1. PROPORTIONS Created by Trudy Magennis

2. Let’s review! What are proportions? An equation in which two ratios are equal is called a proportion An equation in which two ratios are equal is called a proportion A proportion can be written using colon notation like this a : b :: c : d A proportion can be written using colon notation like this a : b :: c : d or as the more recognizable (and useable) equivalence of two fractions. a / b = c / d or as the more recognizable (and useable) equivalence of two fractions. a / b = c / d

3. Proportions In a proportion the product of the means is equal to product of the extremes. In a proportion the product of the means is equal to product of the extremes. 3 : 5 = 6 : 10 3 : 5 = 6 : 10 Means Extremes

4. Proportions Proportions MeansExtremes 6 x 5 = 3 x 10 30 = 30

5. Proportions Determine if the following are proportions. 1)2) Yes!No!

6. Proportions 3 x 60 = 5 x 36 180 = 180 Yes, it is a proportion. 4 x 15 = 8 x 8 6064 No, it is not a proportion.

7. Solving Proportions 4 = 24 4 = 24 y 30 y 30 4(30) = 24y 4(30) = 24y 120 = 24y 120 = 24y 120 = 24y 24 24 24 24 5 = y 5 = y 1. Cross Multiply 1. Cross Multiply 2. Solve for the variable. 2. Solve for the variable.

8. Solving Proportions 10 = 5 10 = 5 y 8 y 8 8(10) = 5y 8(10) = 5y 80 = 5y 80 = 5y 5 5 5 5 16 = y 16 = y 1. Cross Multiply 1. Cross Multiply 2. Solve for the variable 2. Solve for the variable

9. Try one on your own… 3 = 12 3 = 12 y 28 y 28 Correct! 7

10. And another… 6 = 12 6 = 12 n 24 n 24 Correct! 12

11. Proportions Recall that a fraction is always used for part-to- whole comparison, but a ratio can be used for Recall that a fraction is always used for part-to- whole comparison, but a ratio can be used for –part-to-part comparison –part-to-whole comparison –other comparisons such as length-to-width.

12. Practical Examples A proportion is a statement that two given ratios are equal A proportion is a statement that two given ratios are equal Practical examples: Practical examples: –If a punch recipe calls for 1 part of 7-up and 2 parts of orange juice, then you need to use the same ratio (no matter how much of punch you want) in order to keep the taste consistent. –If a punch recipe calls for 1 part of 7-up and 2 parts of orange juice, then you need to use the same ratio (no matter how much of punch you want) in order to keep the taste consistent. –If you are mixing paint to paint your house, you need to keep the ratio (of color pigments to white paint) constant to ensure that the color will remain exactly the same.

13. Word Problems A muffin recipe calls for 7 cups flour for every 2 cups milk. How much flour will you need if you use 5 cups milk? A muffin recipe calls for 7 cups flour for every 2 cups milk. How much flour will you need if you use 5 cups milk? –First set up a proportion then solve for your variable. –Remember proportions are two equivalent ratios set equal to each other. –7 cups flour = x cups flour 2 cups milk 5 cups milk 2 cups milk 5 cups milk

14. Solving the proportion 7 cups flour = x cups flour 7 cups flour = x cups flour 2 cups milk 5 cups milk 2 cups milk 5 cups milk 7(5) = 2x 7(5) = 2x 35 = 2x 35 = 2x 2 2 2 2 17.5 = x 17.5 = x You must use 17.5 cups of flour with 5 cups of milk! You must use 17.5 cups of flour with 5 cups of milk!

15. Mixture Word Problems –To make a certain concentration of a chemical, a scientist mixes 81 ml of the chemical with 180 ml of distilled water. To make more of this chemical concentration, exactly how many milliliters of the chemical should the scientist mix with 260 ml of distilled water? – 81ml chemical = x ml chemical 180 ml water 260 ml water 180 ml water 260 ml water – Remember proportions are two equivalent ratios set equal to each other. – First set up a proportion, then solve for the variable.

16. Solving the proportion 81ml chemical = x ml chemical 180 ml water 260 ml water 81(260) = 180x 81(260) = 180x 21060 = 180x 21060 = 180x 180 180 180 180 117 ml chemical = x 117 ml chemical = x

17. Try one on your own… Sandy mixes 8 ounces of cream cheese with 12 ounces of salsa to make a dip for her party. She wants to use this mixture to make 48 ounces of dip. Exactly how many ounces of cream cheese should she use? Sandy mixes 8 ounces of cream cheese with 12 ounces of salsa to make a dip for her party. She wants to use this mixture to make 48 ounces of dip. Exactly how many ounces of cream cheese should she use? First set up a proportion then solve for your variable. First set up a proportion then solve for your variable. Remember proportions are two equivalent ratios set equal to each other. Remember proportions are two equivalent ratios set equal to each other.

18. And another… Heath mixes gasoline and oil to make fuel for his motorbike. He adds 16 fluid ounces of oil for every 2 gallons of gasoline. Exactly how many fluid ounces of oil does Heath need to add to 3 ¼ gallons of gasoline to make this fuel? Heath mixes gasoline and oil to make fuel for his motorbike. He adds 16 fluid ounces of oil for every 2 gallons of gasoline. Exactly how many fluid ounces of oil does Heath need to add to 3 ¼ gallons of gasoline to make this fuel?

19. In your journals, explain in words how you would solve the following problem. Joseph is mixing cleaning solution with water to clean his kitchen floor. He should use 1 fluid ounce of cleaning solution for every ½ gallon of water. If Joseph fills a bucket with 4 ½ gallons of water, exactly how many fluid ounces of cleaning solution should he use? Joseph is mixing cleaning solution with water to clean his kitchen floor. He should use 1 fluid ounce of cleaning solution for every ½ gallon of water. If Joseph fills a bucket with 4 ½ gallons of water, exactly how many fluid ounces of cleaning solution should he use?

20. Now, let’s do some more practicing!