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].
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].
