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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].
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].
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