Subjective Type

What is the difference between ratios and rates?

Solution

Both rates and ratios are a comparison of two numbers.
A rate is simply a specific type of ratio.
The difference is that a rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a room full of students, there are $$10$$ boys and $$5$$ girls. This means the ratio of boys to girls is $$10:5$$.
If we simplify the ratio, we see that the ratio of boys to girls is $$2:1$$, since $$10\div5=2$$ and $$5\div5=1$$. Thus, there are 2 boys in the room for every $$1$$ girl.
Let's say we'd like to buy a soda for each student in the classroom. The local pizza place offers a group discount on soda purchases: $$ $$10$$ for $$20$$ sodas.
Since we only need $$15$$ sodas, we're wondering how much each soda costs at the discounted rate. To find out, we'll set up two rates, because we have $$2$$ different units, dollars and number of sodas:
If $$\frac{20sodas}{10doller}$$ then $$\frac{1soda}{x}$$
we cross multiply $$x$$
$$20x=10dollers$$
$$x=10\div20$$
$$x=\frac{1}{2}$$
Since our unit is $$, we'll convert $$\frac{1}{2}$$ to dollars. One half of a dollar is $$ $$0.50$$.

SIMILAR QUESTIONS

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Given a line I and a point P on it. How many lines can be drawn passing through the point P?

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