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

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

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

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

Step 1: Identify the denominator

The denominator is: $$ 3 $$

Step 2: Multiply the denominator by the whole number

The whole number is $1$: $$ 3 \times 1 = 3 $$

Step 3: Add the numerator

Add $2$ to the result: $$ 3 + 2 = 5 $$

Step 4: Replace with the new numerator

Now write the result over the same denominator: $$ \frac{5}{3} $$

Check Your Answer

To verify: $$ 5 \div 3 = 1 \text{ remainder } 2 $$

This gives: $$ 1 \frac{2}{3} $$

Which matches the original mixed number.

Summary

To convert a mixed fraction to an improper fraction:

  1. Multiply the denominator by the whole number.
  2. Add the numerator.
  3. Place this result over the original denominator.

So: $$ 1 \frac{2}{3} = \frac{5}{3} $$