Which equations represent proportional relationships?

Question

Select all that apply.

Responses

43=812
4 thirds is equal to 8 over 12

11x4=16.5x6
11 x over 4 is equal to 16 point 5 x over 6

12=918
1 half is equal to 9 over 18

5x6.5=4x5.2
5 x over 6 point 5 is equal to 4 x over 5 point 2
which one is the clostest answer

Answer 1

To determine which equations represent proportional relationships, we need to examine if the two sides of each equation maintain a consistent ratio.

1. 43 = 812: This does not represent a proportional relationship since the numbers are not in a consistent ratio.

2. 4/3 = 8/12: This simplifies to \(4/3 = 2/3\) (since \(8/12\) reduces to \(2/3\)). This is not a valid equation, therefore not proportional.

3. 11x4 = 16.5x6: If we divide both sides by \(x\) (assuming \(x \neq 0\)), we get the ratio \(11/16.5 = 6/4\). This simplifies to \(11/16.5 = 2/3\), which is not equal. Hence, this does not represent a proportional relationship.

4. 12 = 918: This does not represent a proportional relationship since the numbers are not in a consistent ratio.

5. 5x6.5 = 4x5.2: If we divide both sides by \(x\) (assuming \(x \neq 0\)), we are left with \(5/5.2 = 4/6.5\). This can be checked for equality and can be found to be consistent.

Based on this analysis:

• The example which represents a proportional relationship is 5x6.5 = 4x5.2.

The other equations do not establish a proportional relationship. Therefore, the closest answer is 5x6.5 = 4x5.2.