Final answer:
The given expression is evaluated in three ways using the commutative property of addition to illustrate that regardless of the order of operations, the result is 0. This property allows for the rearrangement of terms for addition without affecting the final outcome.
Step-by-step explanation:
The task is to find the result of the expression 10 - 2 - 8 graphically using the commutative property of addition.
To start, we will look at different ways of grouping the terms to illustrate the commutative property. Remember, this property means we can change the order of the numbers being added without changing the result.
Firstly, consider the expression in its original form: 10 - 2 which gives 8, now subtracting 8 gives 0. Graphically this could be represented by an arrow starting at 0, moving 10 units right, then 2 units left, and finally 8 more units left, ending up at the original position, 0.
Secondly, we can rearrange the terms using the commutative property as (10 - 8) - 2. Simplifying within the parentheses first (10 - 8 equals 2), and then subtracting 2 gives 0. The graphical representation would show an arrow moving from 0 to 10, then moving back left 8 units, and then left again by 2 units, returning to the starting point.
Lastly, the expression can be adjusted to 10 - (2 + 8). The sum within the parentheses is 10, and subtracting 10 from 10 results in 0. In graphical terms, this is like moving 10 units to the right and then 10 units back to the left.
All three methods show that no matter how you group the terms using the commutative property, the result remains the same, which is 0.