Question

Gabriel's father has a garden in his backyard the dimensions of the garden are shown 7 3/4 ft and 2 2/3 ft

Part A
calculate the area of the garden show at least one One step before you solve your solution

Answer 1

To calculate the area of Gabriel's father's garden, we need to multiply the length by the width. The dimensions given are \(7 \frac{3}{4}\) ft and \(2 \frac{2}{3}\) ft.

### Step 1: Convert Mixed Numbers to Improper Fractions

**Convert \(7 \frac{3}{4}\) to an improper fraction:**

\[
7 \frac{3}{4} = \left(7 \times 4 + 3\right)/4 = (28 + 3)/4 = 31/4
\]

**Convert \(2 \frac{2}{3}\) to an improper fraction:**

\[
2 \frac{2}{3} = \left(2 \times 3 + 2\right)/3 = (6 + 2)/3 = 8/3
\]

### Step 2: Multiply the Improper Fractions

Now we can find the area by multiplying the two improper fractions:

\[
\text{Area} = \frac{31}{4} \times \frac{8}{3}
\]

### Step 3: Multiply

Now we multiply the numerators and the denominators:

\[
\text{Area} = \frac{31 \times 8}{4 \times 3} = \frac{248}{12}
\]

### Step 4: Simplify the Fraction

Now, let's simplify the fraction:

\[
\frac{248}{12} = \frac{62}{3} \text{ (by dividing both numerator and denominator by 4)}
\]

### Final Answer

Now converting \(\frac{62}{3}\) back into a mixed number gives:

\[
62 \div 3 = 20 \text{ R } 2
\]
Thus,

\[
\frac{62}{3} = 20 \frac{2}{3}
\]

Therefore, the area of the garden is:

\[
\text{Area} = 20 \frac{2}{3} \text{ square feet}
\]