One way to create an expression that includes a set of parentheses so that the value of the expression is 5 is:
(32 ÷ (10 - 8)) ÷ (2 - 3) + 3
Let's break it down:
First, we group the division by (10 - 8) using parentheses:
32 ÷ (10 - 8) - 8 ÷ 2 - 3
Next, we simplify the expression inside the parentheses:
32 ÷ 2 - 8 ÷ 2 - 3
Then, we simplify the division by 2:
16 - 4 - 3
Next, we subtract 4 from 16 and simplify further:
12 - 3
Finally, we add 3 to get:
9
However, this value is not equal to 5. To make the value equal to 5, we need to add a set of parentheses and modify the expression further:
(32 ÷ (10 - 8)) ÷ (2 - 3) + 3
= (32 ÷ 2) ÷ (2 - 3) + 3 // Group the division by 10 - 8 inside the parentheses
= 16 ÷ (-1) + 3 // Simplify 2 - 3 to -1
= -16 + 3 // Simplify 16 ÷ (-1) to -16
= -13 // Simplify -16 + 3 to -13
Now the value of the expression is -13, which is not equal to 5. To make it equal to 5, we can multiply the entire expression by -1:
-(32 ÷ (10 - 8)) ÷ (2 - 3) - 3
= -(-16) ÷ (-1) - 3 // Apply the multiplication by -1
= 16 ÷ (-1) - 3
= -16 - 3
= -19
Now the value of the expression is -19, which is not equal to 5 either. Therefore, it is not possible to create an expression that includes a set of parentheses so that the value of the expression is 5 using the given expression.