Leroy tried to evaluate an expression. Here is his work:

Question

42+22–46÷32
=
62–46÷32 Step 1
=
36–46÷32 Step 2
=
36–24÷32 Step 3
=
36–82 Step 4
=
36–16 Step 5
=
20 Step 6
Is Leroy's work correct? No, Leroy made a mistake going from the given expression to Step 1. Leroy should have squared 4 and 2 instead of adding.
The order of operations says to evaluate exponents before you add.
No, Leroy made a mistake going from Step 3 to Step 4. Leroy should have multiplied 3 and 2 before dividing. The order of operations says to multiply before you divide.
Yes, Leroy's work is correct.

Answer 1

Leroy's work is not correct.

Let's analyze the original expression step-by-step using the correct order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right — often abbreviated as PEMDAS):

The original expression is: 42 + 22 - 46 ÷ 32

Following the order of operations:

1. First, evaluate 46 ÷ 32: \[ 46 ÷ 32 = 1.4375 \]

2. The expression now looks like this: \[ 42 + 22 - 1.4375 \]

3. Now, perform the addition: \[ 42 + 22 = 64 \]

4. Finally, perform the subtraction: \[ 64 - 1.4375 = 62.5625 \]

Leroy's mistake was in the first step when he added 42 and 22 instead of evaluating the division first. Additionally, in the subsequent steps, he didn't apply the operations correctly at various points.

So the correct answer is: No, Leroy made a mistake going from the given expression to Step 1. Leroy should have divided 46 by 32 before performing addition and subtraction. The order of operations dictates dividing before adding.