Question

each of these is a pair of equivalent ratios for each pair explain why they are equivalent ratios.

Answer 1

Given the following set of ratios:

$4\colon5\text{ and 8:10}$$18\colon3\text{ and 6:1}$

To be able to determine if the given sets are equivalent ratios, they must a common constant, k, which is x/y.

$\text{ k = }\frac{x}{y}$

Let's treat the ratio as x:y and find their common constant, k.

At 4:5 and 8:10,

$k_{4\colon5}\text{ = }\frac{4}{5}$$k_{8\colon10}\text{ =}\frac{8}{10}\text{ = }\frac{\frac{8}{2}}{\frac{10}{2}}\text{ = }\frac{4}{5}\text{ ; simplified}$

Since the two ratios have the same common constant, k = 4/5, the two ratios are equivalent.

At 18:3 and 6:1,

$\text{ k}_{18\colon3}\text{ = }\frac{18}{3}\text{ = }\frac{\frac{18}{3}}{\frac{3}{3}}\text{ = }\frac{6}{1}\text{ = 6}$$\text{ k}_{6\colon1}=\frac{6}{1}\text{ = 6}$

Since the two ratios have the same common constant, k = 6, the two ratios are equivalent.