Question

Nancy tried to evaluate an expression. Here is her work:
56÷[51–(5+3)6+4]2
=
56÷[51–86+4]2 Step 1
=
56÷[51–48+4]2 Step 2
=
56÷[3+4]2 Step 3
=
56÷72 Step 4
=
56÷14 Step 5
=
4 Step 6
Is Nancy's work correct?




Questions

Answer 1

Let's evaluate Nancy's work step by step to determine if the calculations are correct.

Starting with the original expression:
\[ 56 ÷ [51 - (5 + 3) \cdot 6 + 4]^2 \]

1. **Step 1:** Simplifying the term inside the brackets:
- Calculate \( (5 + 3) = 8 \)
- Then, \( 8 \cdot 6 = 48 \)
- Substitute back into the brackets:
\[ 56 ÷ [51 - 48 + 4]^2 \]

2. **Step 2:** Continuing from above:
- Here, Nancy has incorrectly written \( 51 - 86 \). The correct continuation should be:
\[ 51 - 48 + 4 \]
- Which simplifies to:
\[ 3 + 4 = 7 \]

3. **Step 3:** So we need to correct her step:
- The brackets now simplify to:
\[ 56 ÷ [7]^2 \]

4. **Step 4:** Evaluating the square:
- \( 7^2 = 49 \)

5. **Step 5:** Now we divide:
\[ 56 ÷ 49 \]
- This equals \( \frac{56}{49} = \frac{8}{7} \), which is approximately 1.142857.

So, to summarize:
- Nancy miscalculated the subtraction in Step 1.
- Her final answer is incorrect; the correct answer is \( \frac{8}{7} \), not 4.

Therefore, **Nancy's work is not correct.**