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Are there different ways to solve the given numerical expression while following the order of operations?
Yes, see solution.
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.
Add terms
Divide by 3
Calculate power
Subtract term
Next, we will simplify the second set of parentheses first.
Divide by 3
Add terms
Calculate power
Subtract term
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.