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------------------------------------------------ Write [tex]$\frac{32}{40}$[/tex] in simplest form.

A. [tex]$\frac{32}{5}$[/tex]
B. [tex]$\frac{32}{40}$[/tex]
C. [tex]$\frac{4}{5}$[/tex]
D. [tex]$\frac{4}{40}$[/tex]

Answer :

To simplify the fraction [tex]\(\frac{32}{40}\)[/tex], you 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 any remainder.

Step-by-step solution:

1. List the factors:
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

2. Find the greatest common factor:
- The common factors of 32 and 40 are 1, 2, 4, and 8.
- The greatest common factor is 8.

3. Divide both the numerator and the denominator by the GCD:
- Divide 32 by 8, which gives 4.
- Divide 40 by 8, which gives 5.

4. Write the simplified fraction:
- The fraction [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

The simplest form of [tex]\(\frac{32}{40}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].