Divide [tex]\frac{40 x}{64 y}[/tex] by [tex]\frac{5 x}{8 y}[/tex].

A. [tex]\frac{25 x^2}{64 y^2}[/tex]

B. [tex]\frac{25}{64}[/tex]

C. 1

D. [tex]\frac{3}{4}[/tex]



Answer :

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