Question

A student simplified (cube root of 125 − 12 ÷ 2)(4 − 6)2 using the following steps: (cube root of 125 − 12 ÷ 2)(4 − 6)2 Step 1: (5 − 12 ÷ 2)(4 − 6)2 Simplify the cube root. Step 2: (−13 ÷ 2) (4 − 6)2 Subtract within first parentheses. Step 3: −6.5(4 − 6)2 Divide within the first parentheses. Step 4: −6.5(4 − 36) Simplify the exponent. Step 5: −6.5(−32) Subtract within the parentheses. Step 6: 208 Multiply. Describe the mistake and explain how to correct it.

Answer 1

The student made mistakes in calculating due to misunderstanding of the order of operation rules in mathematics. The correct calculation is (-1)(-2²) which results in -4.

Step-by-step explanation:

The student made mistakes in Step 2 and Step 4. In Step 2, before subtracting, the division operation should be performed due to the order of operations rule (PEMDAS/BODMAS), which stands for Parenthesis, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). So, 5 - 12 ÷ 2 should be 5 - 6 = -1, not -13 ÷ 2 = -6.5.

In Step 4, when squaring -2 (which is the result of 4 - 6), every number squared is always positive. Therefore, (-2)² is 4, not -4. There is a difference between -(2)² and (-2)². In the first, the square applies only to the 2, while in the latter, it applies to -2.

So, steps should be: Step1: (5 - 12 ÷ 2)(4 - 6)² becomes (-1)(-2²). Step2: (-1)(4). Step 3: -4

Learn more about Order of Operations