To find out how much of the cake is left after Aliyah's siblings and friends ate some, we first need to calculate the total amount of the cake that was consumed.
Her siblings ate \( \frac{1}{4} \) of the cake, and her friends ate \( \frac{2}{3} \) of the cake. We need to add these two fractions together.
To add \( \frac{1}{4} \) and \( \frac{2}{3} \), we first need a common denominator. The least common multiple (LCM) of 4 and 3 is 12.
Now we convert both fractions:
\[ \frac{1}{4} = \frac{3}{12} \]
\[ \frac{2}{3} = \frac{8}{12} \]
Now we can add the two fractions:
\[ \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \]
This means \( \frac{11}{12} \) of the cake was eaten.
To find out how much cake is left, we subtract the amount eaten from the whole cake (1 whole cake):
\[ 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12} \]
So, the amount of cake left is \( \frac{1}{12} \).
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