Which action reduces a fraction by dividing by greatest common factor?

Which action reduces a fraction by dividing by greatest common factor?

• A. Multiply numerator and denominator by their greatest common factor.
• B. Add the numerator and denominator.
• C. Subtract the gcd from both numbers.
• D. Divide numerator and denominator by their greatest common factor.

Answer: (D)

Reducing a fraction means writing it as a smaller pair of numbers that represents the same value. To do this, find the greatest common factor of the numerator and denominator and divide both by that number. For example, 18/24 have a greatest common factor of 6; dividing both parts by 6 gives 3/4, which is in simplest form because 3 and 4 have no common factors other than 1. Other operations don’t preserve the value or don’t produce a simpler form: multiplying both parts by the gcd keeps the fraction equivalent but makes it larger and not reduced, while adding or subtracting the top and bottom changes the value entirely. So dividing numerator and denominator by their greatest common factor is the correct way to reduce a fraction.

Reducing a fraction means writing it as a smaller pair of numbers that represents the same value. To do this, find the greatest common factor of the numerator and denominator and divide both by that number. For example, 18/24 have a greatest common factor of 6; dividing both parts by 6 gives 3/4, which is in simplest form because 3 and 4 have no common factors other than 1. Other operations don’t preserve the value or don’t produce a simpler form: multiplying both parts by the gcd keeps the fraction equivalent but makes it larger and not reduced, while adding or subtracting the top and bottom changes the value entirely. So dividing numerator and denominator by their greatest common factor is the correct way to reduce a fraction.