6.2+Rates

Section 6.2 - Rates

 * Comparing Different Things**

Unlike ratios, rates compare things that are not at all similar - things that would have very different units of measure. An example is comparing miles (length) with gallons (volume). Because the units are different, it is important to remember them, and include them with the actual amounts. 7 miles to 3 gallons. 8 kids to 23 brownies.


 * Rates as Fractions**

Rates are also written as fractions in much the same way as ratios, but with one important difference -- rates are simplified and do not have to be whole numbers, they can have decimals, particularly in the numerator.

Proportions work with rates exactly like they do with ratios, just don't lose track of what the units are that go with the amounts.

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 * Unit Rate**

Unit rate means "how many of the numerator per each denominator?" The division bar in the fraction is understood as "per". Examples of this are miles per gallon, or hours per month, or dollars per hour.

If you need to find the unit rate, you could use a proportion, but there is an easier way -- just divide, but remember to put the result over a denominator of 1.

Here's the problem: I earn $488 for 12.4 hours of work. How much is that per hour? 488 divided by 12.4 = $39.35 per hour or $39.35/1 hour

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There is another application of unit rate that is somewhat tricky, often called unit price. It's what happens when you are shopping and you find three different sized of the same thing for three different prices and you are trying to figure out which is the best deal. We naturally assume the biggest is the best deal, but that is not always the case. Here's the problem: It's pizza night, and I have to choose between the medium pizza that is 11 inches across for $8.50 and the 14 inch large pizza for $11.75. Which is the best deal?

Now this problem is a bit harder than a normal canned vegetable comparison, because with the cans you just have to divide the cost by the number of ounces per can. However, with the pizza, you first have to find the area of each pizza, and then do some division.

Area of a Circle = Pi times the radius squared.

Medium pizza = about 95 square inches (94.985) for $8.50 Large pizza = almost 154 square inches (153.86) for $11.75

When you set that up as a rate, you will be able to divide to get a unit rate. However, it depends on which number you chose for the numerator and which for the denominator, as to what the answer means.




 * Chapter Six Practice Problems**

**Where to from here?**
6.1 Ratios 6.2 Rates 6.3 Percents Chapter Six Summary Chapter Six Homework