To divide the fraction [tex]\(\frac{40x}{64y}\)[/tex] by the fraction [tex]\(\frac{5x}{8y}\)[/tex], we'll follow these detailed steps:
1. Understand the Division of Fractions:
When you divide by a fraction, it is equivalent to multiplying by its reciprocal. Therefore:
[tex]\[
\frac{40x}{64y} \div \frac{5x}{8y} = \frac{40x}{64y} \times \frac{8y}{5x}
\][/tex]
2. Multiply the Fractions:
To multiply the fractions, multiply the numerators together and the denominators together.
[tex]\[
\text{Numerator: } (40x) \times (8y) = 320xy
\][/tex]
[tex]\[
\text{Denominator: } (64y) \times (5x) = 320xy
\][/tex]
3. Combine the Numerators and Denominators:
After the multiplication, we obtain:
[tex]\[
\frac{320xy}{320xy}
\][/tex]
4. Simplify the Fraction:
When the numerator and the denominator are identical, the fraction simplifies to:
[tex]\[
\frac{320xy}{320xy} = 1
\][/tex]
Thus, the result of dividing [tex]\(\frac{40x}{64y}\)[/tex] by [tex]\(\frac{5x}{8y}\)[/tex] is [tex]\(1\)[/tex].
The correct answer is:
C. 1
