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

1 answer

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.