Answer :
To simplify the fraction [tex]\(\frac{32}{40}\)[/tex], we want to find its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Here's how to do it step-by-step:
1. Identify the numerator and the denominator of the fraction. Here, the numerator is 32, and the denominator is 40.
2. Find the greatest common divisor (GCD) of 32 and 40. The GCD is the largest number that can divide both 32 and 40 without leaving a remainder.
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors are 1, 2, 4, and 8, with 8 being the greatest. So, the GCD is 8.
3. Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[
\frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
Therefore, the simplest form of [tex]\(\frac{32}{40}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
Here's how to do it step-by-step:
1. Identify the numerator and the denominator of the fraction. Here, the numerator is 32, and the denominator is 40.
2. Find the greatest common divisor (GCD) of 32 and 40. The GCD is the largest number that can divide both 32 and 40 without leaving a remainder.
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors are 1, 2, 4, and 8, with 8 being the greatest. So, the GCD is 8.
3. Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[
\frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
Therefore, the simplest form of [tex]\(\frac{32}{40}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
