Adding and Subtracting Fractions

The fact that many students struggle to understand how to add and subtract fractions.   The basic notion required is that when fractions have different denominators, they must be renamed to have a common denominator.

Using Number Properties

Problem: “Mele wants to find  1/2 + 1/6. Why can’t the fractions be added directly?” (Answer: Halves and sixths are unlike.)

“How will Mele proceed?”
(Answer: She will convert 1/2 to 3/6, so 1/2 + 1/6 = 3/6 + 1/6 = 4/6.)

Examples: Work out 1/2 – 1/6,  1/8 + 1/2, 7/8 – 1/2, 11/12 – 5/6, 2/3 – 5/12 …

Problem: “Mele wants to work out 8/9 – 5/6 . How will Mele get around the problem of  unlike denominators?” (Answer: Mele must find a way to convert both fractions to  have a common name.)

List the equivalent names for and on the board.

(Answer: 8/9 = 16/18 = 24/27 = 32/36 = 40/45 = 48/48 ...
5/6 = 10/12 = 15/18 = 20/24 = 25/30 = 30/36 = 35/42 = 40/48 = 45/54 ...)

Discuss which denominators appear in both lists. (Answer: 18, 36, 54 ...)

Discuss why 8/9 = 16/18 and 5/6 = 15/18 are the best fractions to use to rename and 8/9 and 5/6  why 8/9 – 5/6 = 1/18.

Examples : Worksheet (Material Master 8–26).

Understanding Number Properties:

Make up an addition problem for fractions with unlike denominators and then solve it.