Name the property the equation illustrates.
9 + (8 + 1) = (9 + 8) + 1
its the associative property of addition
The property illustrated by this equation is the associative property of addition.
The property that the equation illustrates is called the associative property of addition.
To identify this property, you need to first break down the equation and analyze the arrangement of the numbers involved. In this equation, you have three numbers: 9, 8, and 1.
On the left side of the equation, you have 9 as the first number, followed by the expression in parentheses: (8 + 1). This expression must be evaluated first according to the order of operations. When you calculate this expression, you get 9 as the result.
On the right side of the equation, you have the expression in parentheses: (9 + 8), followed by the number 1. Again, you need to evaluate the expression in parentheses first, which results in 17.
Comparing the two sides of the equation, you can see that both sides yield the same final result, despite the numbers being grouped differently. The associative property of addition allows you to regroup the numbers while maintaining the same sum.
In this case, regrouping the numbers means moving the parentheses from the left side to the right side, or vice versa. This reorganization does not change the outcome because addition is an associative operation.
So, by applying the associative property of addition, the equation is valid, and the property demonstrated is the associative property of addition.