Question

erica tried to evaluate the expression 12 + 18 ÷ 3 × (11 - 9). here is her work:
12 + 18 ÷ 3 × (11 - 9)
= 12 + 18 ÷ 3 × 2 step 1
= 12 + 6 × 2 step 2
= 12 + 12 step 3
= 24 step 4
is ericas work correct?
no, erica made a mistake in step 1. erica should have multiplied instead of subtracting. the order of operations says to multiply before you subtract.
no, erica made a mistake in step 2. the brackets mean the numbers inside are grouped together. erica should have multiplied the numbers inside the brackets first.

Explanation:

Step1: Calculate the innermost parentheses

$$11 - 9=2$$

Step2: Calculate the brackets

$$3\times2 = 6$$

Step3: Do the division

$$18\div6=3$$

Step4: Do the addition

$$12 + 3=15$$

Erica made a mistake in Step 2. She should have done \(18\div6\) instead of \(6\times2\). The correct order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left - to - right, Addition and Subtraction from left - to - right) requires that we first simplify the innermost parentheses \((11 - 9)\), then the brackets \([3\times(11 - 9)]\), then perform the division \(18\div[3\times(11 - 9)]\), and finally the addition.

Answer:

No, Erica made a mistake in Step 2. The brackets mean the numbers inside are grouped together. Erica should have divided \(18\) by the result of \(3\times(11 - 9)\) (i.e., \(18\div6\)) instead of multiplying \(6\times2\).