Question

Below are two expressions, the only difference being the presence or absence of parentheses. expression 1:expression 2:5+2×(3+3)×(3−1)5+2×3+3×3−1 calculate the difference between the two expressions; that is, evaluate both expressions then subtract one value from the other value.

Answer 1

To present clearly, these are the following expressions:

Expression 1: 5+2×(3+3)×(3−1)
Expression 2: 5+2×3+3×3−1

The numbers and operations are just the same, but the first expression involves parentheses. In mathematics, when you are presented with multiple operations in one equation, you follow the PEMDAS rule. This rule assigns which operation should be the first priority. The P means parenthesis. So, any expression inside the parenthesis should be calculated first. This is followed by Exponent(E), Multiplication (M), Division (D), Addition (A) and lastly, Subtraction (S). 

Expression 1: 5+2×(3+3)×(3−1)
Do the operations inside the two parentheses first:
5 + 2 × 6 × 2
Then, the next priority is multiplication:
5 + 24 = 29

Expression 2: 5+2×3+3×3−1
Prioritize multiplication:
5 + 6 + 9 -1
Prioritize the addition next.
20 - 1 = 19

The difference of the 2 expressions is: 29 - 19 = 10.