Question

Lola tried to evaluate an expression. Here is her work:
102÷[1+2(16–14)]
=
102÷[1+22] Step 1
=
102÷[1+4] Step 2
=
102[5] Step 3
=
100[5] Step 4
=
500 Step 5
Is Lola's work correct?




Questions

Answer 1

Let's go through Lola's work step by step to see if her calculations are correct.

1. **Starting Expression**:
\[
102 \div [1 + 2(16 - 14)]
\]

2. **Calculate Inside the Parentheses**:
\[
16 - 14 = 2
\]
So now we substitute:
\[
102 \div [1 + 2(2)]
\]

3. **Multiply**:
\[
2(2) = 4
\]
Substitute again:
\[
102 \div [1 + 4]
\]

4. **Add**:
\[
1 + 4 = 5
\]
Substitute again:
\[
102 \div [5]
\]

5. **Final Division**:
\[
102 \div 5 = 20.4
\]

Now, let's compare this with Lola's steps:

- In **Step 1**, she correctly showed:
\[
102 \div [1 + 2(16 - 14)]
\]

- In **Step 2**, she made a mistake:
\[
102 \div [1 + 22]
\]
should have been:
\[
102 \div [1 + 4]
\]

- In **Step 3**, she mistakenly changed the expression to:
\[
102[5]
\]
instead of correctly writing \(102 \div 5\).

The next calculations in **Step 4** and **Step 5** also show she did not have the correct expression.

**Conclusion**: Lola's work is not correct. The correct evaluation of the expression \(102 \div [1 + 2(16 - 14)]\) results in \(20.4\), whereas her answer was \(500\).