The difficulty with expressions like 12 + (7 × 2) - 2(5 + 3) is most likely due to misunderstanding of which concept?

The difficulty with expressions like 12 + (7 × 2) - 2(5 + 3) is most likely due to misunderstanding of which concept?

• A. Order Of Operations
• B. Associative Property
• C. Commutative Property
• D. Distributive Property

Answer: (A)

Order of operations is what this item tests. To get the expression right, follow the standard order: evaluate inside parentheses first, then multiply and divide from left to right, then add and subtract from left to right. So, inside the first parentheses, 7 × 2 equals 14. Inside the second parentheses, 5 + 3 equals 8. This updates the expression to 12 + 14 − 2 × 8. Next, perform the multiplication: 2 × 8 equals 16. Now you have 12 + 14 − 16. Do the addition and subtraction from left to right: 12 + 14 equals 26, and 26 − 16 equals 10. The result is 10. The difficulty often comes from remembering to handle the parentheses properly and to do the multiplication before the addition/subtraction. While you could use the distributive property to expand 2(5+3) into 2×5 + 2×3, which also leads to the same answer, the main idea is applying the order of operations correctly. The associative or commutative properties aren’t the source of the confusion here.

Order of operations is what this item tests. To get the expression right, follow the standard order: evaluate inside parentheses first, then multiply and divide from left to right, then add and subtract from left to right. So, inside the first parentheses, 7 × 2 equals 14. Inside the second parentheses, 5 + 3 equals 8. This updates the expression to 12 + 14 − 2 × 8. Next, perform the multiplication: 2 × 8 equals 16. Now you have 12 + 14 − 16. Do the addition and subtraction from left to right: 12 + 14 equals 26, and 26 − 16 equals 10. The result is 10.

The difficulty often comes from remembering to handle the parentheses properly and to do the multiplication before the addition/subtraction. While you could use the distributive property to expand 2(5+3) into 2×5 + 2×3, which also leads to the same answer, the main idea is applying the order of operations correctly. The associative or commutative properties aren’t the source of the confusion here.