Ratios and Proportions

PowerPoint Tutorial Ratios and Proportions

Overview… In this tutorial you will learn about ratios and proportions. The main goals are… • for you to really understand what the term “per” means …and… • to understand that one variable can be mathematically related to another.

ratios and proportions basic math • Ratios and proportions describe how one value is related to another. You use them frequently in your life without really thinking about it. Here are a few examples… • You work a job at which you get paid $9.00 per hour. • You drive your car at 65 miles per hour. • A tree branch grows 3 inches per year. • The key word in each of these examples is per. “Per” means “for every…” • You get paid $9.00 for every hour you work. • You travel 65 miles for every hour you drive. • The tree branch gets 3 inches longer for every year it grows.

ratios and proportions basic math Let’s take a look at the $9.00 per hour job. This doesn’t tell you how much you’ll get paid after working, but rather how much you’ll get for every hour you work. So if you worked 2 hours at $9.00 per hour you would get paid … $18.00 3 hours … $27.00 4 hours … $36.00 Notice that the ratio can be written as a fraction. This fraction (what you get paid per hour) doesn’t change no matter how long you work… … all equal to 9 dollars per hour

Every once in a while during these tutorials, you’ll get to a check-in slide. When you do, go to your teacher so that she or he can make sure you’ve understood everything up to this point. TEACHER CHECK-IN #1

ratios and proportions basic math • Take a look at the gas station sign to the right. • What does the number 1.95 mean? • How much would it cost to fill an 11 gallon tank with Regular Unleaded gas? • How much more would it cost to fill the same tank with Supreme Unleaded gas? Show at least two ways to solve this problem.

ratios and proportions basic math • Take a look at the gas station sign to the right. • What does the number 1.95 mean? • How much would it cost to fill an 11 gallon tank with Regular Unleaded gas? • How much more would it cost to fill the same tank with Supreme Unleaded gas? Show at least two ways to solve this problem. This means that every gallon of Regular Unleaded gas costs $1.95. 11 gallons x $1.95/gallon = $21.45 • Method 1… • 11 gallons x $2.15/gallon = $23.65 • Method 2… • Every gallon of Supreme is $.20 more than regular. This means that 11 gallons would be 11 x $.20 more than 11 gallons of regular. which is $2.20. So 11 gallons of Supreme would be $21.45 + $2.20 = $23.65.

ratios and proportions basic math • If you bought 9 gallons of gas and paid $18.45 for it, what kind of gas did you buy? • Suppose you have a car that gets 30 mpg. If you bought Regular Unleaded gas, how much would it cost you to drive from St. Louis to Chicago?

ratios and proportions basic math • If you bought 9 gallons of gas and paid $18.45 for it, what kind of gas did you buy? • Suppose you have a car that gets 30 mpg. If you bought Regular Unleaded gas, how much would it cost you to drive from St. Louis to Chicago? 9 gallons x $___/gallon = $18.45 $___/gallon = $18.45 ÷ 9 gallons = $2.05 / gallon You bought Plus Unleaded gas. Keep trying … I’m not going to give youallof the answers (but ask for help if you need it).

ratios and proportions basic math • Another ratio you might be aware of is a text messaging rate for a cell phone. • How much does a typical plan charge per message? • How much would 5 messages cost on this plan? • How many messages could you send for $100.00?

TEACHER CHECK-IN #2

ratios and proportions basic math • PRACTICE PROBLEMS • If a gallon of water weighs about 8 pounds, how much would 4 gallons of water weigh? • If you save 125 dollars every month, how many months would it take you to save 5000 dollars? • How many times will the earth go around the sun in one million years? • According to a survey, 3 out of 5 students at a school have a pet dog and 1 out of 5 have a pet cat. If there are 1600 students, how many have pet dogs? How many have pet cats? How many don’t have any pets? • In the US, a Big Mac costs $3.50. If you have a job that pays $6.00 an hour, how long do you have to work to pay for the Big Mac? Don’t just say “a half and hour” … I want to know exactly how many minutes you would have to work to get that Big Mac! • You are traveling in Japan and see a really cool shirt that costs ¥2372 (that’s 2,372 Yen). If 1 Yen is $0.011, how much does the shirt cost in dollars?

ratios and proportions basic math • APPLICATION PROBLEMS • a) In bag #1at the back of the classroom, there is a bag of pennies and one penny on its own. Use these and the scale to determine how many pennies are in the bag. • b) In bag #2 at the back of the classroom there are a given number of identical cubes. Use the scale to determine the mass of just 1 cube in grams. • c) If there are 2.2 pounds in every kilogram, what is the mass of a 160 pound person in kilograms? • d) If there are 3.78 liters / gallon, how many gallons are there in a swimming pool that holds 1,300,000 liters of water?

Ratios and Proportions