To find out how much of the cake was left after Aliyah's sibling and friends ate from it, we first need to calculate the total amount of the cake that was eaten.
- Sibling's portion: \( \frac{1}{4} \) of the cake.
- Friends' portion: \( \frac{2}{3} \) of the cake.
Next, we need to find a common denominator to add these two fractions. The least common multiple of 4 and 3 is 12.
Now, we convert each fraction:
- \( \frac{1}{4} = \frac{3}{12} \) (multiply both the numerator and denominator by 3)
- \( \frac{2}{3} = \frac{8}{12} \) (multiply both the numerator and denominator by 4)
Now we can add the two fractions:
\[ \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]
So, \( \frac{11}{12} \) of the cake has been eaten.
To find out how much cake is left, we subtract the eaten portion from the whole cake:
\[ 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12} \]
Thus, the amount of cake that is left is \( \frac{1}{12} \) of the original cake.
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