When do i reduce fractions

Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Reducing Fractions Simplest Form A fraction is in simplest form if the greatest common factor GCF of its numerator and denominator is 1 -- that is, if they share no common factors other than 1.

This is sometimes shown as "canceling" the common factors. Try to exactly divide only whole number answers both the top and bottom of the fraction by 2, 3, 5, 7 , That is as far as we can go. The fraction simplifies to 2 9. The fraction simplifies to 2 7. In fact, when checking from smallest to largest we use prime numbers :. For example, notice the three rectangles below where the left-hand side of each rectangle is shaded and the fraction that results represents the shaded part out of the whole rectangle.

All three images represent the same part to whole , which indicates that each resulting fraction is equivalent to the other. And just as this example indicates, our goal is to transform a fraction by creating an equivalent fraction whose terms no longer have any common factors as noted by Lumen Learning. So, we may need to continue to reduce the fraction further in necessary.

Whereas the greatest common factor GCF method will always give us the largest number for which we should divide. And then we identify the GCF from the prime factorization. Remember, when we find the GCF from a list of prime factors, we choose the fewest of what is common. Both methods are perfectly acceptable, and it comes down to personal preference as to which technique you wish to employ.