Hetty ate 25% of a cake.

Brent ate 2/5 of the same cake.
What proportion of the cake is left? Give your answer as a decimal.

1 answer

First, we need to determine what fraction of the cake both Hetty and Brent ate together.

Hetty ate 25% of the cake. To convert this percentage to a fraction:
\[
25\% = \frac{25}{100} = \frac{1}{4}
\]

Brent ate \(\frac{2}{5}\) of the cake.

Next, we add the fractions \(\frac{1}{4}\) and \(\frac{2}{5}\) together. To do this, we need a common denominator.

The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.

Convert each fraction to have a denominator of 20:
\[
\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}
\]
\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\]

Now add the fractions:
\[
\frac{5}{20} + \frac{8}{20} = \frac{13}{20}
\]

Therefore, Hetty and Brent together ate \(\frac{13}{20}\) of the cake.

To find the proportion of the cake that is left, subtract the fraction of the cake they ate from 1 (the whole cake):
\[
1 - \frac{13}{20} = \frac{20}{20} - \frac{13}{20} = \frac{7}{20}
\]

Finally, convert \(\frac{7}{20}\) to a decimal:
\[
\frac{7}{20} = 0.35
\]

So, the proportion of the cake that is left is \(0.35\).