4(6 +12) ÷32+314÷212

Question

Is Adele's work correct?
=4(18) ÷32+3(2)2
Step 1
= 4（18）-9+ 3（4）
Step 2
=72÷9+ 3(4)

=8+ 3(4)
Step 4
=8 + 12
§ dais
= 20
Step 6
No, Adele made a mistake going from the given expression to Step
1. Adele should have multiplied 4 and 6 before adding. The order of operations says to multiply before you add.
No, Adele made a mistake going from Step 1 to Step 2. Adele should have multiplied 3 and 2 before evaluating the exponent. The order of operations says to perform operations inside parentheses before you evaluate the exponent.
Yes, Adele's work is correct.

Answer 1

Let's break down the original expression step by step and evaluate it to determine if Adele's work is correct.

The original expression is:

\[ 4(6 + 12) ÷ 32 + 314 ÷ 212 \]

We will follow the order of operations (PEMDAS/BODMAS):

1. Parentheses first:
   \(6 + 12 = 18\)
   So, we have:
   \[ 4(18) ÷ 32 + 314 ÷ 212 \]

2. Evaluate multiplication and division from left to right:

   • For \(4(18) ÷ 32\):
     \(4 \times 18 = 72\)
     Then, \(72 ÷ 32 = 2.25\)

   • Next, for \(314 ÷ 212\):
     \(314 ÷ 212 \approx 1.4808\)

3. Now our expression simplifies to:
   \[ 2.25 + 1.4808 \] This equals:
   \[ \approx 3.7308 \]

Now, let's evaluate where Adele might have gone wrong:

• In her Step 1, she wrote \( 4(18) ÷ 32 + 3(2)^2\). The initial transformation is incorrect because she incorrectly stated \(314 ÷ 212\) as \(3(2)^2\), which is wrong.

• Adele also incorrectly handled the calculation after that by assuming results from operations that weren't correctly calculated.

Based on the order of operations, Adele made mistakes in both the handling of the expression and the calculations in her steps. Her final answer of 20 is incorrect.

Therefore, the correct answer to the original expression is approximately 3.7308, and it confirms that:

Adele's work is NOT correct.