Addition of Fractions Using the Commutative and Associative Properties A common strategy used when adding whole numbers is to group numbers to represent a value of ten. 4
6 +9
10
+ 9
19
The example below illustrates how this strategy connects to the addition of fractions. Explanation Add Process 6 7
+ 8 8
6 7
+ 8 8
6
in a way that will provide the 8
7
amount needed to combine with to create one 8
Decompose ⎛ 5 1 ⎞ 7
= ⎜ + ⎟ + ⎝ 8 8 ⎠ 8
whole. Regroup using the associative property to “make one.” Determine the sum. =
5 ⎛ 1 7 ⎞
+
+
8 ⎜⎝ 8 8 ⎟⎠
5
= 1 8
Teacher Note: Some students may also incorporate the commutative property in their work as shown in the following example. Explanation Add 6 7
+ 8 8
Process 6 7
+ 8 8
6
n a way that will provide the 8
7
amount needed to combine with to create one 8
Decompose whole. Use the commutative property to reorder the fractions. Use the associative property to regroup the fractions. Determine the sum. ⎛ 1 5 ⎞ 7
= ⎜ + ⎟ + ⎝ 8 8 ⎠ 8
⎛ 5 1 ⎞ 7
= ⎜ + ⎟ + ⎝ 8 8 ⎠ 8
=
5 ⎛ 1 7 ⎞
+
+
8 ⎜⎝ 8 8 ⎟⎠
5
= 1 8