Question

The dimensions of a kitchen are 9 2/3 feet by 8 5/6 feet. What is the area of the kitchen?

37 square feet
40 square feet
73 1/2 square feet
85 7/18square feet

Answer 1

To find the area of the kitchen, we multiply its length and width.

First, we need to convert the mixed numbers into improper fractions.

1. Convert \( 9 \frac{2}{3} \):
\[
9 \frac{2}{3} = 9 + \frac{2}{3} = \frac{27}{3} + \frac{2}{3} = \frac{27 + 2}{3} = \frac{29}{3}
\]

2. Convert \( 8 \frac{5}{6} \):
\[
8 \frac{5}{6} = 8 + \frac{5}{6} = \frac{48}{6} + \frac{5}{6} = \frac{48 + 5}{6} = \frac{53}{6}
\]

Now, we multiply these two improper fractions together to find the area:
\[
\text{Area} = \left(\frac{29}{3}\right) \times \left(\frac{53}{6}\right)
\]

Multiply the numerators and the denominators:
\[
\text{Area} = \frac{29 \times 53}{3 \times 6} = \frac{1537}{18}
\]

Next, we can convert \(\frac{1537}{18}\) into a mixed number. We divide 1537 by 18:
\[
1537 \div 18 = 85.38 \quad (\text{the whole number part is } 85)
\]

Now calculate \( 85 \times 18 = 1530\), then subtract that from 1537 to find the remainder:
\[
1537 - 1530 = 7
\]

So, we can express \(\frac{1537}{18}\) as:
\[
85 \frac{7}{18}
\]

The final area of the kitchen is \( 85 \frac{7}{18} \) square feet.

Thus, the area of the kitchen is:
\[
\boxed{85 \frac{7}{18}} \text{ square feet}
\]