The associative property of addition states that, when adding three numbers, it does not matter in which order they are added. ^{[2]} This is expressed by the equation: a + (b + c) = (a + b) + c.
One way to remember the associative property of addition is to use the root word, 'associate'. So in the associative property of addition, the variables b and c associate closely on one side of the equals, while a and b associate closely on the other side.
A
representation
of the associative property of addition using dots is:
Figure 1: 3+(2+4) = (3+2)+4 = 9. |
Manipulative 1 contains a representation of the associative property of addition that uses the length of a line segment to represent each number. Notice that when the three segments are placed end to end, it doesn't matter which comes first, the total size is the same. Click on the end points and drag them to change the manipulative.
Click on the red, green, and blue points and drag them to change the figure. Why are the bottom three lines always the same length? |
Manipulative 1 - Associative Property of Addition Created with GeoGebra. |
The associative property of addition holds for real numbers, complex numbers, matrices of real and complex numbers, and vectors.
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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