[2 Mark Question Answer]

Question 12 Marks

An $84 m$ long string is cut into pieces each of length $5 \frac{1}{4} m$. How many pieces are obtained?

Answer

$\text { Length of string }=84 m $
$\text { Length of each piece }=5 \frac{1}{4} m =\frac{21}{4} m $
$\text { Number of pieces }=84 \div \frac{21}{4} $
$=84 \times \frac{4}{21}=4 \times 4=16$

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Question 22 Marks

Simplify:
$\frac{1}{2} \text { of } 40+1 \frac{3}{4} \text { of } 2 \frac{2}{9}+2 \frac{1}{5} \times 0$

Answer

$\frac{1}{2} \text { of } 40+1 \frac{3}{4} \text { of } 2 \frac{2}{9}+2 \frac{1}{5} \times 0 $
$=\frac{1}{2} \times 40+\frac{7}{4} \times \frac{20}{9}+\frac{11}{5} \times 0 $
$=20+\frac{35}{9}+0=\frac{180+35}{9}=\frac{215}{9} $
$=23 \frac{8}{9}$

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Question 32 Marks

Simplify:
$\frac{5}{6}-\frac{3}{5}\left(\frac{1}{3}+\frac{2}{11}\right)$

Answer

$\frac{5}{6}-\frac{3}{5}\left(\frac{1}{3}+\frac{2}{11}\right)=\frac{5}{6}-\frac{3}{5}\left(\frac{11+6}{33}\right) $
$=\frac{5}{6}-\frac{3}{5} \times \frac{17}{33}=\frac{5}{6}-\frac{17}{55} $
$=\frac{275-102}{330}=\frac{173}{330}$

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Question 42 Marks

Simplify:
$\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{3}{4}-\frac{4}{5}\right) \div\left(\frac{1}{2}-\frac{2}{5}+\frac{1}{7}\right)$

Answer

$\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{3}{4}-\frac{4}{5}\right) \div\left(\frac{1}{2}-\frac{2}{5}+\frac{1}{7}\right) $
$=\left(\frac{3-2}{6}\right)\left(\frac{15-16}{20}\right) \div\left(\frac{35-28+10}{70}\right) $
$=\left(\frac{1}{6}\right)\left(\frac{-1}{20}\right) \div\left(\frac{17}{20}\right)=\frac{1}{6} \times \frac{-1}{20} \div \frac{17}{70} $
$=\frac{1}{6} \times \frac{-1}{20} \times \frac{70}{17}=-\frac{7}{204}$

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Question 52 Marks

Simplify:
$4 \frac{5}{7}\left(3 \frac{1}{8} \div \frac{11}{12}\right)$

Answer

$4 \frac{5}{7}\left(3 \frac{1}{8} \div \frac{11}{12}\right)=\frac{33}{7}\left(\frac{25}{8} \div \frac{11}{12}\right) $
$=\frac{33}{7}\left(\frac{25}{8} \times \frac{12}{11}\right)=\frac{33}{7}\left(\frac{75}{22}\right)$
$=\frac{33}{7} \times \frac{75}{22}=\frac{225}{14}=16 \frac{1}{14}$

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Question 62 Marks

Simplify:
$\left(\frac{1}{2}+\frac{1}{3}\right) \div\left(\frac{1}{4}-\frac{1}{6}\right)$

Answer

$\left(\frac{1}{2}+\frac{1}{3}\right) \div\left(\frac{1}{4}-\frac{1}{6}\right) $
$=\left(\frac{3+2}{6}\right) \div\left(\frac{3-2}{12}\right)=\left(\frac{5}{6}\right) \div\left(\frac{1}{12}\right) $
$=\frac{5}{6} \times \frac{12}{1} $
$=10$

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Question 72 Marks

Simplify:
$\frac{3}{4} \div\left(\frac{1}{6} \div \frac{1}{2}\right)$

Answer

$\frac{3}{4} \div\left(\frac{1}{6} \div \frac{1}{2}\right) $
$=\frac{3}{4} \div\left(\frac{1}{6} \times \frac{2}{1}\right)=\frac{3}{4} \div\left(\frac{1}{3}\right) $
$=\frac{3}{4} \times \frac{3}{1}=\frac{9}{4}=2 \frac{1}{4}$

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Question 82 Marks

Simplify:
$\frac{4}{7} \div\left(\frac{1}{3} \times 2 \frac{4}{5}\right)$

Answer

$\frac{4}{7} \div\left(\frac{1}{3} \times 2 \frac{4}{5}\right) $
$=\frac{4}{7} \div\left(\frac{1}{3} \times \frac{14}{5}\right)=\frac{4}{7} \div\left(\frac{14}{15}\right) $
$=\frac{4}{7} \times \frac{15}{14}=\frac{60}{98}=\frac{30}{49}$

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Question 92 Marks

Simplify:
$\frac{1}{2} \div\left(\frac{7}{8}-\frac{3}{5}\right)$

Answer

$\frac{1}{2} \div\left(\frac{7}{8}-\frac{3}{5}\right)=\frac{1}{2} \div\left(\frac{5 \times 7-8 \times 3}{40}\right) $
$=\frac{1}{2} \div\left(\frac{35-24}{40}\right)=\frac{1}{2} \div\left(\frac{11}{40}\right) $
$=\frac{1}{2} \times \frac{40}{11}=\frac{20}{11}=1 \frac{9}{11}$

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Question 102 Marks

Simplify:
$5-\left(\frac{8}{11}-3 \frac{3}{11}\right)$

Answer

$5-\left(\frac{8}{11}-3 \frac{3}{11}\right)=5-\left(\frac{8}{11}-\frac{36}{11}\right)$
$=5-\frac{8}{11}+\frac{36}{11}=\frac{55-8+36}{11} $
$=\frac{55+36-8}{11}=\frac{83}{11}=7 \frac{6}{11}$

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Question 112 Marks

Simplify:
$\left(\frac{3}{7} \div \frac{1}{2}\right) \text { of } 1 \frac{1}{7}$

Answer

$\left(\frac{3}{7} \div \frac{1}{2}\right) \text { of } 1 \frac{1}{7}=\frac{3}{7} \times \frac{2}{1} \text { of } \frac{8}{7} \ldots \ldots \ldots\left[\frac{2}{1} \text { of } \frac{8}{7}=\frac{2 \times 8}{7 \times 1}=\frac{16}{7}\right] $
$=\frac{3}{7} \times \frac{16}{7}=\frac{48}{49}$

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Question 122 Marks

Simplify:
$2 \frac{1}{4} \div \frac{2}{7} \text { of } 1 \frac{1}{3} \times \frac{2}{3}$

Answer

$2 \frac{1}{4} \div \frac{2}{7} \text { of } 1 \frac{1}{3} \times \frac{2}{3} \ldots \ldots . .\left[\frac{2}{7} \text { of } 1 \frac{1}{3}=\frac{2}{7} \times \frac{4}{3}=\frac{8}{21}\right]$
$=\frac{9}{4} \div \frac{8}{21} \times \frac{2}{3} $
$=\frac{9}{4} \times \frac{21}{8} \times \frac{2}{3}=\frac{63}{16}=3 \frac{15}{16}$

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Question 132 Marks

Simplify:
$2 \frac{2}{3} \times 3 \frac{1}{2} \div 2 \frac{4}{9}$

Answer

$2 \frac{2}{3} \times 3 \frac{1}{2} \div 2 \frac{4}{9}=\frac{8}{3} \times \frac{7}{2} \div \frac{22}{9}$
$=\frac{8}{3} \times \frac{7}{2} \times \frac{9}{22}=\frac{2 \times 7 \times 3}{11}=\frac{42}{11}=3 \frac{9}{11}$

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Question 142 Marks

Simplify:
$1 \frac{1}{3} \times 1 \frac{2}{7} \text { of } 1 \frac{1}{4}$

Answer

$1 \frac{1}{3} \times 1 \frac{2}{7} \text { of } 1 \frac{1}{4}$
$=\frac{4}{3} \times \frac{9}{7} \times \frac{5}{4}$
$=\frac{4 \times 9 \times 5}{3 \times 7 \times 4}=\frac{15}{7}=2 \frac{1}{7}$

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Question 152 Marks

Simplify:
$1 \frac{5}{8}-2 \frac{1}{6}+3 \frac{3}{4}$

Answer

$1 \frac{5}{8}-2 \frac{1}{6}+3 \frac{3}{4}=\frac{13}{8}-\frac{13}{6}+\frac{15}{4} $
$=\frac{13 \times 3}{8 \times 3}-\frac{13 \times 4}{6 \times 4}+\frac{15 \times 6}{4 \times 6}=\frac{39}{24}-\frac{52}{24}+\frac{91}{24} $
$=\frac{39-52+90}{24}=\frac{129-52}{24}=\frac{77}{24}=3 \frac{5}{24}$

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Question 162 Marks

I bought one dozen bananas and ate five of them. What fraction of the total number of bananas was left?

Answer

Number of bananas bought $=1$
Dozen $=12$
Number of bananas eaten by $m e=5$
Number of bananas left $=12-5=7$
Fraction $=\frac{7}{12}$

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