Question 13 Marks
Fill in the box: $\frac{1}{2}-\square=\frac{1}{6}$
AnswerLet the missing space be $x$
We have,
$\frac{1}{2}-x=\frac{1}{6}$
$x = \frac{1}{2}-\frac{1}{6}$
= $\frac{1 \times 3-1 \times 1}{6}$
= $\frac{3-1}{6}$
= $\frac{2}{6}$
= $\frac{1}{3}$
View full question & answer→Question 23 Marks
Fill in the box: $\square-\frac{1}{5}=\frac{1}{2}$
AnswerLet the missing space be $x$
We have,
$x – \frac{1}{5}=\frac{1}{2}$
$x = \frac{1}{2}+\frac{1}{5}$
$= \frac{1 \times 5+1 \times 2}{10}$
$= \frac{5+2}{10}$
$= \frac{7}{10}$
View full question & answer→Question 33 Marks
Fill in the box: $\square-\frac{5}{8}=\frac{1}{4}$
AnswerLet the missing space be $x$
We have,
$x – \frac{5}{8}=\frac{1}{4}$
$x = \frac{1}{4}+\frac{5}{8}$
$= \frac{1 \times 2+5}{8}$
$= \frac{2+5}{8}$
$= \frac{7}{8}$
View full question & answer→Question 43 Marks
Solve: $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
AnswerHere,
$LCM$ of $3, 4, 2$ is $12,$
Thus,
$\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
$= \frac{2 \times 4+3 \times 3+1 \times 6}{12}$
$= \frac{8+9+6}{12}$
$= \frac{23}{12}$
View full question & answer→Question 53 Marks
Solve: $\frac{5}{6}-\frac{1}{3}$
AnswerHere,
$LCM $of $6$ and $3$ is $12,$
$\frac{5}{6}-\frac{1}{3}$
= $\frac{5 \times 2-1 \times 4}{12}$
= $\frac{10-4}{12}$
= $\frac{6}{12}$
= $\frac{1}{2}$
View full question & answer→Question 63 Marks
Solve: $\frac{3}{4}-\frac{1}{3}$
AnswerHere,
$LCM$ of $4$ and $3$ is $12,$
$\frac{3}{4}-\frac{1}{3}$
= $\frac{3 \times 3-1 \times 4}{12}$
= $\frac{9-4}{12}$
= $\frac{5}{12}$
View full question & answer→Question 73 Marks
Solve: $\frac{4}{5}+\frac{2}{3}$
AnswerHere,
$LCM$ of $5$ and $3$ is $15,$
$\frac{4}{5}+\frac{2}{3}$
= $\frac{4 \times 3+2 \times 5}{15}$
= $\frac{12+10}{15}$
= $\frac{22}{15}$
View full question & answer→Question 83 Marks
Solve: $\frac{2}{5}+\frac{1}{6}$
AnswerHere,
$LCM$ of $5$ and $6$ is $30,$
$\frac{2}{5}+\frac{1}{6}$
= $\frac{2 \times 6+1 \times 5}{30}$
= $\frac{12+5}{30}$
= $\frac{17}{30}$
View full question & answer→Question 93 Marks
Solve: $\frac{5}{7}+\frac{1}{3}$
AnswerHere,
$LCM$ of $7$ and $3$ is $21,$
$\frac{5}{7}+\frac{1}{3}$
= $\frac{5 \times 3+1 \times 7}{21}$
= $\frac{15+7}{21}$
= $\frac{22}{21}$
View full question & answer→Question 103 Marks
Solve: $\frac{4}{9}+\frac{2}{7}$
AnswerHere,
$LCM$ of $9$ and $7$ is $63$
$\frac{4}{9}+\frac{2}{7}$
= $\frac{4 \times 7+2 \times 9}{63}$
= $\frac{28+18}{63}$
= $\frac{46}{63}$
View full question & answer→Question 113 Marks
Solve:$\frac3{10}+\frac7{15}$
Answer$\frac3{10}+\frac7{15}=\frac{3\times3}{10\times3}+\;\frac{7\times2}{15\times2}$ $. . . .[L.C.M.(10,15) = 30]$
$=\;\frac9{30}+\;\frac{14}{30}=\frac{9+14}{30}=\frac{23}{30}\;$
View full question & answer→Question 123 Marks
Solve: $\frac{4}{3}-\frac{1}{2}$
AnswerHere, we have,
$\frac{4}{3}-\frac{1}{2}$
$LCM$ of $3$ and $2$ is $6,$
= $\frac{4 \times 2-1 \times 3}{6}$
= $\frac{8-3}{6}$
= $\frac{5}{6}$
View full question & answer→Question 133 Marks
Solve: $\frac{16}5-\;\frac75$
Answer$\frac{16}5-\;\frac75=\;\frac{16-7}5=\;\frac95=\;1\frac45\;$
View full question & answer→Question 143 Marks
Solve: $4 \frac{2}{3}+3 \frac{1}{4}$
AnswerHere, we have,
$$$4 \frac{2}{3}+3 \frac{1}{4}$
= $\frac{14}{3}+\frac{13}{4}$
= $\frac{14 \times 4+13 \times 3}{12}$
= $\frac{56+39}{12}$
= $\frac{95}{12}$
View full question & answer→Question 153 Marks
Solve: $1 \frac{1}{3}+3 \frac{2}{3}$
AnswerHere, we have,
$1 \frac{1}{3}+3 \frac{2}{3}$
= $\frac{4}{3}+\frac{11}{3}$
= $\frac{4+11}{3}$
= $\frac{15}{3}$
= 5
View full question & answer→Question 163 Marks
Solve: $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
AnswerHere,
$\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
= $\frac{1 \times 3+1 \times 2+1 }{6}$ $[LCM$ of $2, 3, 6$ is $6]$
= $\frac{3+2+1}{6}$
= $\frac{6}{6}$
$= 1$
View full question & answer→Question 173 Marks
Solve: $\frac{2}{3}+\frac{1}{7}$
AnswerGiven that,
$\frac{2}{3}+\frac{1}{7}$
Cross multiplying, we get,
= $\frac{2 \times 7+1 \times 3}{21}$
= $\frac{14+3}{21}$
= $\frac{17}{21}$
View full question & answer→Question 183 Marks
Shubham painted $\frac23$ of the wall space in his room. Her sister Madhavi helped and painted $\frac13$ of the wall space. How much did they paint together ?
AnswerShubham painted $\frac23$ of the wall space in his room and her sister Madhavi painted $\frac13$ of the wall space.
Total space = $\frac23+\frac13\;=\;\frac{2+1}3=\frac33=1$
View full question & answer→Question 193 Marks
Write the fraction appropriately as addition or subtraction
Answer
$\frac26+\frac36\;=\;\;\frac{2+3}6=\frac56$
View full question & answer→Question 203 Marks
Write the fraction appropriately as addition or subtraction:
Answer
$1-\frac35\;=\;\;\frac{5-3}5=\frac25$
View full question & answer→Question 213 Marks
Write the fraction appropriately as addition or subtraction:
Answer
$\frac15+\frac25\;=\;\;\frac{1+2}5=\frac35$
View full question & answer→Question 223 Marks
How quickly can you do this? Fill the appropriate sign. $('<', '=', '>')$
$\frac{3}{4} \square \frac{7}{8}$
AnswerHere, firstly we have to make same denominators
$\frac{3 \times 2}{4 \times 2}=\frac{6}{8}$
Now, the denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
As, $6 < 7$
Therefore,
$\frac{3}{4}<\frac{7}{8}$
View full question & answer→Question 233 Marks
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$\frac{6}{10} \square \frac{4}{5}$
AnswerHere, we have,
$\frac{6}{10}=\frac{3}{5}$
Now, the denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
As, $3 < 4$
Therefore,
$\frac{6}{10}<\frac{4}{5}$
View full question & answer→Question 243 Marks
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$\frac{1}{4} \square \frac{2}{8}$
AnswerHere, we have,
$\frac{2}{8}$ is $\frac{1}{4}$ in reduced form.
Therefore,
$\frac{1}{4}=\frac{2}{8}$
View full question & answer→Question 253 Marks
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$\frac{7}{9} \square \frac{3}{9}$
AnswerHere, we have,
Denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
Therefore,
$\frac{7}{9}>\frac{3}{9}$
View full question & answer→Question 263 Marks
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$\frac{3}{5} \square \frac{6}{5}$
AnswerHere, we have,
Denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
Therefore,
$\frac{3}{5}<\frac{6}{5}$
View full question & answer→Question 273 Marks
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$\frac{3}{4} \square \frac{2}{8}$
AnswerHere, we have,
$\frac{2}{8}=\frac{1}{4}$
Now, the denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
Therefore,
$\frac{3}{4}>\frac{1}{4}$
View full question & answer→Question 283 Marks
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$\frac{2}{4} \square \frac{3}{6}$
AnswerHere, we have
$\frac{2}{4}=\frac{1}{2}$
Also,
$\frac{3}{6}=\frac{1}{2}$
As, $\frac{1}{2}=\frac{1}{2}$
Therefore,
$\frac{2}{4}=\frac{3}{6}$
View full question & answer→Question 293 Marks
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$\frac{5}{7} \square \frac{15}{21}$
AnswerHere, we have
$\frac{15}{21}=\frac{5}{7}$
As, $\frac{5}{7}=\frac{5}{7}$
Therefore,
$\frac{5}{7}=\frac{15}{21}$
View full question & answer→Question 303 Marks
How quickly can you do this? Fill the appropriate sign. $('<', '=', '>')$
$\frac{6}{10} \square \frac{3}{5}$
AnswerHere, we have,
$\frac{6}{10}=\frac{3}{5}$
Now, the denominators of both the fractions are equal
Hence, fraction having greater numerator will be greater
Therefore,
$\frac{6}{10}<\frac{4}{5}$
View full question & answer→Question 313 Marks
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$\frac{1}{2} \square \frac{1}{5}$
AnswerHere, we have,
The numerator of both the fractions are equal.
Hence, fraction having lesser denominator will be greater
Therefore,
$\frac{1}{2}>\frac{1}{5}$
View full question & answer→Question 323 Marks
Make five more such pairs and make appropriate signs.
AnswerFirst Pair$\frac47--\frac67;\;\frac47<\frac67$
Second Pair$\frac59--\frac09;\;\frac59>\frac09$
Third Pair $\frac7{11}--\frac9{11};\;\frac7{11}<\frac9{11}$
Fourth Pair$\frac{11}{15}--\frac{13}{15};\;\frac{11}{15}<\frac{13}{15}$
Fifth Pair$\frac{11}{20}--\frac9{20};\;\frac{11}{20}>\frac9{20}$
View full question & answer→Question 333 Marks
Check whether the given fractions are equivalent :$\frac{7}{13},\frac5{11}$
Answer$\frac73,\frac5{11} $
$7 \times 11 = 77$
$3 \times 5 = 15$
So, $77 \neq 15$
\therefore The given fractions $\frac73$ and $\frac5{11}$ are not equivalent.
View full question & answer→Question 343 Marks
Check whether the given fractions are equivalent: $\frac3{10},\frac{12}{50}$
Answer$\frac3{10},\frac{12}{50} $
$3 \times 50 = 150$
$10 \times 12 = 120$
So, $150 \neq 120$
\therefore The given fractions $\frac3{10}$ and $\frac{12}{50}$ are not equivalent.
View full question & answer→Question 353 Marks
Check whether the given fractions are equivalent :$\frac59,\frac{30}{54}$
Answer$\frac59 = \frac{30}{54} $
$5 \times 54 = 270$
$9 \times 30 = 270$
$ \therefore 5 \times 54 = 9 \times 30$
\therefore The given fractions $\frac59$ and $\frac{30}{54}$ are equivalent.
View full question & answer→Question 363 Marks
Replace $\square$ by the correct number: $\frac{18}{24}=\frac{\square}4$
Answer$\frac{18}{24}=\frac{a}4 $
$ \therefore 18 \times 4 = 24 \times a$
$ \therefore a = \frac{18 ×4}{24}=\frac{72}{24} $
$ \therefore a = 3$
$ \therefore \frac{18}{24}=\frac{3}4$
View full question & answer→Question 373 Marks
Replace $\square$ by the correct number: $\frac{45}{60}=\frac{15}{\square}$
Answer$ \frac{45}{60}=\frac{15}{a} $
$\therefore 45 \times a = 60 \times 15$
$\therefore a = \frac{60 \times 15}{45}=\frac{900}{45} $
$\therefore a = 20$
$\therefore \frac{45}{60}=\frac{15}{20}$
View full question & answer→Question 383 Marks
Replace $\square$ by the correct number: $\frac35=\frac{\square}{20}$
Answer$ \frac35=\frac{a}{20} \therefore 3 \times 20 = 5 \times a$
$\therefore a= \frac{3 \times 20}5=\frac{60}{5} $
$\therefore a = 12.$
$\therefore \frac35=\frac{12}{20}$
View full question & answer→Question 393 Marks
Replace $\square$ by the correct number: $\frac58=\frac{10}{\square}$
Answer$ \frac58=\frac{10}{m} $
$\therefore 5 \times m = 8 \times 10$
$\therefore m = \frac{8 \times 10}5 $
$\therefore m = \frac{80}5 $
$\therefore m = 16$
$\therefore \frac58=\frac{10}{16}$
View full question & answer→Question 403 Marks
Replace $\square$ by the correct number: $\frac27=\;\frac8{\square}$
AnswerIf value taken as m
$\frac27=\;\frac8{m} \therefore 2 \times m = 7 \times 8$
$\therefore m=\;\frac{7\times8}2=\;\frac{56}2=28 $
$\therefore m = 28$
$\therefore \frac27=\;\frac8{28}$
View full question & answer→Question 413 Marks
Express as an improver fraction: $8\frac49$
Answer$8\frac49=\;\frac{(8\times9)+4}9=\;\frac{72\;+4}9=\frac{76}9$
View full question & answer→Question 423 Marks
Express as an improver fraction: $9\frac37$
Answer$9\frac37=\;\frac{(9\times7)+3}7=\;\frac{63\;+3}7=\frac{66}7$
View full question & answer→Question 433 Marks
Express as an improver fraction: $10\frac35$
Answer$10\frac35=\;\frac{(10\times5)+3}5=\;\frac{50\;+3}5=\frac{53}5$
View full question & answer→Question 443 Marks
Express as an improver fraction: $2\frac56$
Answer$2\frac56=\;\frac{(2\times6)+5}6=\;\frac{12\;+5}6=\frac{17}6$
View full question & answer→Question 453 Marks
Express as an improver fraction :$5\frac{6}7 $
AnswerAn improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).
$5\frac{6}7 = \frac{(5× 7) + 6}7 =\frac{35 + 6}7 =\frac{41}7 $
View full question & answer→Question 463 Marks
Express as an improver fraction: $7\frac{3}4$
Answer$7\frac{3}4 = \frac{(7×4) + 3}4 = \frac{28 + 3}4 =\frac{31}4 $
View full question & answer→Question 473 Marks
Write the fraction representing the shaded portion
Answer$\frac{35}9$
$\therefore $$\frac{35}9 = 3\frac{8}9$
View full question & answer→Question 483 Marks
Express as a mixed fracton: $\frac{19}6$
Answer$\frac{19}6= 19 \div 6$
$\therefore$$\frac{19}6 = 3\frac{1}6$ View full question & answer→Question 493 Marks
Express as a mixed fraction: $\frac{28}5$
Answer$ \frac{28}5$
$\therefore $$\frac{28}5 = 5\frac{3}5$
View full question & answer→Question 503 Marks
Express as a mixed fraction: $\frac{17}7$
View full question & answer→Question 513 Marks
Express as a mixed fraction: $\frac{11}5$
Answer$\frac{11}5$
$\therefore$$\frac{11}5 = 2 \frac{1}5$
View full question & answer→Question 523 Marks
Express the following as mixed fracton: $\frac{20}3$
Answer$\frac{20}3 = 20 ÷ 3$
$\therefore$ $\frac{20}3= 6\frac{2}3$
View full question & answer→Question 533 Marks
Kanchan dyes dresses, she had to dye $30$ dresses. She has so far finished $20$ dresses. What fraction of dresses has she finished?
AnswerKanchan had dyes $30$ dresses. She has finished $20$ dresses.
So fraction of dresses she has finished = $\frac{20}{30}=\;\frac{20\div10}{30\;\div\;10}=\;\frac23$
$\therefore $ She has finished $\;\frac23$ fraction of the dresses.
View full question & answer→Question 543 Marks
What fraction of an hour is $40$ minutes?
Answer$1$ hour $= 60$ minutes
$\therefore$ Required fraction = $\frac{60}{40}=\;\frac{60\div10}{40\;\div\;10}=\;\frac64=\;\frac{6\div2}{4\div2}=\frac32$
View full question & answer→Question 553 Marks
What fraction of these circles have $'X's$ in them?
AnswerTotal number of circles $= 8$
Numbers of circles which $'X's$ in them $= 4$
$\therefore $ Required fraction = $\frac48=\;\frac{4\div4}{8\;\div\;4}=\;\frac12$
View full question & answer→Question 563 Marks
Compare $\frac{5}{6}$ and $\frac{13}{15}$.
AnswerThe fractions are unlike.
We should first get their equivalent fractions with a denominator which is a common multiple of $6$ and $15.$
Now, $\frac{5 \times 5}{6 \times 5}=\frac{25}{30}, \frac{13 \times 2}{15 \times 2}=\frac{26}{30}$
Since ${26}>{25}$
Therefore, $\frac{13}{15}>\frac{5}{6}$
View full question & answer→Question 573 Marks
Find the equivalent fraction of $\frac{2}{5}$ with numerator $6.$
AnswerWe know that, $2$ $\times$ $3 = 6.$
Hence, we need to multiply both the numerator and the denominator by $3$ to get the equivalent fraction.
Therefore, $\frac{2}{5}=\frac{2 \times 3}{5 \times 3}=\frac{6}{15} $
$\therefore \frac{6}{15}$ is the required equivalent fraction.
View full question & answer→Question 583 Marks
Express $\frac{7}{3}$ as the mixed fraction:
Answer
i.e. $2$ whole and $\frac{1}{3}$and more, or $2 \frac{1}{3}$
Therefore, $\frac{7}{3}$ = $2 \frac{1}{3}$ View full question & answer→Question 593 Marks
Simplify: $8 \frac{1}{4}-2 \frac{5}{6}$
AnswerHere,
$8 \frac{1}{4}=\frac{(8 \times 4)+1}{4}=\frac{33}{4}$ and $2 \frac{5}{6}=\frac{2 \times 6+5}{6}=\frac{17}{6}$
Now, $\frac{33}{4}-\frac{17}{6}=\frac{33 \times 3}{12}-\frac{17 \times 2}{12}$ (Since $LCM$ of $4$ and $6 = 12$)
$=\frac{99-34}{12}=\frac{65}{12}=5 \frac{5}{12}$
View full question & answer→Question 603 Marks
Express the mixed fraction: $\frac{27}{5}$
Answer
i.e. $5$ whole and $\frac{2}{5}$and more, or $5 \frac{2}{5}$
Here, $\frac{27}{5}$ = $5 \frac{2}{5}$ View full question & answer→Question 613 Marks
Express the mixed fraction: $\frac{11}{3}$
Answer$\frac{11}{3}$ can be expressed as a mixed fraction as,
i.e. $3$ whole and $\frac{2}{3}$ more, or $3 \frac{2}{3}$
Therefore, $\frac{11}{3}$ = $3 \frac{2}{3}$ View full question & answer→Question 623 Marks
Express $\frac{17}{4}$ as mixed fraction:
Answer
i.e. 4 whole and $\frac{1}{4}$and more, or $4 \frac{1}{4}$
Therefore, $\frac{17}{4}$ = $4 \frac{1}{4}$ View full question & answer→