To find out how much of Paige's home was painted last year, we need to determine the fraction of the total that represents the amount she intended to paint and the amount she actually completed.
Paige intended to paint \( \frac{4}{5} \) of the rooms, and by the end of the year, she completed \( \frac{2}{3} \) of the rooms. We need to find the amount that was actually painted out of the total intended.
Since she intended to paint \( \frac{4}{5} \) of the rooms, we want to find the fraction of those rooms that she completed. We will multiply the fraction of rooms she intended to paint \( \frac{4}{5} \) by the fraction she actually completed \( \frac{2}{3} \):
\[ \text{Fraction painted last year} = \left(\frac{4}{5}\right) \times \left(\frac{2}{3}\right) \]
Calculating this gives:
\[ \frac{4 \times 2}{5 \times 3} = \frac{8}{15} \]
So, the amount of Paige’s home that was painted last year is \( \frac{8}{15} \).
The correct response is: 8/15
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