Title: Lesson 5-3
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 5-4

Example 1  Write a Fraction in Simplest Form
Write  in simplest form.

Method 1  Divide by common factors.
	2 is a common factor of 12 and 18, so divide by 2.
		3 is a common factor of 6 and 9, so divide by 3.

The fraction  is in simplest form since 2 and 3 have no common factors greater than 1.

Method 2  Divide by the GCF.
First, find the GCF of the numerator and denominator.
factors of 12:  1, 2, 3, 4, 6, 12
factors of 18:  1, 2, 3, 6, 9, 18
The GCF of 12 and 18 is 6.

Then, divide the numerator and denominator by the GCF, 6.

So,  written in simplest form is .

Example 2 Write Fractions in Simplest Form
Write  in simplest form.

First, find the GCF of the numerator and denominator.
factors of 24:  1, 2, 3, 4, 6, 8, 12, 24
factors of 32:  1, 2, 4, 8, 16, 32
The GCF of 24 and 32 is 8.

Then, divide the numerator and denominator by the GCF, 8.

So,  written in simplest form is .
Example 3  Use Fractions to Solve a Problem
MARATHONS   Officials estimate that 75 of the 120 runners starting a marathon will run the entire race.  Write this fraction in simplest form.

75 = 3 ⋅ 5 ⋅ 5
120 = 2 ⋅ 2 ⋅ 2 ⋅ 3 ⋅ 5

The GCF of 75 and 120 is 3 ⋅ 5, or 15.

The fraction of runners who will run the entire race is .