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].
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].
