Question

Simplify $:$$2\frac{3}{5}$$+$$4\frac{1}{2}$$-$$3\frac{1}{4}$

Answer 1

Step 1: Convert the mixed fractions into improper fractions

Given fractions are $2\frac{3}{5}$‚$4\frac{1}{2}$and $3\frac{1}{4}$

$2\frac{3}{5}$ $=$$\frac{\left(2\times 5\right)+3}{5}$ $=$ $\frac{\left(10\right)+3}{5}$ $=$$\frac{13}{5}$

$4\frac{1}{2}$ $=$$\frac{\left(4\times 2\right)+1}{2}$ $=$ $\frac{\left(8\right)+1}{2}$ $=$ $\frac{9}{2}$

$3\frac{1}{4}$ $=$$\frac{\left(3\times 4\right)+1}{4}$ $=$ $\frac{\left(12\right)+1}{4}$ $=$$\frac{13}{4}$

Step 2: The denominators(bottom numbers) are different .To make it same‚ take the L.C.M of $5,2$ and $4$

L.C.M of $5$‚$2$ and $4$ is $20$

Step 3: Convert both the fractions into equivalent like fractions with their L.C.M as common denominator

$2\frac{3}{5}$ $=$$\frac{13}{5}$ $=$ $\frac{13\times 4}{5\times 4}$ $=$$\frac{52}{20}$

$4\frac{1}{2}$ $=$ $\frac{9}{2}$ $=$ $\frac{9\times 10}{2\times 10}$ $=$$\frac{90}{20}$

$3\frac{1}{4}$ $=$$\frac{13}{4}$ $=$ $\frac{13\times 5}{4\times 5}$ $=$$\frac{65}{20}$

Step 4: Add and subtract the numerators according to the question and put the answers over the denominator

$1\frac{2}{3}$$+$$2\frac{3}{10}$$-$$3\frac{1}{4}$ $=$$\frac{52}{20}$$+$ $\frac{90}{20}$$-$$\frac{65}{20}$ $=$$\frac{52+90-65}{20}$ $=$$\frac{77}{20}$

Step 5: Simplify the fraction

$\Rightarrow \frac{77}{20}$$=$$3\frac{17}{20}$

Hence‚ $2\frac{3}{5}$ $+$$4\frac{1}{2}$$-$$3\frac{1}{4}$$=$$3\frac{17}{20}$