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
part B You found the area of the garden in part one explain briefly without doing any calculations how would you find 5/6 of this area
Part A
calculate the area of the garden show at least one One step before you solve your solution
part B You found the area of the garden in part one explain briefly without doing any calculations how would you find 5/6 of this area
Answers
Answered by
GPT-4o mini
To calculate the area of the garden with dimensions 7 3/4 ft and 2 2/3 ft, follow these steps:
### Part A
**Step 1**: Convert the mixed numbers to improper fractions.
- 7 3/4 can be converted as follows:
\[
7 \times 4 + 3 = 28 + 3 = 31 \Rightarrow \frac{31}{4}
\]
- 2 2/3 can be converted as follows:
\[
2 \times 3 + 2 = 6 + 2 = 8 \Rightarrow \frac{8}{3}
\]
**Step 2**: Multiply the two improper fractions to find the area.
The area \( A \) will be:
\[
A = \left(\frac{31}{4}\right) \times \left(\frac{8}{3}\right)
\]
To multiply fractions, multiply the numerators and then the denominators:
\[
A = \frac{31 \times 8}{4 \times 3} = \frac{248}{12}
\]
**Step 3**: Simplify the fraction.
\[
\frac{248 \div 4}{12 \div 4} = \frac{62}{3}
\]
Thus, the area of the garden is \( \frac{62}{3} \) square feet or approximately 20 2/3 square feet.
### Part B
To find \( \frac{5}{6} \) of the area calculated in Part A, you take the area (which is \( \frac{62}{3} \)) and multiply it by \( \frac{5}{6} \).
This means you would perform the following operation:
\[
\frac{5}{6} \times \frac{62}{3}
\]
By multiplying the numerators and denominators separately, you can find the result. The methodology involves multiplying \( 5 \) and \( 62 \) together for the new numerator, and multiplying \( 6 \) and \( 3 \) together for the new denominator. After execution of these steps, you would simplify if necessary to arrive at the final answer.
### Part A
**Step 1**: Convert the mixed numbers to improper fractions.
- 7 3/4 can be converted as follows:
\[
7 \times 4 + 3 = 28 + 3 = 31 \Rightarrow \frac{31}{4}
\]
- 2 2/3 can be converted as follows:
\[
2 \times 3 + 2 = 6 + 2 = 8 \Rightarrow \frac{8}{3}
\]
**Step 2**: Multiply the two improper fractions to find the area.
The area \( A \) will be:
\[
A = \left(\frac{31}{4}\right) \times \left(\frac{8}{3}\right)
\]
To multiply fractions, multiply the numerators and then the denominators:
\[
A = \frac{31 \times 8}{4 \times 3} = \frac{248}{12}
\]
**Step 3**: Simplify the fraction.
\[
\frac{248 \div 4}{12 \div 4} = \frac{62}{3}
\]
Thus, the area of the garden is \( \frac{62}{3} \) square feet or approximately 20 2/3 square feet.
### Part B
To find \( \frac{5}{6} \) of the area calculated in Part A, you take the area (which is \( \frac{62}{3} \)) and multiply it by \( \frac{5}{6} \).
This means you would perform the following operation:
\[
\frac{5}{6} \times \frac{62}{3}
\]
By multiplying the numerators and denominators separately, you can find the result. The methodology involves multiplying \( 5 \) and \( 62 \) together for the new numerator, and multiplying \( 6 \) and \( 3 \) together for the new denominator. After execution of these steps, you would simplify if necessary to arrive at the final answer.