Rachel has red and yellow paper clips in a box. The ratio of red to yellow paper clips is three to eight. Work out the fraction of paper clips in the box which are red.
Let’s recall the mathematical convention for writing ratio. Order matters. That is to say, since the question states the ratio of red to yellow paper clips is three to eight, that means, for every three red paper clips, there are eight yellow paper clips.
Now we don’t actually know the exact number of paper clips in the box. There could be any multiple of these two numbers. For instance, we could have six red paper clips and 16 yellow paper clips. We could have nine red paper clips and 24 yellow paper clips, and so on.
However, since we don’t know the exact number, we can consider the ratio as parts. There are three parts that represent the number of red paper clips and eight parts that represent the number of yellow paper clips. Three plus eight is 11, so adding these and we can see that there are a total of 11 parts.
We want to know the fraction of the paper clips which are red. We said that there are three parts that represent the number of red paper clips. So the fraction of paper clips in the box which are red is three out of the total number of parts, which is 11. The fraction of the paper clips which are red is three elevenths.