Question

Calculate : $(\frac{2}{3}+\frac{5}{8})\times (\frac{4}{6}+\frac{7}{16})$

• A. $\frac{1653}{1152}$
• B. $\frac{1643}{1152}$
• C. $\frac{1743}{1152}$
• D. $\frac{1463}{1152}$

Answer 1

The correct option is B

$\frac{1643}{1152}$

$(\frac{2}{3}+\frac{5}{8})\times (\frac{4}{6}+\frac{7}{16})$

= $(\frac{2\times 8}{3\times 8}+\frac{5\times 3}{8\times 3})\times (\frac{4\times 8}{6\times 8}+\frac{7\times 3}{16\times 3})$ (Since LCM of 3 and 8 is 24 and LCM of 6 and 16 is 48)

= $(\frac{16}{24}+\frac{15}{24})\times (\frac{32}{48}+\frac{21}{48})$

= $\frac{31}{24}\times \frac{53}{48}$

= $\frac{1643}{1152}$