10.4.13Aim: What are the similarities and

differences between ratio, rates, and unit rates?

Do now: 1) Solve for a:

b = ca + d2) The member of the senior class are planning a dance. They use the equation r =pn to determine the total receipts. What is n expressed in terms of r and p?

Ratio

A ratio of one number to another number is the quotient of the first number divided by the second number. (Where the second number is not zero.)It’s a fraction!A ratio of “a to b” can be written as:(b ≠ 0)

Example

If a drama club has 12 girl members and 9 boy members, then the ratio of girl to boy members is:

What is the ratio of boy to girl members?

If Bill is 24 years old and Glen is 16 years old, then the ratio of Bill’s age to Glen’s age is:

You try!

An oil tank with a capacity of 200 gallons contains 50 gallons of oil. Find the ratio of the number of gallons of oil in the tank to the capacity of the tank.

Equivalent Ratios

Since the ratio is a fraction, we can use the multiplication property of 1 to find many equivalent ratios.

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Simplest Form

A ratio is expressed in simplest form when both terms of the ratio are the whole numbers and when there is no whole number other than 1 that is a factor of both of these terms.

Example the ratio of 24:16 is:

Example

Express each ratio in simplest form as a fraction.36 to 12

You try!

Express each ratio in simplest form using a colon:8 to 32

Practice

1) 8 to 402) 48 to 243) 25 to 40

Continued Ratio

A continued ratio is a comparison between 3 or more quantities.Example: The ratio of the measure of the length, width and height of 75:60:45

Rate

If quantities a and b are measured in different units, then is the rate of a per b.

A unit rate is a rate in which the second part is one. To change the rate into a unit rate, divide both parts of the rate by b.

Example

You are shopping for t-shirts. Which store offers the best deal?Store A: $ 25 dollars for 2 shirtsStore B: $45 for 4 shirtsStore C: $30 for 3 shirts

Store A - $ 25 dollars for 2 shirts

Store B - $45 for 4 shirts

Store C- $30 for 3 shirts

You Try

Find the best deal.$ 44 for 4 DVDs$32 for 2 DVDs$75 for 5 DVDs

Express each rate in lowest terms

1. The ratio of 36 apples to 18 people .

2. The ratio of 48 patients to 6 nurses.

3. The ratio of 90 cents to 10 grams.

4. The ratio of $3 to 9 ounces.

Real Application

Suppose Jack was paid $304 for working 16 hours and Jill earned $246 for working 12 hours. To determine which person earns more money per hour, compare their unit rates

Find the average rate of speed expressed in miles per hour

A vacationer traveled 230 miles in 4 hours.

Find the average rate of speed expressed in miles per hour

A post office truck delivered mail on a 8-mile route in 2 hours.

Practice

1) There are 240 tennis balls in 80 cans, how many tennis balls are in each can?

2) If an 11-ounce can of shaving cream costs 88 cents, what is the unit cost of the shaving cream in the can?

3) Ronald runes 300 meters in 40 seconds. Carlos runs 200 meters in 30 seconds. Who is the faster runner for the short races?

How does the way in which a rate is usually expressed differ from a ratio in

simplest form?

What is the difference between a rate and a unit rate?