Which equations correctly simplify the expression

Question

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.