How do you convert a fraction like $2 \frac{1}{3}$ to an improper fraction?

A mixed fraction is made up of a whole number and a proper fraction. To convert it into an improper fraction, use this rule:

Multiply the denominator by the whole number, then add the numerator.
The result becomes the new numerator, and the denominator stays the same.

Step-by-Step: Convert $2 \frac{1}{3}$ to an Improper Fraction

Step 1: Identify the denominator

The denominator of the fraction is: $$ 3 $$

Step 2: Multiply the whole number by the denominator

The whole number is $2$.
Now multiply: $$ 2 \times 3 = 6 $$

Step 3: Add the numerator

Add the existing numerator $1$: $$ 6 + 1 = 7 $$

Step 4: Place the new numerator over the denominator

Replace the mixed number with: $$ \frac{7}{3} $$

How to Check Your Answer

To check, divide the numerator by the denominator: $$ 7 \div 3 = 2 \text{ remainder } 1 $$

Now rewrite as a mixed fraction: $$ 2 \frac{1}{3} $$

This matches the original number, so the improper fraction $\frac{7}{3}$ is correct ✅

Summary

To convert a mixed number into an improper fraction:

  1. Multiply the whole number by the denominator.
  2. Add the numerator to this product.
  3. Use this total as the new numerator.
  4. Keep the original denominator.

So: $$ 2 \frac{1}{3} = \frac{7}{3} $$