Question

Which equations represent proportional relationships?

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

Answer 1

To determine which equations represent proportional relationships, we need to check if the ratios of the two quantities are equivalent in each equation.

1. **43 = 812**
- This is not a proportional relationship since 43 does not equal 812.

2. **4/3 = 8/12**
- This equation simplifies to 4/3 = 2/3, which is not a true statement, so it does not represent a proportional relationship.

3. **11x4 = 16.5x6**
- To compare, we can rearrange it:
\( \frac{11}{16.5} = \frac{6}{4} \)
Reducing both fractions gives us:
\( \frac{11}{16.5} = \frac{2}{3} \) and \( \frac{6}{4} = \frac{3}{2} \).
These are not equivalent, so this equation does not represent a proportional relationship.

4. **12 = 918**
- This is not a proportional relationship since 12 does not equal 918.

5. **5x6.5 = 4x5.2**
- Checking the ratio:
\( \frac{5}{4} = \frac{5.2}{6.5} \) simplifies to \( \frac{5}{4} \) and \( \frac{5.2}{6.5} \) can be checked:
\( 5/4 = 1.25 \) and \( 5.2/6.5 = 0.8 \), which are not equal.
Thus, this equation does not represent a proportional relationship.

After analyzing all the equations, **none of them represent proportional relationships.**