1. Use the associative property to rewrite the expression 97 + (3 + 13)
I rewrote this as (97 + 3) + 13 since the associative property is about changing the grouping. The answer in the back of the book says 97 + (3 + 13) -- the same as the original problem.
2. Use the distributive property to simplify (2x + 3) - (x - 6)
I got -2x squared + 9x + 18 but the answer in the back of the book says x + 9
Could you explain where I went wrong on this problem please?
Why did you square 2x?
(2x + 3) - (x - 6)
2x - x = x
3 + 6 = 9
(2x + 3) - (x - 6) = x + 9
I think I was looking at it as the two parentheses were multiplied together but I see now! Thank you.
What about the first question?
You are right about the first question.
You're welcome.
97 + 16 = 113
In the first problem, you correctly applied the associative property by changing the grouping of the numbers. However, both your answer and the answer in the back of the book are correct because addition is associative. That means you can group numbers in any order you like, and the result will be the same.
Here's a step-by-step explanation:
Original expression: 97 + (3 + 13)
Using the associative property, you can change the grouping:
(97 + 3) + 13
Simplifying inside the parentheses:
100 + 13
Adding the remaining numbers:
113
So, both 97 + (3 + 13) and (97 + 3) + 13 are equivalent and give the same result of 113.
Now let's move on to the second problem:
Expression: (2x + 3) - (x - 6)
To simplify this using the distributive property, we need to distribute the subtraction sign to both terms inside the parentheses:
Expression after distribution: (2x + 3) - x + 6
Now, let's simplify further by combining like terms:
2x - x = x
3 + 6 = 9
Putting it all together: x + 9
Therefore, the simplified form of (2x + 3) - (x - 6) is x + 9. It seems you made an error when combining the terms in the second step, which led to the incorrect answer -2x squared + 9x + 18. Remember to carefully combine like terms and perform the necessary operations accurately.