Question

Estimate the expression. Name the property used in each step. 11+2(8−7)

Answer 1

To estimate the expression 11+2(8-7), simplify inside the parentheses to get 1, multiply by 2 to get 2, and finally add to 11 to conclude with 13. The properties used are Subtraction Property of Equality, Multiplicative Identity Property, and Commutative Property of Addition. Always check your final answer for reasonableness.

Step-by-step explanation:

To estimate the expression 11+2(8-7), we follow these steps:

1. We start by simplifying the expression inside the parentheses, which is 8-7. This equals 1, using the Subtraction Property of Equality.
2. Next, we multiply this result by 2. So, 2(1) equals 2, which is done using the Multiplicative Identity Property.
3. Finally, we add this result to 11. Adding 11+2 gives us 13, and this step uses the Commutative Property of Addition.
4. To check if the answer is reasonable, we confirm that the operations were done correctly and according to the order of operations. Knowing that 2(8-7) is the same as 2 and adding it to 11 gives us 13, which is indeed a reasonable result.

The properties used, in order, were the Subtraction Property of Equality, the Multiplicative Identity Property, and the Commutative Property of Addition. Eliminating terms to simplify the algebra and checking the final answer for reasonableness are good practices in mathematics.