How can the GCF be used to write a fraction?

1 Answer
May 6, 2016

Answer:

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

Explanation:

The GCF (greatest common factor) can be used to express a fraction in simplest terms:

  • Find the GCF of the numerator and denominator.

  • Divide both the numerator and denominator by the GCF.

#color(white)()#
For example, to express #70/42# in lowest terms, first find the GCF of #70# and #42#.

My favourite method to find the GCF of two numbers goes as follows:

  • Divide the larger number by the smaller to get a quotient and remainder.

  • If the remainder is zero, then the smaller number is the GCF.

  • Otherwise, repeat with the smaller number and the remainder.

So in my example:

#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#.

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Having found the GCF, we can now write:

#70/42 = ((70/14)) / ((42/14))= 5/3#

Alternatively, we can express the division implicitly:

#70/42 = (5 xx color(red)(cancel(color(black)(14))))/(3 xx color(red)(cancel(color(black)(14)))) = 5/3#