Question

Complete the following stepped-out solution to show that 15+g+32⋅23 is equivalent to 16+g.

15 + g + 3/2 ⋅ 2/3
15 + g + __ - Inverse Property of Multiplication.
15+__+g - Commutative Property of Addition.
16+g - Addition

Answer 1

[AI-generated answer — Bot GPT 3.5]

15 + g + 3/2 ⋅ 2/3

To use the Inverse Property of Multiplication, we need to find the inverse of 3/2 and 2/3.
The inverse of a number is the reciprocal of that number. The reciprocal of a fraction is found by flipping it upside down.
So, the inverse of 3/2 is 2/3 and the inverse of 2/3 is 3/2.

By applying the Inverse Property of Multiplication, we can rewrite the expression as:
15 + g + 3/2 ⋅ 2/3 = 15 + g + 3/2 ⋅ 3/2

Now, let's simplify the multiplication of fractions:
3/2 ⋅ 3/2 = 9/4

So the expression becomes:
15 + g + 9/4

Now, let's rearrange the terms using the Commutative Property of Addition to group like terms together:
15 + 9/4 + g

Finally, let's simplify the expression:
15 + 9/4 = (15 * 4 + 9) / 4 = (60 + 9) / 4 = 69/4

So the final simplified expression is:
69/4 + g

However, this final expression is not equivalent to 16 + g. Therefore, there might be a mistake in the question or the steps taken.