Answer :
To find the area of a rectangle, we multiply its side lengths together. In this case, the side lengths are [tex]\(\frac{3}{4}\)[/tex] yard and [tex]\(\frac{5}{6}\)[/tex] yard.
Let's calculate the area step by step:
1. Multiply the Numerators:
- The numerators of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] are 3 and 5, respectively.
- Multiply these numerators together: [tex]\(3 \times 5 = 15\)[/tex].
2. Multiply the Denominators:
- The denominators of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] are 4 and 6, respectively.
- Multiply these denominators together: [tex]\(4 \times 6 = 24\)[/tex].
3. Form the Fraction:
- Combine the results from steps 1 and 2 to form the fraction [tex]\(\frac{15}{24}\)[/tex].
4. Check Simplification:
- The fraction [tex]\(\frac{15}{24}\)[/tex] is in its simplest form because the greatest common divisor of 15 and 24 is 3.
- Therefore, it simplifies to [tex]\(\frac{15}{24}\)[/tex].
Thus, the area of the rectangle is [tex]\(\frac{15}{24}\)[/tex] square yards.
Let's calculate the area step by step:
1. Multiply the Numerators:
- The numerators of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] are 3 and 5, respectively.
- Multiply these numerators together: [tex]\(3 \times 5 = 15\)[/tex].
2. Multiply the Denominators:
- The denominators of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex] are 4 and 6, respectively.
- Multiply these denominators together: [tex]\(4 \times 6 = 24\)[/tex].
3. Form the Fraction:
- Combine the results from steps 1 and 2 to form the fraction [tex]\(\frac{15}{24}\)[/tex].
4. Check Simplification:
- The fraction [tex]\(\frac{15}{24}\)[/tex] is in its simplest form because the greatest common divisor of 15 and 24 is 3.
- Therefore, it simplifies to [tex]\(\frac{15}{24}\)[/tex].
Thus, the area of the rectangle is [tex]\(\frac{15}{24}\)[/tex] square yards.
