High School

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

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 can divide both numbers without leaving a remainder.

1. Find the GCD of 32 and 40:
- List the factors of each number:
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
- Identify the common factors: 1, 2, 4, 8
- The greatest common factor is 8.

2. Divide both the numerator and the denominator by their GCD:
- Divide the numerator: [tex]\( \frac{32}{8} = 4 \)[/tex]
- Divide the denominator: [tex]\( \frac{40}{8} = 5 \)[/tex]

3. Write the simplified fraction:
- The simplified form of [tex]\(\frac{32}{40}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].

So, the fraction [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

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