Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
2. Order of Operations and Evaluating Expressions
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Exercise 53 Page 14

Are there different ways to solve the given numerical expression while following the order of operations?

Yes, see solution.

Practice makes perfect

We are given a numerical expression. (1 +5)^2 -(18÷ 3) We are asked if we can perform the operations in different orders and still obtain the correct answer. Recall that when performing several operations, we should follow the order of operations to guarantee that our result is correct.

Order of Resolution Operation
1^(st) Parentheses
2^(nd) Exponents and Roots
3^(rd) Multiplication and Division
4^(th) Addition and Subtraction

According to this, we need to first simplify anything that is contained in parentheses. However, notice that there are two sets of parentheses in our expression. Therefore, we can solve either of them first and we should still get the same correct result. Let's verify this. We will simplify the first set of parentheses first.

(1 +5 )^2 -(18÷ 3)
6^2 -(18÷ 3)
6^2 - 6
36 - 6
30

Next, we will simplify the second set of parentheses first.

(1 +5)^2 - (18÷ 3 )
(1 +5)^2 - 6
6^2 - 6
36 - 6
30

As we can see, we arrived at the same result no matter which parenthetical expression we simply first. This is because we are still following the order of operations since both parentheses have the same priority. (1 +5 )^2 - (18÷ 3 ) However, we could not perform other operations first, such as the subtraction between the two sets of parentheses.