1. Ratio Notes A ratio is a comparison of two numbers by division. Each number in a ratio is called a term. Ratios can be written three ways and SHOULD ALWAYS BE SIMPLIFIED. Ex: The ratio 4 to 5 can be written 1. 4 to 5 2. 4:5 3. 4 / 5

2. Equal Ratios are ratios that name the same number. They have the same simplest form. To find equal ratios, multiply or divide both the numerator and denominator of a ratio by the same number 4/7 = 8/14 Ratios are proportional if they simplify to the same ratio. Ex: 8:10 = 12:15 because both simplify to 4:5

3. Write a ratio in three ways to compare each. 1.Lions to deer_______________________ 2.Parrot to swans_______________________ 3.Swans to lions_______________________ 4.Deer to parrot_______________________ 5.Swans to deer_______________________ 6.Deer to swans_______________________ 2 to 4, 2:4, 2 / 4 = 1 / 2

4. Write each ratio as a fraction in simplest form. (4 pumpkins, 2 watermelon, 12 bananas) 1.Watermelon to pumpkins_________ 2.Pumpkins to bananas _________ 3.Pumpkins to watermelon _________ 4.Watermelon to bananas _________ 5.Bananas to watermelon _________ 6.Bananas to pumpkins _________

5. Unit Rates A Rate is a ratio that compares two quantities measured in different units. Ex. 150 heartbeats to 2 minutes A unit rate is the rate for one unit of a given quantity. Always has the denominator of 1. 150 divided by 2 = 75 The unit rate is 75 heartbeats per minute. Unit Price – a unit rate that gives the cost per unit.

6. Finding Unit Rates If you are given the price of many items, but you need the price for one item individually, then you need to know the unit rate. Or if you are given the rate for 20 laps around a track, but you want to know the speed PER LAP – you need to know a unit rate. Two options: 1.You can use a proportion to solve 2.You can use basic division to solve

7. Practice with Unit Rates You want to break these down into the “unit” rate. How many miles in 1 min? How many dollars you make in 1 hour? Etc. 760 miles in 30 min $42.50 in 8 hours 450 yards gained in 3 football games 286 shots made in 20 basketball games

8. Finding the “better buy” You use unit rates to determine the better buy when you are comparison shopping! Ex: At Kroger 12-packs of diet coke are $4.99 per pack. At Wal Mart 24-packs of diet coke are $7.59 per pack. Which store has the better price on diet cokes? You must find the price PER COKE (which is known as the unit price)!

9. Which is the better buy? 30 lollipops for $2.50 or 20 lollipops for $1.50? 2 football tickets for $45.50 or 3 tickets for $60.00? 6 itunes downloads for $5.99 or 10 itunes downloads for $9.50? 35 valentines for $3.99 or 50 valentines for $5.00?

10. Proportions A proportion is two equivalent ratios. We say that two ratios are “proportional” to one another. Use cross products to determine if two ratios are proportional. –Example: You can also use proportions to find a missing value in a problem. –You will actually use cross multiplication here, and an algebra equation to solve for missing values.

11. 1. There are 54 boys and 48 girls in the Leopard team. What is the ratio of girls to boys? 2. Tell me if the following ratios form a proportion. Show your work. 3 15 5 35 3.Solve to find the missing value in the following proportion:4 = X 7 35

12. EXAMPLES: Example: You can buy 20 CD’s in a pack for $30.00. How much does each individual CD cost? Proportion:Division:

13. Find the unit rate for each situation. $80 for 10 shirts $20 for 4 toys $56 for 8 hours $120 for 5 shirts $45 for 9 boxes

14. Write the unit rate as a ratio. Then find an equal ratio. The cost is $4.25 for 1 item. Find the cost of 4 items. The cost is $10.10 for 1 item. Find the cost of 10 items. The cost is $8.50 for 1 item. Find the cost of 4 items. There are 2.54 cm in 1 inch. How many cm are in 6 inches? There are 365 days in 1 year. How many days are in 2 years?

15. Scale Drawings Scale: the ratio that compares a length in a drawing or model to the length in the original Example: 1 cm = 100 miles Scale Drawing: a drawing that is similar but either larger or smaller than the actual object, for example, a road map or a building blueprint. Let’s define perimeter and area: –Perimeter = the distance around an object –Area = the amount of space an object covers

16. How to use Scale Drawing Ex: Ali uses a scale of 1in : 10 feet to build a model of the White House. The White House is 58 feet tall. How tall will her model be? 1. Write the scale as a ratio Model (in)  1 Actual (ft) 10 2. Set up a proportion: 1in = h in 10 ft 58 ft 3. Cross Multiply 4. Solve for missing value

17. Questions on map scale Scale Drawing – Blueprints & Area/Perimeter 6 in 8 in Scale: 1 in : 5 feet What is the actual width? 1in = 6 in (width) 5 ft x ft What is the actual length? What is the actual area and perimeter?

18. Finding Distances on a Map Use the map and scale to find the actual distance from Montgomery to Tuskegee. *Sometimes you will have to use a ruler and measure, sometimes it will tell you how far two things are on a map. 1. Write scale as a ratio 2. Find distance between places on map. 3. Set up a proportion 4. Cross multiply 5. Solve for missing value. Scale: 1 cm = 10 miles Distance from Montgomery to Tuskegee on the map: 3 cm

19. Similar Figures Similar Figures: have the same shape, but are not necessarily the same size. Corresponding angles are congruent (equal) Lengths of corresponding sides are proportional (but not equal)

20. Use Proportions to find missing sides or numbers 5 cm 8 cm 10 cm y 3 cm x Corresponding sides A = Corresponding sides A Corresponding sides B Corresponding sides B 5 cm = 3 cm 10 cm x Now, just cross multiply and solve for x!

21. Practice On a sunny day, a tree casts a shadow that is 116 feet long. A woman who is 5 feet tall casts a shadow that is 10 feet long. Draw a simple picture, and set up a proportion to find the height of the tree.

22. P. O. D. 2/9/09 1.There are 12 inches in 1 foot. How many inches are in 5 feet? 2.There are 60 minutes in 1 hour. How many minutes are in 3 hours? 3.There are 4 quarts in 1 gallon. How many quarts are in 3 gallons? 4.What is the unit price if a loaf of cinnamon bread costs $3.99 and there are 30 slices in the loaf?

23. P. O. D. 2/10/09 1.What is the unit rate if a loaf of bread costs $2.00 and there are 16 slices of bread in the loaf? 2.Tell me whether these ratios form proportions. Show your work. 3.Find the missing value: 4.If it takes 10 cups of flour to make 3 cakes, then how many cups of flour do you need to make 5 cakes?