2 Marks Questions

Question 512 Marks

Find the equivalent fraction of $\frac{6}{11}$ having:
Denominator $77$

Answer

Let, $\frac{6}{11}=\frac{\Box}{77}$
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 $\frac{42}{77}$.

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Question 522 Marks

Find the sum: $\frac{4}{15}+\frac{17}{20}$

Answer

We 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 $\Big(\frac{60}{20}=3,17\times3=51\Big)$
$=\frac{67}{60}$
$=1\frac{7}{60}$

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Question 532 Marks

Find the sum: $1\frac{3}{5}+2\frac{4}{5}$

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 $1\frac{3}{5}+2\frac{4}{5}$
$=\frac{8}{5}+\frac{14}{5}$
$=\frac{(8+14)}{5}$
$=\frac{22}{5}$
$=4\frac{2}{5}$

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Question 542 Marks

Draw number lines and locate the following points: $\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{8}{5}$

Answer

Draw $0$ 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 $2$. $\Big(1 <\frac{8}{5} < 2\Big)$

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Question 552 Marks

Find the difference: $4\frac{3}{7}-2\frac{4}{7}$

Answer

Difference of like fractions = Difference of numerator ÷ Common denominator
$4\frac{3}{7}-2\frac{4}{7}$ $=\frac{31}{7}-\frac{18}{7}$
$=\frac{(31-18)}{7}$ $=\frac{13}{7}$

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Question 562 Marks

Find the equivalent fraction of $\frac{6}{11}$ having:
Numerator 60

Answer

Let, $\frac{6}{11}=\frac{60}{\Box}$
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 $\frac{60}{110}$.

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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 $\Big(\frac{24}{12}=2,2\times29=58\Big)$

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Question 582 Marks

Find the equivalent fraction of $\frac{3}{5}$ having: Denominator $30$

Answer

Let, $\frac{3}{5}=\frac{\Box}{30}$ 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 $\frac{18}{30}$.

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Question 592 Marks

Convert the following into a mixed fraction:$\frac{101}{8}$

Answer

On dividing $101$ by $8$,
We get, Quotient $= 12$ Remainder $= 5$
Therefore, $\frac{101}{8}=12+\frac{5}{8}$ $=12\frac{5}{8}$

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Question 602 Marks

Determine: $\frac{3}{4}$ of $28$ rackets

Answer

$\frac{3}{4}$ of $28$ rackets $=\frac{3}{4}\times28$ $=3\times7$ $=21$

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Question 612 Marks

Represent the following fractions on the number line:
$\frac{3}{8}$

Answer

Draw 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 $P.$

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Question 622 Marks

Determine:
$\frac{3}{4}$ of $32$ books

Answer

$\frac{3}{4}$ of $32$ books
$=\frac{3}{4}\times32$
$=3\times8$
$=24$

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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, $\frac{7}{12}+\frac{9}{16}$
$=\frac{28}{48}+\frac{27}{48}$
$=\frac{(28+27)}{48}$
$=\frac{55}{48}$
$=1\frac{7}{48}$

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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
$\frac{4}{9}+\frac{8}{9}$
$=\frac{(4+8)}{9}$
$=\frac{12}{9}$
$=\frac{4}{3}$
$=1\frac{1}{3}$

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Question 652 Marks

Find the equivalent fraction of $\frac{56}{70}$ with Denominator $10$

Answer

Let $\frac{56}{70}=\frac{\Box}{10}$ 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 $\frac{8}{10}$.

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Question 662 Marks

Convert the following into a mixed fraction:$\frac{17}{5}$

Answer

On dividing $17$ by $5$,
We get, Quotient = $3$ Remainder = $2$
Therefore, $\frac{17}{5}=3+\frac{2}{5}$
$=3\frac{2}{5}$

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Question 672 Marks

Determine: $\frac{2}{3}$ of $27$ pens

Answer

$\frac{2}{3}$ of $27$ pens $=\frac{2}{3}\times27$ $=2\times9$ $=18$

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Question 682 Marks

Represent the following fractions on the number line: $\frac{5}{9}$

Answer

Draw 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 $P.$

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Question 692 Marks

Draw number lines and locate the following points: $\frac{1}{4},\frac{1}{2},\frac{3}{4},\frac{4}{4}$

Answer

Draw 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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MATHS 2 Marks Questions