Ratios & Rates
Objective:7.1.01 Develop and use ratios, proportions, and
percents to solve problems.
Essential Questions: What are the differences between ratios, rates, and unit rates?
Ratios & Rates
Vocabulary:Ratio: a comparison of two numbers by division.Equivalent Ratios: two or more ratios that form
equivalent fractions. (Example: 1/2 = 5/10)Rate: a ratio of two measurements having
different kinds of units. (Example: buy 7 pencils for $2)
Unit Rate: a rate that has been simplified so it has a denominator of 1. (Examples: $9 per pound; 6 ounces per serving)
Ratios & Rates
So What Do We Really Use Ratios for In The Real World…
RATES & UNIT RATES
But Before We Can Look At Rates And Unit Rates We Have To Understand Ratios
Ratios & Rates
Real World:Two different packages of batteries are shown below. Determine which is less expensive per battery, the 4-pack or the 8-pack.
4-pack $3.60 8-pack $6.80
We know the 8-pack is a better deal per battery
Ratios & Rates
But Before We Can Really Understand Rates And Unit Rates We Have To Understand Ratios
Ratios & Rates
(1) What is the ratio of soccer balls to the total number of balls?
6 to 14 6:14 6 out of 14 6/14
3 to 7 3:7 3 out of 7 3/7
(2) What is the ratio of basketballs to the total number of balls?
8 to 14 8:14 8 out of 14 8/14
4 to 7 4:7 4 out of 7 4/7
Ratios & Rates
Lets Look At Some…
Ratios
Ratios & Rates
Example 1: Write a ratio that compares the number of footballs to the number of soccer balls.
# of Footballs TO # of Soccer Balls4 to 6 OR 4:6 OR 4/62 to 3 OR 2:3 OR 2/3
Ratios & Rates
Example 1: Write a ratio that compares the number of footballs to the number of soccer balls.
Footballs 4 2Soccer Balls 6 3
▪ The ratio of footballs to soccer balls is 2:3, 2/3 or 2 to 3. ▪ For every 2 footballs there are 3 soccer balls.
Ratios & Rates
Example 2: Write a ratio that compares the number of hamburgers to the number of snacks.
# of Hamburgers TO Total # of Snacks4 to 12 OR 4:12 OR 4/12
1 to 3 OR 1:3 OR 1/3
Ratios & Rates
Example 2: Write a ratio that compares the number of hamburgers to the number of snacks.
Hamburgers 4 1Snacks 12 3
▪ The ratio of hamburgers to snacksis 1:3, 1/3 or 1 to 3.
▪ There is 1 hamburger for every 3 snacks.▪ For every 3 snacks 1 is a hamburger.
Ratios & Rates
Example 3: The ratio of the number of bones in a human’s ears to the total number of bones in the human skull is 3:11. If there are 21 bones in the human ear, how many bones are in the human skull?
6 bones in the human ear
Ratios & Rates
Example 4: The ratio of the number of games won to the number of games lost last season was 3:2. If the basketball team won 18 games last season, how many did they lose?
The team lost 12 games
Ratios & Rates
Lets Look At Some…
Rates & Unit Rates
Ratios & Rates
What about the G-UNIT RATE:(1) When a rate contains a denominator of 1, we call this a unit rate.
(2) We can use unit rates to determine whether deals are good or bad.
(3) For instance, is it better to buy four individual rolls of paper towels for $1.29 each, or a pack of four for $5.04.
Ratios & Rates
Example 5: Dr. Rodriguez drove 391 miles on 17 gallons of gas. How many miles could he have driven with just one gallon of gas?
÷17
391 miles w miles 17 gallons 1 gallon
÷17
Answer: 23 miles/gallon
Ratios & Rates
Example 6: Mr. Williams was at Wal-Mart buying some wrapping paper to wrap his Christmas presents. The paper he bought was $2.73 for 7 yards of paper. What was the cost per yard?
÷7
$2.73 x dollars 7 yards 1 yard
÷7 Answer: $0.39 per yard
Ratios & Rates
Example 7: Is it better to buy four single rolls of paper towels for $1.29 each, or a pack of four for $5.04? By how much?
The 4-Pack is CheaperBy $0.06
Ratios & Rates
Example 8: Jacob filled his 60 gallon fish tank in 5 minutes. How fast was water being poured into the tank?
÷5
60 gallons w gallons 5 minutes 1 minute
÷5
Answer: 12 gallons per minute
Ratios & Rates
Independent Practice:Express as a ratio in simplest form.1. 3 sailboats to 6 motorboats2. 14 lions to 10 tigersExpress each as a unit rate.3. $18 for 3 CDs4. 8 tomatoes for $4.40
Ratios & Rates
Independent Practice:Answers.1. 3/6 or 3:6 or 3 to 62. 7/5 or 7:5 of 7 to 5Answers.3. $6 per CD4. 1 tomato for $0.55 or $0.55/tomato
Ratios & Rates
Independent Practice:Express as a ratio in simplest form.1. 5 ducks to 10 geese2. 15 roses to 10 carnationsExpress each as a unit rate.3. 48 televisions on 4 trucks4. $5.28 for 24 pencils
Ratios & Rates
Independent Practice:Answers.1. 1/6 or 1:6 or 1 to 62. 5/4 or 5:4 of 5 to 4Answers.3. 12 televisions/truck4. $0.22/pencil
Ratios & Rates
Real World:As you all know, cans of Coca-Cola are sold in different size packages. For instance, Piggly Wiggly currently has the following Coca-Cola packages on sale for the following prices. Which of the four is the best deal? If I wanted to buy 48 cans of Coke, what would be the best to do it?
$0.65 $2.99 $4.08 $9.12
Ratios & Rates
HOMEWORK
Ratios & Rates
Top Related