How can the GCF be used to write a fraction?

Question

Riley Anderson · Accepted Answer

Divide both the numerator and denominator by their GCF to get a fraction in lowest terms.

To put a fraction in simpler words, use the greatest common factor, or GCF: Determine the numerator's and denominator's GCF. Divide the denominator by the GCF and the numerator by it. #color(white)()# For example, to express #70/42# in lowest terms, first find the GCF of #70# and #42#. The following is my preferred technique for determining the GCF of two numbers: To find the remainder and quotient, divide the larger number by the smaller one. The GCF is the smaller number if the remainder is zero. If not, repeat with the remainder and the smaller number. Thus, in my instance: #70/42 = 1# with remainder #28# #42/28 = 1# with remainder #14# #28/14 = 2# with remainder #0# So the GCF of #70# and #42# is #14#. #color(white)()# Having found the GCF, we can now write: #70/42 = ((70/14)) / ((42/14))= 5/3# As an alternative, we can indicate the division subtly: #70/42 = (5 xx color(red)(cancel(color(black)(14))))/(3 xx color(red)(cancel(color(black)(14)))) = 5/3#

Mila Anderson · Answer

undefined The greatest common factor (GCF) can be used to write a fraction in simplest form. To do this, you divide both the numerator and the denominator of the fraction by their greatest common factor. This process reduces the fraction to its simplest form, meaning that the numerator and denominator share no common factors other than 1.

For example, consider the fraction 24/36.

First, find the greatest common factor of 24 and 36, which is 12.

Then, divide both the numerator and the denominator by 12:

24 ÷ 12 = 2
36 ÷ 12 = 3

So, 24/36 simplifies to 2/3.

In summary, using the GCF allows us to simplify fractions by dividing both the numerator and denominator by their greatest common factor, resulting in a fraction in its simplest form.