A land developer wants to divide up 3 3/4 acres of land into equally-sized lots for houses. She wants to build 10 houses. How big can she make each lot?

Write your answer as a fraction or as a whole or mixed number.

acres

1 answer

To find the size of each lot, you need to divide the total area of land by the number of houses.

First, convert the mixed number \( 3 \frac{3}{4} \) acres into an improper fraction:

\[ 3 \frac{3}{4} = 3 \times 4 + 3 = 12 + 3 = 15 \quad \text{(which is } \frac{15}{4} \text{ acres)} \]

Next, divide the total area by the number of houses:

\[ \text{Size of each lot} = \frac{\text{Total land}}{\text{Number of houses}} = \frac{\frac{15}{4}}{10} \]

To divide by 10, we can multiply by the reciprocal of 10:

\[ \frac{\frac{15}{4}}{10} = \frac{15}{4} \times \frac{1}{10} = \frac{15}{40} \]

Now, simplify \( \frac{15}{40} \):

\[ \frac{15}{40} = \frac{3}{8} \quad \text{(divide both the numerator and denominator by 5)} \]

So, the size of each lot is:

\[ \boxed{\frac{3}{8}} \text{ acres} \]