1. Ratio & Unit Rate
Pre-Algebra

3. A ratio is a comparison of two numbers or measures using division.
A ratio can be written three ways:
3:5 3/ to 5
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4. Ratios are often expressed as fractions in simplest or as a decimal.
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5. What ratios can we form from the tiles above?
A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways.
What ratios can we form from the tiles above?
12 to 8
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6. Create as many ratios as possible
Create as many ratios as possible. Write each ratio three different ways.
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7. Simplest Form
Write the ratio 50 to 300 in simplest form.
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8. Simplest Form
Write the ratio 60¢ per dozen in simplest form.
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9. Look over the ratios you have written
Look over the ratios you have written. Is there another way that you can write those ratios?
The ratio illustrated here is four filled cells to ten total cells.
The ratio shown here is two filled cells to five total cells.
What do you know about these two ratios? How can you prove your answer?
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10. Unit Rate “How much for just 1?”
To find the Unit Rate, you would find the cost or amount for 1. Or the rate when the denominator is 1.
“How much for just 1?”
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11. Unit Rate If it costs $78 for 13 sandwiches, What is the unit rate?
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12. The cost of a 12-ounce box of Cheerios is $3. 29
The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18-ounce box. Find the unit rate to find the better buy.
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13. Mile per Gallon
M.P.G. stands for miles per gallon and is usually used for gas mileage in cars.
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14. Unit Rate
If it takes 11 gallons to drive 250 miles, What is the unit rate or m.p.g.?
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15. Solving Word Problems X=22.7 mpg Write problem as proportions:
Solve using cross multiplication.
X=22.7 mpg
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16. Finding Unit Rate can save you money!
Unit Price: Price per Item
Measure or Count of Items
Allows shoppers to compare the prices of items quickly and easily

17. Unit Price = $2 50 plates = $0.40 per plate Genuardi’s Unit Price
Paper
Plates
= $0.40 per plate
Unit Price = $2
9 oz.
For
9 oz.
= $0.22 per oz.
Cereal
Unit Price = $2
13.75 oz
For
13.75 oz.
= $0.15 per oz.
Coffee

18. Oranges
4 lb. Bag
$2.99
Unit Price?
M & M’s
14 oz. Bag for $2.69
Unit Price?

19. What is the better buy? Safeway Select Detergent 300 oz.
$10.99
What is the Unit Price?
Wisk Laundry Detergent
100 oz.
$4.99
What is the Unit Price?
What is the better buy?

20. Which is the better buy? Dixie plates $2.49 24 count
Unit Price (per plate)?
Hefty plates
2 for $4.00
50 count (each pkg.)
Unit Price (per plate)?
Which is the better buy?

21. Genuardi's Giant Food Stores Which is the better buy? Cheerios
3 for $6
13.75 oz. boxes
Unit Price (per oz.)?
Giant Food
Stores
Cheerios
3 for $7.00
15 oz. boxes
Unit Price (per oz.)?
Which is the better buy?

22. Bounty: 8 rolls
$5.99
Thirsty: 2 rolls
$2.99
Now you want to compare these two brands, which are both on sale. You have determined that you want 8 rolls of paper towels. Which brand will you buy?

23. Proportion Example: Write the original proportion.
Use the cross product property.
Divide both sides by 6 to isolate the variable, then simplify.

24. Now you try it!
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25. You Try It!
If the average person lives for 75 years, how long would that be in seconds?

26. You Try It!
If the average person lives for 75 years, how long would that be in seconds?
To solve this problem we need to convert 75 years to seconds. We can do this by breaking the problem down into smaller parts by converting years to days, days to hours, hours to minutes and minutes to seconds.
There are days in one year, 24 hours in one day, 60 minutes in 1 hour, and 60 seconds in a minute.
Multiply the fractions, and use unit analysis to determine the correct units for the answer.

27. You Try It!
John constructs a scale model of a building. He says that 3/4th feet of height on the real building is 1/5th inches of height on the model.
What is the ratio between the height of the model and the height of the building?
If the model is 5 inches tall, how tall is the actual building in feet?

28. You Try It!
What is the ratio between the height of the model and the height of the building?
What two pieces of information does the problem give you to write a ratio?
For every 3/4th feet of height on the building…
the model has 1/5th inches of height.
Therefore the ratio of the height of the model to the height of the building is…
This is called a scale factor.

29. You Try It!
If the model is 5 inches tall, how tall is the actual building in feet?
To find the actual height of the building, use the ratio from the previous step to write a proportion to represent the question above.
Use the cross product.
Isolate the variable, then simplify.
Don’t forget your units.