In this lesson, students continue to find differences of fractions, with a focus on mixed numbers. There are many ways to find these differences, including:

• Finding equivalent fractions with a common denominator, and then finding their difference.
• Adding on, exploiting the whole-number parts of the mixed numbers.
• Using equivalent expressions, which helps to find a common denominator for both the whole-number parts and the fractional parts of the numbers.

The second and third strategies have close analogies in arithmetic with whole numbers. One way to find a difference, such as , is to add on to 28, first 2, then 5, and then 100, to find that the difference is 107. For a difference of fractions, such as , the corresponding reasoning would be to add to , then 1, and then , to find that the difference is . Students also could rewrite the expression as , and then find the differences , , and . With the fraction difference, they can rewrite as and then subtract or from , again getting a result of . Students are not expected to bring out these connections, but it is important to see that the techniques students used for finding whole-number differences also can be used, with appropriate modification, for finding mixed-number differences.