To simplify the fraction [tex]\(\frac{24}{54}\)[/tex] to its simplest form, we need to follow these steps:
1. Identify Common Factors:
- First, we need to find the greatest common divisor (GCD) of the numerator (24) and the denominator (54). The GCD is the largest positive integer that divides both numbers without leaving a remainder.
2. Divide by the GCD:
- Once we've identified the GCD, we divide both the numerator and the denominator by this number to simplify the fraction.
Let's go through the steps in detail:
1. Find the GCD:
- We look for the largest number that can divide both 24 and 54 completely.
- The GCD of 24 and 54 is 6.
2. Simplify the Fraction:
- Now, we divide both the numerator and the denominator by their GCD (6).
[tex]\[
\text{Simplified numerator} = \frac{24}{6} = 4
\][/tex]
[tex]\[
\text{Simplified denominator} = \frac{54}{6} = 9
\][/tex]
So, the fraction [tex]\(\frac{24}{54}\)[/tex] simplifies to [tex]\(\frac{4}{9}\)[/tex].
Therefore, the equivalent fraction in its simplest form is [tex]\(\frac{4}{9}\)[/tex].
