Miguel’s steps in evaluating an expression are as given. Miguel’s Work 32 divided by 2 times open paren 2 cubed minus 4 close paren Step 1: is equal to 32 divided by 2 times open paren 8 minus 4 close paren Step 2: is equal to 32 divided by 2 times 4 Step 3: is equal to 32 divided by 8 Step 4: is equal to 4 What, if any, was Miguel’s mistake?
Answer
A
Miguel incorrectly multiplied before dividing in step 3.
B
Miguel made no mistakes.
C
Miguel should have used the distributive property in step 1.
D
Miguel incorrectly evaluated 2 cubed in step 1.
Explanation
Miguel correctly evaluated 2³ as 8 and then calculated 8 − 4 = 4. In 32 ÷ 2 × 4, division and multiplication have equal priority, so work from left to right: 32 ÷ 2 = 16, then 16 × 4 = 64. Miguel instead multiplied 2 × 4 before dividing, so choice A, “Miguel incorrectly multiplied before dividing in step 3,” identifies his mistake.
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