1. Ratios, Rates and Unit Rates
Unit Conversion
Ratios, Rates and Unit Rates

2. Movie and television screens range in shape from almost perfect squares to wide rectangles. An aspect ratio describes a screen by comparing its width to its height. Common aspect ratios are 4:3, 37:20, 16:9, and 47:20. Most high-definition TV screens, like the one at the left, have an aspect ratio of 16:9

3. A ratio is a comparison of two quantities
A ratio is a comparison of two quantities. (1/3, 5/15, 15/45) Rate – is a comparison of two quantities measured in different units, i.e., (90 mi/3 hrs). Unit rates – are rates in which the second quantity is a single unit (1), i.e., (90 mi/3 hrs = 30 mi/1 hr). Unit price – is a unit used to compare cost per item, i.e., (4 apples for $1 = 1 apple/$0.25). Conversion factor – the ratio of two quantities that are equal, but each measured in different units. (60 min/1 hr, 5,280 ft/1 mi)

4. A package of 8 dinner rolls costs $2. 00
A package of 8 dinner rolls costs $ A package of 10 dinner rolls cost $ Which is the better buy? How would you determine which was the best bargain? Explain.

5. The best buy would be the first item, 8 rolls for $2.00.
One way to compare prices is to use unit prices, such as the price per roll.
The / means “per” unit.
$2.00/8 = $0.25 per roll
.25¢/roll
$2.79/10 = $.279 or .279¢ cents per roll
.28¢/roll
The best buy would be the first item, 8 rolls for $2.00.

6. Try these for practice 1) Pens can be purchased in a 5-pack for $1
Try these for practice 1) Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $ Which is the better buy? 2) Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for $ Which is the better buy?
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7. 3) Find the unit price of 6 stamps for $2. 22
3) Find the unit price of 6 stamps for $ ) Find the unit rate of 8 heartbeats in 6 seconds. 5) What is the better buy, a half dozen carnations for $4.75 or a dozen for $9.24? 6) Which is the better buy, 4 pens for $5.16 or a ten-pack for $12.90?

8. Dimensional analysis using conversion factors
Analyze Units
Dimensional analysis using conversion factors

9. Determine the missing values below.
____ inches = 1 foot
____ centimeters = 1 meter
____ ounces = 1 pound
____ seconds = 1 minute
____ minutes = 1 hour
Facts like these allow people to convert from one measurement to another. These are called conversion factors.

10. A radio control car travels 30 feet across the floor in 11
A radio control car travels 30 feet across the floor in 11.8 seconds, how fast is that in miles per hour. The problem is stated in feet and seconds. The question asks for the answer in units of miles and hours.

11. First we create conversion factors -(the ratio of two equal quantities, each measured in different units.) to change from seconds to hours and then feet to miles.
60 sec/1 min
60 min/1 hr
5280 ft/ 1 mi
These conversion factors will help to change from feet/second to miles/hour.
The problem is the remote controlled car travels 30 feet in 11.8 seconds, we want to know how fast that is in (mph) miles per hour.

12. After cross multiplication, only the hour and mile units are left.
Do not include the numbers yet. Notice what happens to the units. By factoring out in cross multiplication, only mi/hr remain.
After cross multiplication, only the hour and mile units are left.

13. We can simplify the problem and multiply by several conversion factors at once. Let’s look to see how this can be accomplished.

14. anything times itself is itself squared.
CAUTION Sometimes when determining a conversion factor, you may write the units in the incorrect place in the ratio. For units to cancel, they must be on opposite sides of the fraction bar. See the example below.
Remember,
anything times itself is itself squared.
miles · miles = miles2

15. Try these problems using dimensional analysis.
Think!
What conversion factors should I use?
A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling?
A model airplane flies 22 feet in 2 seconds. What is the plane’s speed in miles per hour?
A yellow jacket can fly 4.5 meters in 9 seconds. How fast in kilometers per hour can a yellow jacket fly?