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 snacks

is 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