Question

A student was asked to simplify the following
$\frac{7}{5-2\frac{2}{3}}÷\frac{3-\frac{2}{3-1\frac{1}{2}}}{4-1\frac{1}{2}}-\frac{5}{7}\times [\frac{7}{10}+1\frac{1}{5}\times \frac{3\frac{1}{3}-2\frac{1}{2}}{2\frac{5}{21}-2}]$$+\frac{\frac{3}{1.6}+\frac{5}{3.2}}{\frac{5}{4.8}+\frac{1}{9.6}}$

His answer was $3\frac{1}{5}$ Find the percentage error in the answer.

• A. $10\%$
• B. $20\%$
• C. $25\%$
• D. $30\%$

Answer 1

The correct option is C $25\%$

Given exp $=\frac{7}{5-\frac{8}{3}}÷\frac{3-\frac{2}{3-\frac{3}{2}}}{4-\frac{3}{2}}$
$-\frac{5}{7}[\frac{7}{10}+\frac{6}{5}\times \frac{\frac{10}{3}-\frac{5}{2}}{\frac{47}{21}-2}]+\frac{\frac{30}{16}+\frac{50}{32}}{\frac{50}{48}+\frac{10}{96}}$
$=\frac{7}{\frac{7}{3}}÷\frac{3-\frac{2}{\frac{3}{2}}}{\frac{5}{2}}-\frac{5}{7}[\frac{7}{10}+\frac{6}{5}\times \frac{\frac{20-15}{6}}{\frac{47-42}{21}}]+\frac{\frac{15}{8}+\frac{25}{16}}{\frac{25}{24}+\frac{5}{48}}$

$3÷[(3-\frac{4}{3})\times \frac{2}{5}]-\frac{5}{7}[\frac{7}{10}+\frac{6}{5}\times \frac{\frac{5}{6}}{\frac{5}{21}}]+\frac{\frac{55}{16}}{\frac{55}{48}}$

$=3÷[\frac{5}{3}\times \frac{2}{5}]-\frac{5}{7}[\frac{7}{10}+\frac{6}{5}\times \frac{21}{6}]+\frac{48}{16}$

$=3÷\frac{2}{3}-\frac{5}{7}[\frac{7}{10}+\frac{21}{5}]+3$

$=\frac{9}{2}-\frac{5}{7}\times \frac{7}{10}-\frac{5}{7}\times \frac{21}{5}+3$

$=\frac{9}{2}-\frac{1}{2}-3+3=\frac{8}{2}=4$

$\therefore$ Percentage error $=(\frac{4-3\frac{1}{5}}{3\frac{1}{5}}\times 100)\%$

$=(\frac{4-\frac{16}{5}}{\frac{16}{5}}\times 100)\%=(\frac{\frac{4}{5}}{\frac{16}{5}}\times 100)\%=25\%$