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What is the simplest form of the fraction below?

[tex]\frac{32}{40}[/tex]

A. [tex]\frac{4}{7}[/tex]
B. [tex]\frac{4}{5}[/tex]
C. 8

Answer :

To simplify the fraction [tex]\(\frac{32}{40}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

1. Find the GCD of 32 and 40:

The factors of 32 are: 1, 2, 4, 8, 16, 32.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.

The largest common factor is 8. So, the GCD of 32 and 40 is 8.

2. Simplify the fraction:

To simplify [tex]\(\frac{32}{40}\)[/tex], divide both the numerator and the denominator by their GCD:

[tex]\[
\frac{32}{40} = \frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]

Therefore, the simplest form of the fraction [tex]\(\frac{32}{40}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].

The correct choice is B. [tex]\(\frac{4}{5}\)[/tex].

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