118)}{30}$
$=\frac{113}{30}$
$=3\frac{23}{30}$
View full question & answer→Question 283 Marks
Reduce the following fractions into its simplest form: $\frac{84}{98}$
AnswerHere, numerator $= 84$ and
denominator $= 98$
Factors of $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 42$ and $84$
Factors of $98$ are $1, 2, 7, 14, 49$ and $98$
Common factors of $84$ and $98$ are $1, 2, 7$ and $14 H.C.F$. of $84$ and $98$ is $14$
$\therefore\frac{84}{98}=\frac{84\div14}{98\div14}=\frac{6}{7}$
Hence, the simplest form of $\frac{84}{98}$ is $\frac{6}{7}$.
View full question & answer→Question 293 Marks
Simplify:
$\frac{5}{6}-\frac{4}{9}+\frac{2}{3}$
AnswerWe have, $\frac{5}{6}-\frac{4}{9}+\frac{2}{3}$
$\begin{array}{c|c}3&3,6,9\\\hline3&1,2,3\\\hline2&1,2,1\\\hline&1,1,1\end{array}$
$L.C.M.$ of $3, 6$ and $9 = (2 \times 3 \times 3) = 18$
$=\frac{(15+8+12)}{18}$
$\Big(\frac{18}{6}=3,3\times5=15\Big)$
$\Big(\frac{18}{9}=2,2\times4=8\Big)$ and
$\Big(\frac{18}{3}=6,6\times2=12\Big)$
$=\frac{(27-8)}{18}$
$=\frac{19}{18}$
$=1\frac{1}{18}$
View full question & answer→Question 303 Marks
Find the difference:
$2\frac{7}{9}-1\frac{8}{15}$
Answer$\begin{array}{c|c}3&9,15\\\hline3&3,5\ \ \\\hline5&1,5\ \ \\\hline&1,1\ \ \end{array}$
$L.C.M$ of $9$ and $15 = (3 \times 3 \times 5) = 45$
$2\frac{7}{9}-1\frac{8}{15}$
$=\frac{25}{9}-\frac{23}{15}$
$=\frac{(125-69)}{45}$
$=\frac{56}{45}$
$=1\frac{11}{45}$
$\Big(\frac{45}{9}=5,5\times25=125\Big)$
and $\Big(\frac{45}{15}=3,3\times23=69\Big)$
View full question & answer→Question 313 Marks
Simplify:$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$
AnswerWe have:$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$
$=\frac{53}{6}-\frac{27}{8}+\frac{31}{12}$
$\begin{array}{c|c}2&6,8,12\\\hline2&3,4,6\ \\\hline3&3,2,3\ \\\hline2&1,2,1\ \\\hline&1,1,1\ \end{array}$
$L.C.M.$ of $6, 8$ and $12 = (2 \times 2 \times 2 \times 3) = 24$
$=\frac{(212-81+62)}{24}$
$\Big(\frac{24}{6}=4,4\times53=212\Big)$
$\Big(\frac{24}{8}=23,3\times7=81\Big)$ and
$\Big(\frac{24}{12}=2,2\times31=62\Big)$$=\frac{(274-81)}{24}$
$=\frac{193}{24}$
$=8\frac{1}{24}$
View full question & answer→Question 323 Marks
Show that the following fractions is in the simplest form: $\frac{25}{36}$
AnswerHere, numerator $= 25$ and denominator $= 36$
Factors of $25$ are $1, 5$ and $25$
Factors of $36$ are $1, 2, 3, 4, 6, 9, 12, 18$ and $36$
Common factor of $25$ and $36$ is $1$ Thus,
$H.C.F$. of $25$ and $36$ is $1$
Hence, $\frac{25}{36}$ is the simplest form.
View full question & answer→Question 333 Marks
Find the sum: $2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$
AnswerWe have, $L.C.M$. of $4, 8$ and $16 = (2 \times 2 \times 2 \times 2) = 16$
$\begin{array}{c|c}2&4,8,16\\\hline2&2,4,8\\\hline2&1,2,4\\\hline2&1,1,2\\\hline&1,1,1\end{array}$
Therefore, $2+\frac{3}{4}+1\frac{5}{8}+3\frac{7}{16}$
$=\frac{2}{1}+\frac{3}{4}+\frac{13}{8}+\frac{55}{16}$
$=\frac{(32+12+26+55)}{16}$
$\Big(\frac{16}{1}=16,6\times2=32\Big)$
$\Big(\frac{16}{4}=4,4\times3=12\Big)$
$\Big(\frac{16}{8}=2,2\times13=26\Big)$ and
$\Big(\frac{16}{16}=1,1\times55=55\Big)$
$=\frac{125}{16}$
$=7\frac{13}{16}$
View full question & answer→Question 343 Marks
Compare the fractions given below: $\frac{7}{8},\frac{9}{10}$
Answer$L.C.M$. of $8$ and $10 = (2 \times 5 \times 2 \times 2) = 40$
Now, we convert $\frac{7}{8}$ and $\frac{9}{10}$
into equivalent fractions having $40$ as the denominator.
$\therefore\frac{7}{8}=\frac{7\times5}{8\times5}=\frac{35}{40}$ and
$\frac{9}{10}=\frac{9\times4}{10\times4}=\frac{36}{40}$
Clearly, $\frac{35}{40}<\frac{36}{40}$
$\therefore\frac{7}{8}<\frac{9}{10}$
View full question & answer→Question 353 Marks
Simplify:$8-3\frac{1}{2}-2\frac{1}{4}$
AnswerWe have:$8-3\frac{1}{2}-2\frac{1}{4}$
$=\frac{8}{1}-\frac{7}{2}-\frac{9}{4}$
$\begin{array}{c|c}2&1,2,4\\\hline2&1,1,2\\\hline&1,1,1\end{array}$
$L.C.M.$ of $1, 2$ and $4 = (2 \times 2) = 4$
$=\frac{(32-14-9)}{4}$
$\Big(\frac{4}{1}=4,4\times8=32\Big)$
$\Big(\frac{4}{2}=2,2\times7=14\Big)$ and
$\Big(\frac{4}{4}=1,1\times9=9\Big)$
$=\frac{(32-23)}{34}$
$=\frac{9}{4}$
$=2\frac{1}{4}$
View full question & answer→Question 363 Marks
In one day, a rickshaw puller earned $\text{Rs.}\ 137\frac{1}{2}$. Out of this money, he spent $\text{Rs.}\ 56\frac{3}{4}$ on food. How much money is left with him?
AnswerMoney left with the rickshaw puller $=$ Money earned by him in a day $-$ Money spent by him on food
$=\text{Rs.}\ \Big(137\frac{1}{2}-56\frac{3}{4}\Big)$
$L.C.M.$ of $2$ and $4 = (2 \times 2) = 4$
$=\text{Rs.}\ \Big(\frac{275}{2}-\frac{227}{4}\Big)$
$\Big(\frac{4}{2}=2,2\times275=550\Big)$ and $\Big(\frac{4}{4}=1,1\times227=227\Big)$
$=\text{Rs.}\ \Big(\frac{550-227}{4}\Big)$
$=\text{Rs.}\ \Big(\frac{323}{4}\Big)$
$=\text{Rs.}\ 80\frac{3}{4}$ Hence, $\text{Rs.}\ 80\frac{3}{4}$ is left with the rickshaw puller.
View full question & answer→Question 373 Marks
Find the sum:
$\frac{2}{3}+3\frac{1}{6}+4\frac{2}{9}+2\frac{5}{18}$
AnswerWe have,
$L.C.M.$ of $3, 6, 9$ and $18 = (3 \times 3 \times 2) = 18$
$\begin{array}{c|c}3&3,6,9,18\\\hline3&1,2,3,6\ \ \\\hline2&1,2,1,2\ \ \\\hline&1,1,1,1\ \end{array}$
Therefore,
$\frac{2}{3}+3\frac{1}{6}+4\frac{2}{9}+2\frac{5}{18}$
$=\frac{2}{3}+\frac{19}{6}+\frac{38}{9}+\frac{41}{18}$
$=\frac{(12+57+76+41)}{18}$
$\Big(\frac{18}{3}=6,6\times2=12\Big)$
$\Big(\frac{18}{6}=3,3\times19=57\Big)$
$\Big(\frac{18}{9}=2,2\times38=76\Big)$
and $\Big(\frac{18}{18}=1,1\times41=41\Big)$
$=\frac{186}{18}$
$=\frac{31}{3}$
$=10\frac{1}{3}$
View full question & answer→Question 383 Marks
Find the difference: $\frac{5}{6}-\frac{4}{9}$
Answer$\begin{array}{c|c}3&6,9\\\hline2&2,3\\\hline3&1,3\\\hline&1,1\end{array}$
$L.C.M$ of $6$ and $9 = (3 \times 2 \times 3) = 18$
Now, we have:
$\frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}$
$\frac{4}{9}=\frac{4\times2}{9\times2}=\frac{8}{18}$
Therefore,
$\frac{5}{6}-\frac{4}{9}$
$=\frac{15}{18}-\frac{8}{18}$
$=\frac{(15-8)}{18}$
$=\frac{7}{18}$
View full question & answer→Question 393 Marks
Convert the fractions $\frac{1}{2},\frac{ 2}{3}, \frac{4}{9}$ and $\frac{5}{6}$ into like fractions.
AnswerThe given fractions are $\frac{1}{2},\frac{ 2}{3}, \frac{4}{9},\frac{5}{6}$
$L.C.M$. of $2, 3, 9$ and $6 = (2 ⨯ 3 ⨯ 3) = 18$
Now, we have: $\frac{1}{2}=\frac{1\times9}{2\times9}=\frac{9}{18}$
$\frac{2}{3}=\frac{2\times6}{3\times6}=\frac{12}{18}$
$\frac{4}{9}=\frac{4\times2}{9\times2}=\frac{8}{18}$
$\frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}$
Hence, $\frac{9}{18},\frac{12}{18}, \frac{8}{18}$ and $\frac{15}{18}$ are like fractions.
View full question & answer→Question 403 Marks
Find the sum:
$3+1\frac{4}{15}+1\frac{3}{20}$
AnswerWe have,
$L.C.M$. of $15$ and $20 = (2 \times 2 \times 3 \times 5) = 60$
$\begin{array}{c|c}5&15,20\\\hline3&3,4\ \ \ \ \\\hline2&1,4\ \ \ \ \\\hline2&1,2\ \ \ \ \ \\\hline&1,1\ \ \ \ \ \end{array} $
Therefore,
$3+1\frac{4}{15}+1\frac{3}{20}$
$=\frac{3}{1}+\frac{19}{15}+\frac{23}{20}$
$=\frac{(180+76+69)}{60}$
$\Big(\frac{60}{1}=60,60\times3=180\Big)$
$\Big(\frac{60}{15}=4,4\times19=76\Big)$
and $\Big(\frac{60}{20}=3,3\times23=69\Big)$
$=\frac{325}{60}$
$=\frac{65}{12}$
$=5\frac{5}{12}$
View full question & answer→Question 413 Marks
Simplify:$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$
AnswerWe have:$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$
$=\frac{37}{6}-\frac{26}{5}+\frac{10}{3}$
$\begin{array}{c|c}2&6,5,3\\\hline3&3,5,3\\\hline5&1,5,1\\\hline&1,1,1\end{array}$
$L.C.M$. of $6, 5$ and $3 = (2 \times 5 \times 3) = 30$
$=\frac{(185-156+100)}{30}$
$\Big(\frac{30}{6}=5,5\times37=185\Big)$
$\Big(\frac{30}{5}=6,6\times26=156\Big)$ and
$\Big(\frac{30}{3}=10,10\times10=100\Big)$
$=\frac{(285-156)}{30}$
$=\frac{129}{30}$
$=\frac{43}{10}$
$=4\frac{3}{10}$
View full question & answer→Question 423 Marks
Find the sum: $2\frac{7}{10}+3\frac{8}{15}$
AnswerWe have, $L.C.M$. of $10$ and $15 = (2 \times 3 \times 5) = 30$
$\begin{array}{c|c}5&10,15\\\hline2&2,3\\\hline3&1,3\\\hline&1,1\end{array} $
Therefore, $2\frac{7}{10}+3\frac{8}{15}$
$=\frac{27}{10}+\frac{53}{15}$
$=\frac{(81+106)}{30}$
$\Big(\frac{30}{10}=3,3\times27=81\Big)$ and
$\Big(\frac{30}{15}=2,2\times53=106\Big)$
$=\frac{187}{30}$
$=6\frac{7}{30}$
View full question & answer→Question 433 Marks
Reduce $\frac{84}{98}$ to the simplest form.
AnswerThe factors of $84$ are $1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84$
The factors of $98$ are $1, 2, 7, 14, 49, 98$
The common factors of $84$ and $98$ are $1, 2, 7, 14$
The $H.C.F.$ of $84$ and $98$ is $14$
Dividing both the numerator and the denominator by the
$H.C.F \frac{84}{98}=\frac{84\div14}{98\div14}=\frac{6}{7}$
View full question & answer→Question 443 Marks
Compare the fractions given below:
$\frac{4}{5},\frac{7}{10}$
Answer$L.C.M.$ of $5$ and $10 = (5 \times 2) = 10$
Now, we convert $\frac{4}{5}$ into equivalent fractions having $10$ as the denominator.
$\therefore\frac{4}{5}=\frac{4\times2}{5\times2}=\frac{8}{10}$
Clearly, $\frac{8}{10}<\frac{7}{10}$
$\therefore\frac{4}{5}<\frac{7}{10}$
View full question & answer→Question 453 Marks
Simplify:$2+\frac{11}{15}-\frac{5}{9}$
AnswerWe have:$2+\frac{11}{15}-\frac{5}{9}$
$\begin{array}{c|c}3&1,15,9\\\hline3&1,5,3\ \\\hline5&1,5,1\ \\\hline&1,1,1\ \end{array}$
$L.C.M.$ of $15$ and $9 = (3 \times 3 \times 5) = 45$
$=\frac{(90+33-25)}{45}$
$\Big(\frac{45}{1}=45,45\times2=90\Big)$
$\Big(\frac{45}{15}=3,3\times11=33\Big)$ and
$\Big(\frac{45}{9}=5,5\times5=25\Big)$
$=\frac{(98+8)}{45}$
$=\frac{98}{45}$
$=2\frac{8}{45}$
View full question & answer→Question 463 Marks
Compare the fractions given below: $\frac{4}{9},\frac{5}{6}$
Answer$L.C.M.$ of $9$ and $6 = (3 \times 3 \times 2) = 18$
Now, we convert $\frac{4}{9}$ and $\frac{5}{6}$ into equivalent fractions having $18$ as the denominator.
$\therefore\frac{4}{9}=\frac{4\times2}{9\times2}=\frac{8}{18}$ and
$\frac{5}{6}=\frac{5\times3}{6\times3}=\frac{15}{18}$
Clearly, $\frac{8}{18}<\frac{15}{18}$
$\therefore\frac{4}{9}<\frac{5}{6}$
View full question & answer→Question 473 Marks
Of $\frac{3}{4}$ and $\frac{5}{7}$, which is greater and by how much?
AnswerLet us compare $\frac{3}{4}$ and $\frac{5}{7}$ By
cross multiplying: $3 ⨯ 7 = 21$ and $4 ⨯ 5 = 20$
Clearly, $21 > 20$
$\therefore\frac{3}{4}>\frac{5}{7}$
Their difference: $\frac{3}{4}-\frac{5}{7}$
$L.C.M.$ of $4$ and $7 = (2 \times 2 \times 7) = 28$
$(28\div4=7,7\times3=21)$ and $(28\div7=4,4\times5=20)$
$=\frac{21-20}{28}$
$=\frac{1}{28}$
Hence, $\frac{3}{4}$ is greater than $\frac{5}{7}$ by $\frac{1}{28}$.
View full question & answer→Question 483 Marks
Find the equivalent fraction of $\frac{3}{5}$ having denominator $30.$
AnswerLet $\frac{3}{5}=\frac{}{30}$
$30 = 5 ⨯ 6$
So, we have to multiply the numerator by $6$ to get the equivalent fraction having denominator $30$
$\therefore\frac{3}{5}=\frac{3\times6}{5\times6}=\frac{18}{30}$
Thus, $\frac{18}{30}$ is the equivalent fraction of $\frac{3}{5}$.
View full question & answer→Question 493 Marks
Find the difference: $\frac{5}{8}-\frac{7}{12}$
Answer$\begin{array}{c|c}2&8,12\\\hline2&4,6\\\hline2&2,3\\\hline3&1,3\\\hline&1,1\end{array}$
$L.C.M$ of $2$ and $8 = (2 \times 2 \times 2 \times 3) = 24$
Now, we have:
$\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$
$\frac{7}{12}=\frac{7\times2}{12\times2}=\frac{14}{24}$
Therefore,
$\frac{5}{8}-\frac{7}{12}$
$=\frac{15}{24}-\frac{14}{24}$
$=\frac{(15-14)}{4}$
$=\frac{1}{24}$
View full question & answer→Question 503 Marks
While coming back home from his school, Kishan covered $4\frac{3}{4}\text{km}$ by rickshaw and $1\frac{1}{2}\text{km}$ on foot. What is the distance of his house from the school?
AnswerDistance from Kishan's house to school $=$ Distance covered by him by rickshaw $+$ Distance covered by him on foot
Thus, we have:$\Big(4\frac{3}{4}+1\frac{1}{2}\Big)\text{km}$
$=\frac{19}{4}+\frac{3}{2}\text{km}$
$=\frac{(19+6)}{4}\text{km}$
$=\frac{25}{4}\text{km}$
$=6\frac{1}{4}\text{km}$
$(L.C.M $.of $2$ and $4 = (2 × 2) = 4$
$\begin{array}{c|c}2&2,4\\\hline2&1,2\\\hline&1,1\end{array}$
Hence, the distance from Kishan's house to school is $6\frac{1}{4}\text{km}$.
View full question & answer→