High School

What is the simplified form of the fraction below?

[tex]\frac{24}{30}[/tex]

A. [tex]\frac{2}{3}[/tex]
B. 4
C. [tex]\frac{5}{6}[/tex]
D. [tex]\frac{3}{4}[/tex]

Answer :

To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we need to find a common factor that can divide both the numerator (24) and the denominator (30).

1. Find the Greatest Common Divisor (GCD): First, identify the greatest common divisor of 24 and 30. The GCD is the largest number that can divide both numbers without leaving a remainder.

- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

The common factors are 1, 2, 3, and 6. The greatest of these is 6.

2. Divide by the GCD: Now, divide both the numerator and the denominator by their greatest common divisor, which is 6.

- Divide 24 by 6: [tex]\(24 \div 6 = 4\)[/tex]
- Divide 30 by 6: [tex]\(30 \div 6 = 5\)[/tex]

3. Write the Simplified Fraction: After dividing, the simplified form of the fraction is [tex]\(\frac{4}{5}\)[/tex].

Comparing this with the options provided:

- A. [tex]\(\frac{2}{3}\)[/tex]
- B. 4
- C. [tex]\(\frac{5}{6}\)[/tex]
- D. [tex]\(\frac{3}{4}\)[/tex]

None of these match [tex]\(\frac{4}{5}\)[/tex]. The options given do not include the correct simplified form of the fraction [tex]\(\frac{24}{30}\)[/tex], which is actually [tex]\(\frac{4}{5}\)[/tex].