3 Marks Question

Question 13 Marks

(i) (a) Provide the number in the box $\square$, such that
$
\frac{2}{3} \times \square=\frac{10}{30}
$
(b) The simplest form of the number obtained in $\square$ is ____________ .
(ii) (a) Provide the number in the box $\square$, such that $\frac{3}{5} \times \square=\frac{24}{75}$.
(b) The simplest form of the number obtained in $\square$ is ____________ .

Answer

(i) (a) $\frac{2}{3} \times \square=\frac{10}{30}$
Here, $2 \times 5=10$ and $3 \times 10=30$
Hence, the required number in the box is $\frac{5}{10}$.
(b) Simplest form of $\frac{5}{10}=\frac{1}{2}$
[dividing numerator and denominator by 5]
(ii) (a) $\frac{8}{15}$ (b) $\frac{8}{15}$

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Question 23 Marks

Which is greater?
$\frac{1}{2}$ of $\frac{6}{7}$ or $\frac{2}{3}$ of $\frac{3}{7}$

Answer

$\frac{1}{2}$ of $\frac{6}{7}$

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Question 33 Marks

Which is greater?
$\frac{2}{7}$ of $\frac{3}{4}$ or $\frac{3}{5}$ of $\frac{5}{8}$

Answer

We have, $\frac{2}{7}$ of $\frac{3}{4}=\frac{2}{7} \times \frac{3}{4}=\frac{1}{7} \times \frac{3}{2}=\frac{3}{14}$
[dividing numerator and denominator by 2 ]
and $\frac{3}{5}$ of $\frac{5}{8}=\frac{3}{5} \times \frac{5}{8}$
[dividing numerator and denominator by 5 ]
$
=\frac{3 \times 1}{1 \times 8}=\frac{3}{8}
$
LCM of 14 and $8=2 \times 2 \times 2 \times 7=56$
On converting both the fractions into like fractions, we get
$
\frac{3}{14}=\frac{3 \times 4}{14 \times 4}=\frac{12}{56} \text { and } \frac{3}{8}=\frac{3 \times 7}{8 \times 7}=\frac{21}{56}
$
$\because 21>12$, so $\frac{21}{56}>\frac{12}{56}$ i.e. $\frac{3}{8}>\frac{3}{14}$
Hence, $\frac{3}{5}$ of $\frac{5}{8}$ is greater than $\frac{2}{7}$ of $\frac{3}{4}$.

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Question 43 Marks

Shade:
(i) $\frac{1}{2}$ of the circles in box (a).
(ii) $\frac{2}{3}$ of the triangles in box (b).
(iii) $\frac{3}{5}$ of the squares in box (c).

Answer

(i) Number of circles $=12$
$\therefore \frac{1}{2}$ of the circles in box (a) $=\frac{1}{2} \times 12=\frac{12}{2}=6$
Hence, the shaded figure is shown below:

(ii) Do same as part (i)
(iii) Do same as part (i)

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Question 53 Marks

Some pictures (a) to (c) are given below. Tell which of them show:
(i) $3 \times \frac{1}{5}=\frac{3}{5}$
(ii) $2 \times \frac{1}{3}=\frac{2}{3}$
(iii) $3 \times \frac{3}{4}=2 \frac{1}{4}$

Answer

(i) We have, $3 \times \frac{1}{5}=\frac{3}{5} \Rightarrow \frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{3}{5}$
It shows that, on combining three figures, in each of them out of 5 parts, 1 part is shaded.
It is represented by the Figure (c).
(ii) (a)
(iii) (b)

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Question 63 Marks

Find the division of a decimal number by 10,100 or 1000 in the following table:

$31.5 \div 10=3.15$	$231.5\div10=$	$1.5 \div 10=$	$29.36 \div 10=$
$31.5 \div 100=0.315$	$231.5 \div 100=$	$1.5 \div 100=$	$29.36 \div 100=$
$31.5 \div 1000=0.0315$	$231.5 \div 1000=$	$1.5 \div 1000=$	$29.36\div1000=$

Answer

The complete table is shown below:

$31.5 \div 10=3.15$	$231.5\div10=23.15$	$1.5 \div 10=0.15$	$29.36 \div 10=2.936$
$31.5 \div 100=0.315$	$231.5 \div 100=2.315$	$1.5 \div 100=0.015$	$29.36 \div 100=0.2936$
$31.5 \div 1000=0.0315$	$231.5 \div 1000=0.2315$	$1.5 \div 1000=0.0015$	$29.36\div1000=0.02936$

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Question 73 Marks

Observe these products and fill in the blanks.

$7 \times \frac{1}{7}=1$	$\frac{5}{4} \times \frac{4}{5}$____________
$\frac{1}{9} \times 9=$____________	$\frac{2}{7} \times$ ____________=1
$\frac{2}{3} \times \frac{3}{2}=\frac{2 \times 3}{3 \times 2}=\frac{6}{6}=1$	____________$\times \frac{5}{9}=1$

Answer

The complete table is shown below:

$7 \times \frac{1}{7}=1$	$\frac{5}{4} \times \frac{4}{5}=\frac{5 \times 4}{4 \times 5}=\frac{20}{20}=1$
$\frac{1}{9} \times 9=$1	$\frac{2}{7} \times \frac{7}{2}=1$
$\frac{2}{3} \times \frac{3}{2}=\frac{2 \times 3}{3 \times 2}=\frac{6}{6}=1$	$\frac{9}{5} \times \frac{5}{9}=1$

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Question 83 Marks

What happens to the value of the product, when we multiply two improper fractions?

$\frac{7}{3} \times \frac{5}{2}=\frac{35}{6}$	$\frac{35}{6}>\frac{7}{3}, \frac{35}{6}>\frac{5}{2}$	Product is greater than each of the fractions
$\frac{6}{5} \times \frac{\square}{3}=\frac{24}{15}$
$\frac{9}{2} \times \frac{7}{\square}=\frac{63}{8}$
$\frac{3}{\square} \times \frac{8}{7}=\frac{24}{14}$

Answer

The complete table is shown below :

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Question 93 Marks

What happens to the value of the product, when we multiply two proper fractions?

$\frac{2}{3} \times \frac{4}{5}=\frac{8}{15}$	$\frac{8}{15}<\frac{2}{3}, \frac{8}{15}<\frac{4}{5}$	Product is less than each of the fractions
$\frac{1}{5} \times \frac{2}{7}=$ $\square$
$\frac{3}{5} \times \frac{\square}{8}=\frac{21}{40}$
$\frac{2}{\square} \times \frac{4}{9}=\frac{8}{45}$

Answer

The complete table is shown below :

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