What does it mean to simplify a fraction?

What does it mean to simplify a fraction?

• A. To divide numerator and denominator by their greatest common factor.
• B. To multiply numerator and denominator by their greatest common factor.
• C. To add the greatest common factor to numerator and denominator.
• D. To subtract the greatest common factor from numerator and denominator.

Answer: (A)

To simplify a fraction means rewriting it with smaller numbers while keeping the same value. The way to do this is by dividing both the top (numerator) and the bottom (denominator) by their greatest common factor—the largest number that divides both parts exactly. When you divide by that number, you remove any shared factors, leaving the fraction in lowest terms. For example, 8/12 can be reduced because both 8 and 12 are divisible by 4. Dividing both by 4 gives 2/3, which is in simplest form because 2 and 3 have no common factors other than 1. If the greatest common factor is 1, the fraction is already simplified. The other actions—multiplying, adding, or subtracting the greatest common factor from the numerator and denominator—would change the value of the fraction, so they aren’t valid ways to simplify.

To simplify a fraction means rewriting it with smaller numbers while keeping the same value. The way to do this is by dividing both the top (numerator) and the bottom (denominator) by their greatest common factor—the largest number that divides both parts exactly. When you divide by that number, you remove any shared factors, leaving the fraction in lowest terms.

For example, 8/12 can be reduced because both 8 and 12 are divisible by 4. Dividing both by 4 gives 2/3, which is in simplest form because 2 and 3 have no common factors other than 1.

If the greatest common factor is 1, the fraction is already simplified. The other actions—multiplying, adding, or subtracting the greatest common factor from the numerator and denominator—would change the value of the fraction, so they aren’t valid ways to simplify.