How do you simplify sums or differences?

When the numerator and denominator of a sum or difference have common factors other than 1, the sum or difference needs to be written in simplest form.

Example 1:

To write the sum of fractions in simplest form:

Tom has of a package of markers and of another package of markers. The sum of the two packages totals of a whole package of markers.

The sum is not in simplest form because the numerator and denominator have a common factor other than 1. Find the simplest form of the sum.

First, find the greatest common factor by listing all the factors for 21 and 24.

factors of 21: 1, 3, 7, 21
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

The greatest common factor is 3 because it is the largest number that can divide evenly into both the numerator and denominator.