Definition: Equivalent ratios are ratios that express the same relationship, found by multiplying or dividing both quantities of a ratio by the same nonzero number.
How do equivalent ratios work?
Two ratios are equivalent when one is a scaled copy of the other. Multiply or divide both terms by the same number and the relationship stays unchanged, just like a recipe doubled or halved.
How can you build a table of them?
Start with 2:5 and keep multiplying by whole numbers:
- 2:5
- 4:10
- 6:15
- 8:20
Each row is equivalent to the first. A ratio table like this is handy for finding a missing value.
How do you test two ratios?
Compare the multipliers. Is 9:21 equivalent to 3:7? Dividing 9 by 3 gives 3, and dividing 21 by 3 gives 7, so you divide both terms of 9:21 by 3 and get 3:7. Yes, they match.
What is the common slip?
Adding the same number to both terms breaks the relationship. From 2:5, adding 3 to each gives 5:8, which is not equivalent, because 5 is 2.5 times 2 but 8 is only 1.6 times 5.