Question

Tap the correct value for each of the following expressions:
$3\frac{1}{5}-2\frac{3}{5}=$ and
$3\frac{1}{4}-3\frac{1}{3}=$

• A. $\frac{3}{5}$
• B. $\frac{5}{12}$
• C. $\frac{1}{12}$
• D. $\frac{2}{3}$

Answer 1

Answer: (A), (C)

$\frac{1}{12}$

$3\frac{1}{5}-2\frac{3}{5}$
Let's convert mixed fraction to an improper fraction.
$3\frac{1}{5}=\frac{3\times 5+1}{5}=\frac{16}{5}$
and $2\frac{3}{5}=\frac{2\times 5+3}{5}=\frac{13}{5}$

$\therefore 3\frac{1}{5}-2\frac{3}{5}=\frac{16}{5}-\frac{13}{5}$

Concept: As these are like fractions, subtract the numerators and place over the same denominators

$\therefore \frac{16}{5}-\frac{13}{5}=\frac{16-13}{5}$
$=\frac{3}{5}$

$\text{Now,}3\frac{1}{3}-3\frac{1}{4}$
Let's convert mixed fraction to an improper fraction.

$3\frac{1}{3}=\frac{3\times 3+1}{3}=\frac{10}{3}$

and $3\frac{1}{4}=\frac{3\times 4+1}{4}=\frac{13}{4}$

$\therefore 3\frac{1}{3}-3\frac{1}{4}=\frac{10}{3}-\frac{13}{4}$

As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 3 and 4

Multiples of 3: 3, 6, 9, 12, 15, ..
Multiples of 4: 4, 8, 12, 16, 20, ..

12 is the common multiple of 3 and 4. So, LCM of 3 and 4 is 12.

Step 2: Now, we have to convert the denominators of both the fractions into 12 (LCM of 3 and 4) without changing the fraction value.

$\frac{10}{3}=\frac{10\times 4}{3\times 4}=\frac{40}{12}$

$\frac{13}{4}=\frac{13\times 3}{4\times 3}=\frac{39}{12}$

$\therefore 3\frac{1}{3}-3\frac{1}{4}=\frac{40}{12}-\frac{39}{12}$

$=\frac{40-39}{12}$

$=\frac{1}{12}$

$\therefore 3\frac{1}{5}-2\frac{3}{5}=\frac{3}{5}$

$\text{and}3\frac{1}{4}-3\frac{1}{3}=\frac{1}{12}$