Solution:
A) Calculate the area of the piece of fabric.
1. Given dimensions of the fabric:
- Length: \frac{7}{8} yard
- Width: \frac{4}{5} yard
2. Use the formula for the area of a rectangle: \text{Area} = \text{Length} \times \text{Width}
\text{Area} = \frac{7}{8} \times \frac{4}{5}
3. Multiply the fractions:
- Multiply numerators: 7 \times 4 = 28
- Multiply denominators: 8 \times 5 = 40
4. Area of the fabric:
\text{Area} = \frac{28}{40}
5. Simplify the fraction:
\frac{28}{40} = \frac{7}{10}
B) Calculate the area each person gets when shared equally.
1. Divide the area by 2:
\text{Area each person gets} = \frac{\frac{7}{10}}{2}
2. Rewrite the division as multiplication by reciprocal:
\text{Area each person gets} = \frac{7}{10} \times \frac{1}{2}
3. Perform the multiplication:
- Multiply numerators: 7 \times 1 = 7
- Multiply denominators: 10 \times 2 = 20
4. Area each person gets:
\text{Area each person gets} = \frac{7}{20}
Answer:
The area of the piece of fabric is \frac{7}{10} square yards. Each person gets a piece of fabric with an area of \frac{7}{20} square yards.