A fraction is given as
100
24
. To simplify this fraction, you can:
A. Divide both the numerator and denominator by 2. B. Multiply both the numerator and denominator by 4. C. Divide both the numerator and denominator by 4. D. Multiply both the numerator and denominator by 2.
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{100}{24} ), the most effective method is to divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 100 and 24 is 4. Therefore, the correct option from the provided choices is C. Divide both the numerator and denominator by 4.
Step-by-Step Explanation:
- Identify the Fraction: The fraction we need to simplify is ( \frac{100}{24} ).
- Find the GCD: To simplify a fraction, it is essential to find the GCD of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
- The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- The common factors are 1, 2, and 4, with the largest being 4.
- Divide by the GCD: Now that we have the GCD, we divide both the numerator and the denominator by 4:
[
\frac{100 \div 4}{24 \div 4} = \frac{25}{6}
] - Result: The simplified form of the fraction ( \frac{100}{24} ) is ( \frac{25}{6} ).
Why Not the Other Options?
- Option A (Divide by 2): If we divide both by 2, we get ( \frac{50}{12} ), which is still not in its simplest form.
- Option B (Multiply by 4): Multiplying by 4 gives us ( \frac{400}{96} ), which complicates the fraction further instead of simplifying it.
- Option D (Multiply by 2): This results in ( \frac{200}{48} ), also not simplified.
Conclusion
The correct method for simplifying ( \frac{100}{24} ) is to divide both the numerator and the denominator by their GCD, which is 4, yielding the simplified fraction ( \frac{25}{6} ). This approach maintains the equality of the fraction while making it easier to work with in further calculations or comparisons.