Question

Which equations correctly simplify the expression
198
18
?
Select all that apply.

Responses

198
18
=
180
18
+
18
18
=
11
198 over 18 is equal to 180 over 18 plus 18 over 18 is equal to 11

198
18
=
180
18
⋅
18
18
=
11
198
18
=
180
18
⋅
18
18
=
11

198
18
=
22
⋅
9
18
=
9
18
⋅
22
18
=
11
198
18
=
22
⋅
9
18
=
9
18
⋅
22
18
=
11

198
18
=
22
⋅
9
9
⋅
2
=
9
9
⋅
22
2
=
11
198
18
=
22
⋅
9
9
⋅
2
=
9
9
⋅
22
2
=
11

198
18
=
190
10
+
8
8
=
11

Answer 1

To simplify the expression \( \frac{198}{18} \), we can follow these steps:

First, let's determine what \( \frac{198}{18} \) simplifies to:

1. Divide the numerator and denominator by their greatest common divisor (GCD):
- The GCD of 198 and 18 is 9.
- \( \frac{198 \div 9}{18 \div 9} = \frac{22}{2} \)

2. \( \frac{22}{2} = 11 \)

Now, let's examine the provided responses:

1. **Response 1**:
\( 198 \, / \, 18 = 180 \, / \, 18 + 18 \, / \, 18 = 11 \)
**This is incorrect**. Although \( \frac{18}{18} = 1 \), the left side does not equal the right side as stated.

2. **Response 2**:
\( 198 \, / \, 18 = 180 \, / \, 18 \cdot 18 \, / \, 18 = 11 \)
**This is incorrect**. This expression isn't logical as it tries to multiply non-equivalent expressions.

3. **Response 3**:
\( 198 \, / \, 18 = 22 \cdot 9 \, / \, 18 = 9 \, / \, 18 \cdot 22 \, / \, 18 = 11 \)
**This is correct** because it properly simplifies to \( \frac{22}{2} = 11 \).

4. **Response 4**:
\( 198 \, / \, 18 = 22 \cdot 9 \, / \, 9 \cdot 2 = 9 \, / \, 9 \cdot 22 \, / \, 2 = 11 \)
**This is also correct**. It also simplifies similarly to \( \frac{22}{2} = 11 \).

5. **Response 5**:
\( 198 \, / \, 18 = 190 \, / \, 10 + 8 \, / \, 8 = 11 \)
**This is incorrect**. The expression here is not equal to \( 11 \).

Based on this analysis, the **correct responses** are **Response 3** and **Response 4**.