Answer :

To express the fraction [tex]\( \frac{24}{30} \)[/tex] in its lowest terms, we need to simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. Here's how you can do it step by step:

1. Identify the Numerator and Denominator:
- The numerator is 24.
- The denominator is 30.

2. Find the GCD of 24 and 30:

- List the factors of 24: [tex]\( 1, 2, 3, 4, 6, 8, 12, 24 \)[/tex].
- List the factors of 30: [tex]\( 1, 2, 3, 5, 6, 10, 15, 30 \)[/tex].

Now, find the largest number that appears in both lists. The common factors are [tex]\( 1, 2, 3, \)[/tex] and [tex]\( 6 \)[/tex]. So, the greatest common divisor is 6.

3. Simplify Both the Numerator and Denominator by Dividing them by the GCD:

- Divide the numerator (24) by the GCD (6):
[tex]\[
\frac{24}{6} = 4
\][/tex]

- Divide the denominator (30) by the GCD (6):
[tex]\[
\frac{30}{6} = 5
\][/tex]

4. Write the Simplified Fraction:

- The fraction [tex]\( \frac{24}{30} \)[/tex] simplifies to [tex]\( \frac{4}{5} \)[/tex].

So, the fraction [tex]\( \frac{24}{30} \)[/tex] in lowest terms is [tex]\( \frac{4}{5} \)[/tex].

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