Question

Show how to model the sum of \(-3,2,\) and \(-1\) in two ways. Make a sketch to illustrate both ways.

Short answer

The sum of -3, 2, and -1 is -2. It can be illustrated by two sketches on the number line: one showing the sequential addition (-3 to -1 to -2), and the other showing the addition grouped by signs (-3 to -4 to -2).

Step-by-step solution

Model the sum sequentially

Start with the first number \(-3\), then add the second number \(2\), and finally add the third number \(-1\). \[ -3+2=-1 \]; \[ -1+(-1)=-2 \]. To sketch this process, one can create a number line ranging from -4 to 3. Place points at -3, -1 (i.e., -3+2), and -2 (i.e., -1+(-1)).

Model the sum grouped by signs

Group the numbers according to their signs, meaning that add -3 and -1 together because they are both negative, then add the result to 2. \[ -3+(-1)=-4 \]; \[ -4+2=-2 \]. On a number line ranging from -4 to 3, put points at -3, -4 (i.e., -3+(-1)), and -2 (i.e., -4+2).

Comparing both models

From both ways, you can see that the final result is the same. This demonstrates that the order in which the numbers are added (or grouped) does not affect the sum according to the associative property of addition.