Question

Evaluate: $\frac{(3\frac{2}{3}{)}^2-(2\frac{1}{2}{)}^2}{(4\frac{3}{2}{)}^2-(3\frac{1}{3}{)}^2}$ $÷$ $\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$

• A. $\frac{35}{53}$
• B. $\frac{37}{53}$
• C. $\frac{42}{59}$
• D. $\frac{47}{60}$

Answer 1

Answer: (B)

$\frac{37}{53}$

$\frac{(3\frac{2}{3}{)}^2-(2\frac{1}{2}{)}^2}{(4\frac{3}{2}{)}^2-(3\frac{1}{3}{)}^2}÷\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$

$=\frac{(3\frac{2}{3}+2\frac{1}{2})(3\frac{2}{3}-2\frac{1}{2})}{(4\frac{3}{2}+3\frac{1}{3})(4\frac{3}{2}-3\frac{1}{3})}÷\frac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$

$=\frac{3\frac{2}{3}+2\frac{1}{2}}{4\frac{3}{2}+3\frac{1}{3}}$

$=\frac{\frac{11}{3}+\frac{5}{2}}{\frac{11}{2}+\frac{10}{3}}$

$=\frac{\frac{22+15}{6}}{\frac{33+20}{6}}$

$=\frac{37}{53}$