Question

Which equation represents a proportional relationship?

Responses

815=430
8 over 15 is equal to 4 over 30

36=63
3 sixths is equal to 6 thirds

2x12=3x18
2 x over 12 is equal to 3 x over 18

4x18=x18
4 x over 18 is equal to x over 18

Answer 1

To determine which equation represents a proportional relationship, we need to look for relationships where two ratios are equivalent.

1. **815 = 430**: This is a false equation and does not represent a proportional relationship.

2. **8 over 15 is equal to 4 over 30**: Let's check if these ratios are equivalent:
\[
\frac{8}{15} = \frac{4}{30}
\]
Cross-multiplying gives:
\[
8 \times 30 = 240 \quad \text{and} \quad 4 \times 15 = 60
\]
Since \(240 \neq 60\), this is not a proportional relationship.

3. **36 = 63**: This is also a false equation and does not represent a proportional relationship.

4. **3 sixths is equal to 6 thirds**: Let's check this one:
\[
\frac{3}{6} = \frac{6}{3}
\]
We simplify both sides:
\[
\frac{3}{6} = \frac{1}{2} \quad \text{and} \quad \frac{6}{3} = 2
\]
Since \(\frac{1}{2} \neq 2\), this is not a proportional relationship.

5. **2x12 = 3x18**: Let's check if these represent a proportional relationship by simplifying:
\[
\frac{2}{3} = \frac{18}{12} \Rightarrow 18 \div 6 = 3 \quad \text{and} \quad 12 \div 6 = 2
\]
Cross-multiplying gives:
\[
2 \times 18 = 36 \quad \text{and} \quad 3 \times 12 = 36
\]
Since both sides are equal, this does represent a proportional relationship.

6. **4x18 = x18**: This can be simplified by factoring out \(x\):
\[
4x18 = x18
\]
Dividing both sides by \(18\) (assuming \(18 \neq 0\)):
\[
4x = x
\]
This implies an equation but does not provide a direct proportion as one ratio against another for non-zero \(x\).

In summary, the only statement that represents a proportional relationship is:

**2x12 = 3x18**.