Question

The value of $3\frac{1}{12}$ - $[1\frac{3}{4}$+$[$ 2$\frac{1}{2}$ - $(1\frac{1}{2}$ - $\frac{1}{3}$ $)]]$

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $0$

Answer 1

Answer: (D)

$0$

We have, 3$\frac{1}{12}$ - $[$ 1$\frac{3}{4}$ +$[2\frac{1}{2}$ - $(1\frac{1}{2}$ - $\frac{1}{3})]]$
= $\frac{37}{12}$ - $[$ $\frac{7}{4}$ +$[\frac{5}{2}$ - $(\frac{3}{2}$ - $\frac{1}{3}$ $)]]$
= $\frac{37}{12}$ - $[\frac{7}{4}$ + $[\frac{5}{2}$ - $(\frac{9-2}{6})]]$ $[\because$ LCM of 2,3 =6$]$
= $\frac{37}{12}$ - $[\frac{7}{4}$ + $(\frac{5}{2}$ - $\frac{7}{6})]$
=$\frac{37}{12}$ - $(\frac{7}{4}$ + $(\frac{15-7}{6})]$ $[\because$ LCM of 2, 6 = 6$]$
=$\frac{37}{12}$ - $[\frac{7}{4}$ + $\frac{8}{6}$ $]$
= $\frac{37}{12}$ - $[\frac{21+16}{12}$ $]$ $[\because$ LCM of 4, 6 = 12 $]$
= $\frac{37}{12}$ - $\frac{37}{12}$ = 0