Ratios, Rates, Distance and Proportions

TSW write and simplify ratios.TSW determine unit rate.TSW calculate rates involving cost per unit to determine the best buy.

DO NOW (not later):

Compare the number of boys to girls in the class.

The number of boys =

The number of girls =

If we compare boys to girls we get

___ boys to _____ girls.

What do we call a comparison between two or more quantities?

RATIOWe just found the RATIO of boys to girls.

Is the ratio of girls to boys the same ?

No, when writing a ratio, ORDER matters.

How many basketballs to footballs are there?

For every 4 basketballs there are 6 footballs.

The ratio is 4 to 6.

What are some other ways we can write the ratio of basketball to footballs?

4 to 6

4 : 6

4

6

First quantity to Second quantity

First quantity : Second quantity

First quantity divided by the second quantity (as a fraction).

Every ratio can be written in 3 ways:

Careful!!

Order matters in a ratio.

4 to 6

Is NOT the same as

6 to 4

Practice problem # 1

You have 100 different shirts. There are 20 blue shirts and 80 black shirts.a) Write the ratio of blue to black shirts 3

different ways.

b) Write the ratio in simplest form.

c) Explain what this ratio tells us.

d) How many black shirts do you have?

Solution - # 1

a) Write the ratio of blue to black shirts 3 different ways.

20 to 80 , 20 : 80, 20 80

b) Write the ratio in simplest form. 1

4 c) Explain what this ratio tells us. For every two blue shirts,

there are 3 black shirts.

d) How many black shirts do you have?

1x + 4x = 100

5x = 100

x = 20

There are 4x black shirts so 2 (40) = 80 black

shirts

Practice Word Problems (1)Mindy has 72 candy bars. If

the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.

(2)Explain what this ratio tell us.

RateIn a ratio, if the numerator and

denominator are measured in different units then the ratio is called a rate.

A unit rate is a rate per one given unit, like 60 miles per 1 hour.

Example: You can travel 120 miles on 6 gallons of gas. What is your fuel efficiency in miles per gallon.

120 miles = 20 miles 6 gallons 1 gallon

Your fuel efficiency is 20 miles per gallon.

Unit Price A unit rate involving money is a unit

price.

Unit price is used to determine the best buy.

Example: A 24 ounce box of cereal costs $5.28. What is the unit price of the cereal?

Just divide 5.28 by 24. Therefore, you are paying $0.22 per ounce of cereal.

Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price?

Additional Example 4A: Finding Unit Prices to Compare Costs

Divide the price by the number of pens.

price for packagenumber of pens

=$1.955

= $0.39

price for packagenumber of pens

= $6.2015

$0.41

The 5-pack for $1.95 has the lower unit price.

Check It Out! Example 4B

John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price?

$2.1924

= $0.09

= $3.7936

$0.11

The 24 oz jar for $2.19 has the lower unit price.

price for bottlenumber of ounces

price for bottlenumber of ounces

Divide the price by the number of ounces.

Determine the better buy!

Six rolls cost $0.90. Twelve rolls cost $1.68.

Which is the better deal?

The big can held 16 ounces and cost 80 cents.

The small can held 12 ounces and cost 72 cents.

Which can was the better buy?

Determine the better buy!