Question

Tucker is painting his pool deck over the weekend. The area of the deck is 76
1
2
square meters. He paints
2
3
of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?
Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.
square meters

Answer 1

Tucker's deck area is \( 76 \frac{1}{2} \) square meters. We first need to express this mixed number as an improper fraction.

To convert \( 76 \frac{1}{2} \) into an improper fraction:

\[
76 \frac{1}{2} = 76 + \frac{1}{2} = \frac{76 \times 2}{2} + \frac{1}{2} = \frac{152}{2} + \frac{1}{2} = \frac{152 + 1}{2} = \frac{153}{2}
\]

Now, Tucker paints \( \frac{2}{3} \) of the deck before lunch. We will calculate the area he painted:

\[
\text{Area painted} = \frac{2}{3} \times \frac{153}{2}
\]

To calculate this, we multiply the fractions:

\[
\frac{2}{3} \times \frac{153}{2} = \frac{2 \times 153}{3 \times 2} = \frac{153}{3} = 51 \text{ square meters}
\]

Next, we need to find out how much of the deck is left to paint after lunch. We do this by subtracting the area he painted from the total area of the deck:

\[
\text{Area left} = 76 \frac{1}{2} - \text{Area painted}
\]

Converting \( 76 \frac{1}{2} \) again to its improper form, we have:

\[
\text{Area left} = \frac{153}{2} - 51
\]

Now we need to express \( 51 \) as a fraction with the same denominator:

\[
51 = \frac{51 \times 2}{2} = \frac{102}{2}
\]

Now we can subtract:

\[
\text{Area left} = \frac{153}{2} - \frac{102}{2} = \frac{153 - 102}{2} = \frac{51}{2}
\]

Finally, we can convert \( \frac{51}{2} \) back to a mixed number:

\[
\frac{51}{2} = 25 \frac{1}{2}
\]

Thus, the area of the pool deck that Tucker has left to paint after lunch is:

\[
\boxed{25 \frac{1}{2}} \text{ square meters}
\]