This document provides instruction on using proportions to solve rate problems, which involve comparing two different quantities. It explains that a unit rate means how much something costs for one unit. Students are taught to write two fractions representing the facts in the problem, set them equal using the "product of the means equals the product of the extremes" formula, and solve. Several examples are worked through, such as finding the rate of miles traveled per minute or dollars per hour. Students are directed to practice similar rate and unit rate problems involving quantities like time, distance, cost, and other units.

1. Skill8 Unit Rates Calculator Use allowed Pages 70-74 and 24-31
This lesson uses proportions to solve what can be presented as “word problems” about
rates. The term “unit rate” means how much for one. The problem below shows one
way to figure out how much one magazine costs. It is not necessary to simplify the 16/12
to 4/3 to figure it out.
Basically, we can just divide 16 dollars by 12 magazines to get 1.33 dollars for one
Magazine. That is called the “unit rate” or price for one magazine.
Notice in the problem above that we are comparing two different kinds of things.
Dollars (or cost) and a number of magazines. We will use this idea of “rates” to
solve problems about two different kinds of things.

2. Proportions page 25
We will use an important idea from mathematics to solve these problems. I like to
call it “the product of the means – the product of the extremes.” It isn’t necessary
for us to go into a lot of detail about this if you just understand what it means. Read
more about this on page 25 A and B if you have it in your book.
Note: This has NOTHING to do with multiplying fractions. I like to say “you just
multiply the top number from one side by the bottom number from the other side
and then set that multiplication equal to the multiplication of the other top number
by the bottom number of the other side.”
In the problems we will be solving, there will be two different quantities involved in
the problem. Usually there will be two sentences that give two different sets of facts
about these quantities. We will write a fraction for each sentence and set the fractioons
equal to each other. The use the product of the means = the product of the extremes
to solve.
Solve: 2 times N = 7 times 8
2n = 56 then divide both sides by 2
n = 56 This should look familiar.

3. Now we will start solving problems like you might see on the test.
From page 27. Page 29 and 30 have some problems worked out.
Notice the two quantities in this problem---miles and minutes. Make a fraction ratio
for the first sentence. ( put miles over minutes but you could have put minutes over
miles. Then write a fraction for the second sentence. Use a letter for the part you don’t
know which is “how long” or minutes for 4.8 miles.
Of the four parts of the problem, you will be given three. Use a letter for the one part
you don’t know. Look at the work. Do you see how I wrote the second line?
Solve like any other equation. It would take 40 minutes.
Note: There are other ways to solve these. It doesn’t matter what way you use.
Just be sure it makes sense and you get it right.

4. I put dollars over hours for both sentences.
Change the fractions to decimals.
I put miles over hours.
So, 262. 5 miles in 1 ¼ hours.

5. Some unit rate problems from page 70. Don’t worry if you don’t know the
units like BTU, etc. Just use the numbers.

6. Try some problems on page 74. They have answers.

7. A very practical problem you might see is a “better buy” problem. Given two
items at different prices, pick which is the cheapest.