When we say that two ratios are equivalent, we mean that they represent the same relationship between two quantities, even though the numbers involved in the ratios may be different. In simplest terms, two ratios are equivalent if they can be expressed as the same fraction when simplified.
For example, consider the ratios 1:2 and 2:4. At first glance, the numbers in these ratios are different, but if we simplify the second ratio (2:4), we get 1:2. This indicates that both ratios are equivalent, meaning they represent the same proportional relationship. In practical terms, if you have a recipe that calls for 1 cup of sugar for every 2 cups of flour, it is equivalent to a recipe that calls for 2 cups of sugar for every 4 cups of flour. Both ratios maintain the same proportion of sugar to flour.
To check if two ratios are equivalent, you can cross-multiply: for ratios a:b and c:d, if a*d = b*c, then the ratios are equivalent. Using our previous example, if we set 1:2 equal to 2:4, we can cross-multiply (1*4 = 2*2) which yields 4 = 4, confirming their equivalence.