Question

Can $2+\frac{1}{3}$ be written as $2\frac{1}{3}?$

• A. Yes
• B. No
• C. Cannot be determined

Answer 1

The correct option is A Yes

Given: $2+\frac{1}{3}\text{and}2\frac{1}{3}$
Let's solve the each term one by one

First term: $2+\frac{1}{3}=\frac{2}{1}+\frac{1}{3}$

1 and 3 are the denominators of both the fractions respectively.

Let's convert the unlike fractions into like fractions
Multiples of 1: 1, 2, 3, 4, ..
Multiples of 3: 3, 6, 9, 12, ..
LCM(1, 3) = 3

Now we have to convert the denominators in both the fractions into 3 (LCM of 1 and 3)

$2=\frac{2}{1}=\frac{2\times 3}{1\times 3}=\frac{6}{3}$
and $\frac{1}{3}$ is already in its third form.

$\therefore 2+\frac{1}{3}=\frac{6}{3}+\frac{1}{3}$
$=\frac{6+1}{3}$
$=\frac{7}{3}$

Second term: $2\frac{1}{3}$
Convert the fraction into the simplest form
$2\frac{1}{3}=\frac{3\times 2+1}{3}$
$=\frac{7}{3}$

Hence, $2+\frac{1}{3}$ can be written as $2\frac{1}{3}.$