Questions: Are the ratios 2:3 and 3:4 equivalent?

Solution Steps

To determine if two ratios are equivalent, we can compare their cross products. If the cross products are equal, the ratios are equivalent; otherwise, they are not.

We are given two ratios: \[ \text{ratio1} = \frac{2}{3} \quad \text{and} \quad \text{ratio2} = \frac{3}{4} \]

To determine if the ratios are equivalent, we calculate the cross products: \[ \text{cross\_product1} = 2 \times 4 = 8 \] \[ \text{cross\_product2} = 3 \times 3 = 9 \]

We compare the two cross products: \[ 8 \neq 9 \] Since the cross products are not equal, the ratios are not equivalent.

Final Answer