Question

Petri did the following problem but got the wrong answer. She needs to correct her mistake and turn the problem back in.

(5 - 3)^2 ÷ 3 · 7 + 1
25 - 9 ÷ 3 · 7 + 1
25 - 3 · 7 + 1
25 - 21 + 1
4 + 1
5

What correction does Petri need to make?

She needs to subtract 5 - 3 first.
She needs to change 25 to 10.
She needs to add before she multiplies.
She needs to multiply 3 times 7 before she divides.

Answer 1

To find the correct answer, let's re-evaluate the expression step by step according to the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

The expression is:

\[
(5 - 3)^2 ÷ 3 · 7 + 1
\]

1. **Calculate inside the parentheses first**:
\[
5 - 3 = 2
\]

2. **Square the result**:
\[
2^2 = 4
\]

3. **Now substitute back into the expression**:
\[
4 ÷ 3 · 7 + 1
\]

4. **Perform the division and multiplication from left to right**:
\[
4 ÷ 3 \approx 1.33333 \quad (\text{or } \frac{4}{3})
\]

5. **Now multiply by 7**:
\[
\frac{4}{3} · 7 = \frac{28}{3} \approx 9.33333
\]

6. **Finally, add 1**:
\[
\frac{28}{3} + 1 = \frac{28}{3} + \frac{3}{3} = \frac{31}{3} \approx 10.33333
\]

Petri's mistake was in not following the correct order of operations. Based on the evaluation above, the correct sequence was not followed—specifically, she should have divided and then multiplied instead of incorrectly applying operations.

Among the options given, the most appropriate correction is:

**She needs to multiply 3 times 7 before she divides.**

This correction highlights that multiplication should be considered as part of the order of operations relative to division in the problem provided.