Ratios & Percentages
Introduction to :
Many people use the terms "ratio" and "proportion" as though they mean the same thing, but (red alert!) they do not mean the same thing.
- Ratios compare one part to a different part
- Proportions compare one part to the whole. The term proportion also refers to an equation with ratios on each side of the equal sign.
For example, if you consider the number of boys and girls in your math class, a ratio would compare the number of girls to boys, while a proportion would compare the number of girls to the total number of students in your class.
Ratios can be written three different ways. If your town has vampires and werewolves, the ratio of vampires to werewolves can be written as:
You will notice that the last way looks a lot like a fraction. And, like a fraction, ratios and proportions can be reduced, exactly as you would reduce a fraction. By dividing both numbers by , the ratio can be written as:
Ratios & Proportions Example 1
At a local book store, for every one hundred books sold, 68 of them are fiction. What is the proportion of nonfiction books sold?
Since 68 of every 100 sold are fiction, it’s a safe bet that the remaining books are nonfiction. So, nonfiction books for every 100 sold. Proportions are usually written as fractions, so:
, which reduces to (by dividing by 4) .
Ratios & Proportions Example 2
James has quite a bit of free time each day. He often spends 4 hours on the computer and the other 2 hours playing basketball. What is his ratio of basketball to computer time? What proportion of his free time is spent on basketball?
To answer the first question, compare the number of basketball (jamming) hours (2) to the number of computer hours (4).
That’s 2:4. This ratio can be reduced to 1:2, by dividing each by 2.
For the second question, compare jamming hours (2) to the total free time (). You could write this proportion like a fraction:
, then reduce it to by dividing the numerator and denominator by 2.
Refer to the following table for questions #1-4.
Weekend Box Office Actuals (U.S.)
December 4-6, 2009
|This Week||Title||Distributor||Weekend Gross Sales||Cumulative Gross Sales||# of Theaters|
|1||The Blind Side||Warner Bros Pictures||$20,440,000||$129,264,000||3326|
|2||The Twilight Saga: New Moon||Summit Entertainment||$15,704,000||$255,639,424||4124|
|4||Disney's A Christmas Carol||Walt Disney Pictures||$7,520,000||$115,006,000||2546|
|5||Old Dogs||Walt Disney Pictures||$6,901,000||$33,934,000||3425|
|8||Ninja Assassin||Warner Bros. Pictures||$5,030,000||$29,790,000||2503|
|9||Planet 51||Sony Pictures||$4,300,000||$33,966,000||2904|
|10||Everybody's Fine||Miramax Films||$4,027,000||$4,027,000||2112|
Ratios & Proportions Exercise 1
What is the ratio of weekend gross sales for New Moon to The Blind Side?
Ratios & Proportions Exercise 2
What proportion of the top ten movies are distributed by Sony Pictures?
Ratios & Proportions Exercise 3
What proportion of 2012's cumulative gross sales was earned during the weekend of December 4-6th?
Ratios & Proportions Exercise 4
What is the ratio of movie theaters showing The Blind Side to New Moon?