Question

nina writes the expression in the box.
18 + 2 × 3² - 36 ÷ 4
where should nina place parentheses for the expression to equal 45?
○ 18 + (2 × 3)² - 36 ÷ 4
○ 18 + 2 × 3² - (36 ÷ 4)
○ (18 + 2) × 3² - 36 ÷ 4
○ 18 + 2 × (3²) - 36 ÷ 4

Explanation:

Step1: Evaluate Option 1

Calculate \(18 + (2\times3)^{2}-36\div4\)
First, \(2\times3 = 6\), then \(6^{2}=36\), \(36\div4 = 9\)
So \(18 + 36-9=45\)? Wait, \(18 + 36=54\), \(54 - 9 = 45\)? Wait no, \(18+36 = 54\), \(54-9 = 45\)? Wait, let's recalculate:
\(18+(2\times3)^{2}-36\div4=18 + 6^{2}-9=18 + 36-9=45\)? Wait, \(18+36 = 54\), \(54 - 9=45\). Wait, but let's check other options.

Step2: Evaluate Option 2

\(18 + 2\times3^{2}-(36\div4)\)
\(36\div4 = 9\), \(3^{2}=9\), \(2\times9 = 18\), so \(18+18 - 9=27
eq45\)

Step3: Evaluate Option 3

\((18 + 2)\times3^{2}-36\div4\)
\(18 + 2=20\), \(3^{2}=9\), \(20\times9 = 180\), \(36\div4 = 9\), \(180-9 = 171
eq45\)

Step4: Evaluate Option 4

\(18 + 2\times(3^{2})-36\div4\)
This is the original expression without changing the order of operations (since \(3^{2}\) is already calculated first). \(3^{2}=9\), \(2\times9 = 18\), \(36\div4 = 9\), so \(18+18 - 9=27
eq45\)
Wait, earlier for Option 1, let's recalculate:
\(18+(2\times3)^{2}-36\div4=18 + 6^{2}-9=18 + 36-9=45\). Yes, that's correct. Wait, but let's check again.
Wait, \(2\times3 = 6\), \(6^{2}=36\), \(36\div4 = 9\), \(18+36 = 54\), \(54 - 9=45\). Yes. But wait, the first option is \(18+(2\times3)^{2}-36\div4\). Wait, but let's check the third option again. Wait, no, the third option is \((18 + 2)\times3^{2}-36\div4=20\times9 - 9=180 - 9=171\). The second option: \(18 + 2\times9-9=18 + 18-9=27\). The fourth option is same as original, which is \(18 + 18-9=27\). Wait, but the first option: \(18+(2\times3)^{2}-36\div4=18 + 36-9=45\). So that's correct. Wait, but let's check the problem again. The question is "Where should Nina place parentheses for the expression to equal 45". So the first option: \(18+(2\times3)^{2}-36\div4\) gives 45. Wait, but let's recalculate:
\(2\times3 = 6\), square is 36. \(18 + 36=54\), \(36\div4 = 9\), \(54-9 = 45\). Yes. So the correct option is the first one? Wait, but wait, the first option is \(18+(2\times3)^{2}-36\div4\). Wait, but let's check the third option again. Wait, no, the third option is \((18 + 2)\times3^{2}-36\div4=20\times9 - 9=171\). So the first option is correct. Wait, but maybe I made a mistake. Wait, let's check the original expression: \(18 + 2\times3^{2}-36\div4\). The original value is \(18 + 2\times9 - 9=18 + 18-9=27\). So to get 45, we need to change the order. Let's see:

Option 1: \(18+(2\times3)^{2}-36\div4=18 + 36-9=45\). Correct.

Option 2: \(18 + 2\times3^{2}-(36\div4)=18 + 18-9=27\).

Option 3: \((18 + 2)\times3^{2}-36\div4=20\times9 - 9=171\).

Option 4: \(18 + 2\times(3^{2})-36\div4=18 + 18-9=27\).

So the correct option is the first one: \(18+(2\times3)^{2}-36\div4\)

Wait, but let's check again. \(2\times3 = 6\), squared is 36. \(18 + 36=54\), \(36\div4 = 9\), \(54 - 9=45\). Yes. So the answer is the first option.

Answer:

A. \(18 + (2\times3)^{2}-36\div4\)