2 Marks

Question 12 Marks

By using the following clues, find who am I?
i) Each of my numerator and denominator is a single digit number.
ii) The sum of my numerator and denominator is a multiple of 3.
iii) The product of my numerator and denominator is a multiple of 4.

Answer

The numerator may be any one of $1,2,3,4,5,6,7,8,9$ and the denominator may be any one of 1,2, $3,4,5,6,7,8,9$. Sum of numerator and denominator is a multiple of 3 .$\therefore$ Possible proper fractions are $\frac{1}{2}, \frac{1}{5}, \frac{1}{8}, \frac{2}{4}, \frac{2}{7}, \frac{3}{6}, \frac{3}{9}, \frac{4}{5}, \frac{4}{8}, \frac{5}{7}, \frac{6}{9}$ Also given the product of numerator and denominator is a multiple of 4 .
$\therefore$ Possible fractions are $\frac{1}{8}, \frac{2}{4}, \frac{4}{5}, \frac{4}{8}$

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Question 22 Marks

A painter painted $\frac{3}{8}$ of the wall of which one third is painted in yellow colour. What fraction is the yellow colour of the entire wall?

Answer

$\text { Painted portion of the wall }=\frac{3}{8}$
Of Which the yellow colour painted $=\frac{1}{3}$
$\therefore$ Yellow colour in the entire wall $=\frac{1}{3}$ of $\frac{3}{8}$
$ =\frac{1}{3} \times \frac{3}{8}$
$=\frac{1}{8} $
$\frac{1}{8}$ of the wall is painted yellow.

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Question 32 Marks

Divide the following:
$9 \frac{2}{3} \div 1 \frac{2}{3}$

Answer

$9 \frac{2}{3} \div 1 \frac{2}{3}=\frac{29}{3} \div \frac{5}{3}$
$=\frac{29}{3} \times \frac{3}{5}$
$=\frac{29}{5} \ldots\left[\text { Reciprocal of } \frac{5}{3} \text { is } \frac{3}{5}\right]$
$\text { 5) } \frac{5}{29}$
$\frac{25}{4}$
$=5 \frac{4}{5}$
$9 \frac{2}{3} \div 1 \frac{2}{3}=5 \frac{4}{5}$

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Question 42 Marks

Divide the following:
$\frac{4}{3} \div \frac{5}{9}$

Answer

$\frac{4}{3} \div \frac{5}{9}=\frac{4}{3} \times \frac{9}{5} \ldots\left[\text { Reciprocal of } \frac{5}{9} \text { is } \frac{9}{5}\right]$
$\frac{2}{36} \frac{30}{6}$
$=\frac{36}{15}$
$=2 \frac{6}{15}$
$=2 \frac{2}{5}$
$\frac{4}{3} \div \frac{5}{9}=2 \frac{2}{5}$

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Question 52 Marks

Divide the following:
$4 \frac{1}{5} \div 3 \frac{3}{4}$

Answer

Divide the following:
$4 \frac{1}{5} \div 3 \frac{3}{4}$
$ 4 \frac{1}{5} \div 3 \frac{3}{4}=\frac{21}{5} \div \frac{15}{4}$
$=\frac{21}{5} \times \frac{4}{15} \ldots\left[\text { Reciprocal of } \frac{15}{4} \text { is } \frac{4}{15}\right] $
$75$) $\frac{1}{84}$
$ \frac{75}{9}$
$=\frac{84}{75}$
$=1 \frac{9}{75}$
$=1 \frac{3}{25}$
$4 \frac{1}{5} \div 3 \frac{3}{4}=1 \frac{3}{25} $

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Question 62 Marks

Multiply the following:
$3 \frac{5}{7} \times 1 \frac{1}{13}$

Answer

$3 \frac{5}{7} \times 1 \frac{1}{13}=\frac{26}{7} \times \frac{14}{13}$
$3 \frac{5}{7} \times 1 \frac{1}{13}=4$

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Question 72 Marks

Multiply the following:
$8 \frac{1}{3} \times 5$

Answer

$8 \frac{1}{3} \times 5=\left(8+\frac{1}{3}\right) \times 5$
$=40+\frac{5}{3}$
$=40+1 \frac{2}{3}$
$=40+1+\frac{2}{3}$
$=41 \frac{2}{3}$
$8 \frac{1}{3} \times 5=41 \frac{2}{3}$

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Question 82 Marks

Multiply the following:
$\frac{3}{8} \times \frac{4}{5}$

Answer

$\frac{3}{8} \times \frac{4}{5}=\frac{3 \times 4}{8 \times 5}$
$=\frac{12}{40}$
$=\frac{3}{10}$
$\frac{3}{8} \times \frac{4}{5}=\frac{3}{10}$

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Question 92 Marks

Subtract $1 \frac{3}{5}$ from $2 \frac{1}{3}$

Answer

$2 \frac{1}{3}-1 \frac{3}{5}=\frac{7}{3}-\frac{8}{5}$
$=\frac{(7 \times 5)-(8 \times 3)}{15} $
$ =\frac{35-24}{15}$
$=\frac{11}{15} $
$ 2 \frac{1}{3}-1 \frac{3}{5}=\frac{11}{5} z$

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Question 102 Marks

Simplify : $7 \frac{2}{7}-3 \frac{4}{21}$

Answer

$7 \frac{2}{7}-3 \frac{4}{21}=(7-3)+\frac{2}{7}-\frac{4}{21} $
$=4+\frac{6}{21}-\frac{4}{21} $
$ =4+\frac{6-4}{21} $
$ =4+\frac{2}{21}$
$ =4 \frac{2}{21} $
$ 7 \frac{2}{7}-3 \frac{4}{21}=4 \frac{2}{21}$

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Question 112 Marks

Find the difference between $\frac{8}{9}$ and $\frac{2}{7}$

Answer

$\frac{8}{9}=\frac{8 \times 7}{9 \times 7}=\frac{56}{63} $
$ \frac{2}{7}=\frac{2 \times 9}{7 \times 9}=\frac{18}{63} $
$ \frac{56}{63}>\frac{18}{63} $
$ \therefore \frac{8}{9}>\frac{2}{7} $
$ \frac{8}{9}-\frac{2}{7}=\frac{56}{63}-\frac{18}{63}
$$=\frac{56-18}{63} $
$ =\frac{38}{63} $
$ \frac{8}{9}-\frac{2}{7}=\frac{38}{63}$

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Question 122 Marks

What is the total of $3 \frac{1}{3}$ and $4 \frac{1}{6} ?$

Answer

$\text { Total of } 3 \frac{1}{3} \text { and } 4 \frac{1}{6}=3 \frac{1}{3}+4 \frac{1}{6}$
$=3+\frac{1}{3}+4+\frac{1}{6}$
$=(3+4)+\frac{1}{3}+\frac{1}{6} $
$=7+\frac{2}{6}+\frac{1}{6} $
$=7+\frac{3}{6} $
$=7+\frac{1}{2} $
$ =7 \frac{1}{2}$
$3 \frac{1}{3}+4 \frac{1}{6}=7 \frac{1}{2}$

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Question 132 Marks

Simplify : $1 \frac{3}{5}+5 \frac{4}{7}$

Answer

$1 \frac{3}{5}+5 \frac{4}{7}=1+\frac{3}{5}+5+\frac{4}{7} $
$=(1+5)+\frac{3}{5}+\frac{4}{7}$
$ =6+\frac{(3 \times 7)+(4 \times 5)}{35} $
$=6+\left(\frac{21+20}{35}\right)$
$ =6+\frac{41}{35} $
$ =6+1 \frac{6}{35} $
$ =6+1+\frac{6}{35} $
$ =7+\frac{6}{35}$
$ =7 \frac{6}{35} $
$ \therefore 1 \frac{3}{5}+5 \frac{4}{7}=7 \frac{6}{35}$

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Maths 2 Marks

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