Question

Simplify $1\frac{1}{2}+4\frac{3}{4}-2\frac{1}{6}$ and select the correct answer from the given four alternative answers :

• A. $4\frac{1}{12}$
• B. $3\frac{1}{12}$
• C. $3\frac{7}{12}$
• D. $4\frac{7}{12}$

Answer 1

The correct option is A

$4\frac{1}{12}$

Justification of correct answer:

To simplify: $1\frac{1}{2}+4\frac{3}{4}-2\frac{1}{6}$

Convert all the above mixed fractions into improper fractions, we get

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

$4\frac{3}{4}=\frac{19}{4}$

$2\frac{1}{6}=\frac{13}{6}$

Now convert all the above unlike fractions into like fractions by obtaining L.C.M of their denominators, we get

L.C.M of $2,4$and$6=12$

$\frac{3}{2}=\frac{3\times 6}{2\times 6}=\frac{18}{12}$

$\frac{19}{4}=\frac{19\times 3}{4\times 3}=\frac{57}{12}$

$\frac{13}{6}=\frac{13\times 2}{6\times 2}=\frac{26}{12}$

$1\frac{1}{2}+4\frac{3}{4}-2\frac{1}{6}$$=\frac{3}{2}+\frac{19}{4}-\frac{13}{6}$

$=\frac{18}{12}+\frac{57}{12}-\frac{26}{12}$

$=\frac{18+57-26}{12}$

⇒ $1\frac{1}{2}+4\frac{3}{4}-2\frac{1}{6}$ $=\frac{49}{12}$

⇒$1\frac{1}{2}+4\frac{3}{4}-2\frac{1}{6}$$=\frac{49}{12}$or$4\frac{1}{12}$

Thus, option A is the correct answer