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Recall the definition of a ratio.
See solution.
We are asked to describe how we can use ratios to compare quantities. In general, there are two kinds of comparisons that we can make using ratios. To better describe each of them, let's picture an example situation.
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The inter-school chess tournament attracts students from all over the county every year. This year, 20 seventh graders and 15 eighth graders signed up to participate in the tournament. |
When we talk about the turnout at the chess tournament, we can compare the number of seventh graders that are participating to the number of eighth graders. This gives us the ratio of 20 seventh graders to 15 eighth graders. There are different algebraic ways that we can express this ratio. 20 to 15 ⇔ 20: 15 ⇔ 20/15 We can also use a bar diagram to represent the relationship between these quantities. The length of each bar will equal the number of students in each grade participating in the chess tournament. Let's see a diagram.
Another type of ratio to consider for this problem is the ratio comparing the number of students in each grade to the total number of participants. We know that in this tournament there are 20+ 15 = 35 participants in total. This gives us a ratio of 20 seventh graders to 35 chess players. Again, we can write this ratio in different ways. 20 to 35 ⇔ 20: 35 ⇔ 20/35 Here is what the bar diagram of this ratio would look like.
