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Question 15 Marks
Simplify:
$7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\frac{1}{3}-\frac{1}{6}}\Big)\Big\}\Big]$
Answer
Given expression:

$=7\frac{1}{2}-\Big[2\frac{1}{4}\div\Big\{1\frac{1}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{3}{2}-\overline{\overline{\frac{1}{3}}-\frac{1}{6}}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{3}{2}-\frac{1}{6}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\Big(\frac{9-1}{6}\Big)\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{1}{2}\times\frac{4}{3}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{5}{4}-\frac{2}{3}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\Big\{\frac{15-8}{12}\Big\}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\div\frac{7}{12}\Big]$

$=\frac{15}{2}-\Big[\frac{9}{4}\times\frac{12}{7}\Big]$

$=\frac{15}{2}-\frac{27}{7}$

$\frac{105-54}{14}=\frac{51}{14}=3\frac{9}{14}$

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Question 25 Marks
Simplify: $4\frac{4}{5}\div\Big\{2\frac{1}{5}-\frac{1}{2}\Big(1\frac{1}{4}-\overline{\frac{1}{4}-\frac{1}{5}}\Big)\Big\}$
Answer
Given expression: $=4\frac{4}{5}\div\Big\{2\frac{1}{5}-\frac{1}{2}\Big(1\frac{1}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{5}{4}-\overline{\overline{\frac{1}{4}}-\frac{1}{5}}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{5}{4}-\frac{1}{20}\Big)\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{1}{2}\Big(\frac{25-1}{20}\Big)\Big\}$
$=\frac{24}{5}\Big\{\frac{11}{5}-\frac{1}{2}\times\frac{24}{20}\Big\}$
$=\frac{24}{5}\div\Big\{\frac{11}{5}-\frac{12}{20}\Big\}$
$=\frac{24}{5}\div\Big\{\frac{44-12}{20}\Big\}$
$=\frac{24}{5}\div\frac{32}{20}$
$=\frac{24}{5}\times\frac{20}{32}$
$=\frac{3}{4}\times4=3$
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