Question

Convert the given pair of fractions into like fractions: $\frac{1}{3}$ and $\frac{2}{5}$.

• A. $\frac{5}{15}$ and $\frac{6}{15}$
• B. $\frac{1}{3}$ and $\frac{6}{15}$
• C. $\frac{5}{15}$ and $\frac{2}{5}$
• D. $\frac{1}{3}$ and $\frac{2}{5}$

Answer 1

The correct option is A $\frac{5}{15}$ and $\frac{6}{15}$

Like fractions have the same denominator. But here we have 3 and 5 as the denominators in the given pair of fractions $\frac{1}{3}$ and $\frac{2}{5}$.

Let's convert the given fractions into like fractions using LCM method

Multiples of 3: 3, 6, 9, 12, 15...
Multiples of 5: 5, 10, 15...
$\therefore LCM(3,5)=15$

Now, we multiply $\frac{1}{3}$ and $\frac{2}{5}$ with $5$ and $3$ respectively to make their denominators as $15.$

$\therefore \frac{1}{3}=\frac{1\times 5}{3\times 5}=\frac{5}{15}$

and $\frac{2}{5}=\frac{2\times 3}{5\times 3}=\frac{6}{15}$

Hence, $\frac{5}{15}$ and $\frac{6}{15}$ are a pair of like fractions of $\frac{1}{3}$ and $\frac{2}{5}.$