Ratios are used to compare values. They tell us how much of one thing there is compared to another. For example, ratios can be used to compare the number of girl puppies to boy puppies that were born. If we have a total of six puppies, where two are girls and four are boys, we can write that in ratio form as 2:4 (girls:boys). We can also write it in factor form as 2/4. To compare the number of boy puppies to girl puppies, we can simply rewrite our ratio with the number of boys first as 4:2 (boys:girls) or 4/2.
Proportions are related to ratios in that they tell you when two ratios are equal to each other. Let’s see how proportions work for our puppies. Our first ratio of girls to boys is 2:4 for our litter of six. If our next litter had a ratio of 4:8 of girls to boys, it would be proportional to our first litter; because if we divide each of our ratios, we will find that they are equal: 2 / 4 = 0.5 and 4 / 8 = 0.5, as well. My ratios are proportional if they divide into the same number.
When things are proportional, they are also similar to each other, meaning that the only difference is the size. For our two litters of puppies, the ratio of girls to boys is the same. The only difference is that the second litter is twice as big as the first.
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