PROPORTIONS and MIXTURE PROBLEMS

1. PROPORTIONS and MIXTURE PROBLEMS Created by Trudy Magennis

2. Let’s review! What are proportions? • 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 • or as the more recognizable (and useable) equivalence of two fractions. a/b = c/d

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

4. Proportions Means Extremes 6 x 5 = 3 x 10 30 = 30

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

6. Proportions 4 x 15 = 8 x 8 3 x 60 = 5 x 36 180 = 180 60 64 Yes, it is a proportion. No, it is not a proportion.

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

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

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

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

11. Proportions • 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 of mixtures • A proportion is a statement that two given ratios are equal  • 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 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. Mixture Word Problems • 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 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?

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

15. Mixture Word Problems • First set up a proportion, then solve for the variable. • Remember proportions are two equivalent ratios set equal to each other. • 81ml chemical = x ml chemical • 180 ml water 260 ml water • 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?

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

17. Try one on your own… • First set up a proportion then solve for your variable. • Remember proportions are two equivalent ratios set equal to each other. • 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?

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?

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?

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