Question

brad tried to evaluate an expression. here is his work:
$2^3 - 2^2 + 24 \div 12 \cdot 3$
$= 8 - 4 + 24 \div 12 \cdot 3$ \quad step 1
$= 8 - 4 + 2 \cdot 3$ \quad \quad step 2
$= 8 - 4 + 6$ \quad \quad \quad step 3
$= 4 + 6$ \quad \quad \quad \quad step 4
$= 10$ \quad \quad \quad \quad \quad step 5
is brads work correct?
no, brad made a mistake going from step 1 to step 2. brad should have multiplied 12 and 3 before dividing. the order of operations says to multiply before you divide.
no, brad made a mistake going from step 3 to step 4. brad should have added 4 and 6 before subtracting. the order of operations says to add before you subtract.
yes, brads work is correct.

Explanation:

Step1: Evaluate exponents

$$2^{3}=8, 2^{2} = 4$$

Step2: Perform division and multiplication from left - to - right

$$24\div12 = 2$$
$$2\times3=6$$

Step3: Perform addition and subtraction from left - to - right

$$8 - 4=4$$
$$4 + 6=10$$

Brad's work is correct. He followed the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left - to - right), Addition and Subtraction (from left - to - right)). He first evaluated the exponents in Step 1. Then, in Step 2, he did the division \(24\div12 = 2\) (since division and multiplication have the same priority and we go from left - to - right). Then in Step 3, he did the multiplication \(2\times3 = 6\). In Step 4 and 5, he did the subtraction and addition from left - to - right (\(8-4 = 4\) and \(4 + 6=10\))

Answer:

Yes, Brad's work is correct.