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?

Step 1: Calculate the fraction of the cake remaining after Ali ate his share. The whole cake is represented by 1. Ali ate $\frac{1}{3}$ of the cake. Fraction left after Ali = $1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$

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

Step 3: Calculate the total fraction of the cake eaten by both Ali and Jason. 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 = $\frac{1 \times 2}{3 \times 2} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$

Step 4: Calculate the fraction of the cake that was still uneaten. 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 $\boxed{\frac{1}{2}}$.

Send me the next one 📸