Example 10. Ali ate 1/3 of a cake and Jason ate 1/4 of what was left. What fraction of the cake was still uneaten?

The whole cake is represented by 1. Ali ate $\frac{1}{3}$ of the cake.
Fraction left after Ali = $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$

Jason ate $\frac{1}{4}$ of what was left. "What was left" is $\frac{2}{3}$ of the cake.
Fraction Jason ate = $\frac{1}{4} \times \frac{2}{3} = \frac{1 \times 2}{4 \times 3} = \frac{2}{12} = \frac{1}{6}$

Total eaten = Fraction Ali ate + Fraction Jason ate
Total eaten = $\frac{1}{3} + \frac{1}{6}$
To add these fractions, find a common denominator, which is 6.
Total eaten = $\frac{1 \times 2}{3 \times 2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

Fraction uneaten = Whole cake - Total eaten
Fraction uneaten = $1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2}$

The fraction of the cake that was still uneaten is $\frac{1}{2}$.