PROPORTIONSPROPORTIONS

Created by Trudy MagennisCreated by Trudy Magennis

Let’s review! What are Let’s review! What are proportions?proportions?

An equation in which two ratios are equal is An equation in which two ratios are equal is called a called a proportionproportion

A proportion can be written using colon A proportion can be written using colon notation like this notation like this a : b :: c : da : b :: c : d

or as the more recognizable (or as the more recognizable (and useableand useable) )

equivalence of two fractions. equivalence of two fractions. aa//bb = = cc//dd

ProportionsProportions

In a proportion the product of the means In a proportion the product of the means is equal to product of the extremesis equal to product of the extremes ..

3 : 5 = 6 : 103 : 5 = 6 : 10

Means

Extremes

ProportionsProportions

3

5

6

1 0

Means Extremes

6 x 5 = 3 x 10

30 = 30

3

5

6

1 0

ProportionsProportions

5

3

6 0

3 6

Determine if the following are proportions.

1) 8

1 5

4

8

2)

Yes! No!

ProportionsProportions

5

3

6 0

3 6

8

1 5

4

8

3 x 60 = 5 x 36

180 = 180

Yes, it is a proportion.

4 x 15 = 8 x 8

60 64No, it is not a proportion.

Solving ProportionsSolving Proportions

44 = = 2424

y 30y 30

4(30) = 24y4(30) = 24y

120 = 24y120 = 24y

120120 = = 24y24y

24 2424 24

5 = y5 = y

1. Cross Multiply1. Cross Multiply

2. Solve for the 2. Solve for the variable.variable.

Solving ProportionsSolving Proportions

1010 = = 55 y 8y 8 8(10) = 5y8(10) = 5y 80 = 5y80 = 5y 8080 = = 5y5y 5 55 5 16 = y16 = y

1. Cross Multiply1. Cross Multiply 2. Solve for the 2. Solve for the

variablevariable

Try one on your own…Try one on your own…

33 = = 1212

y 28y 28

Correct! 7

And another…And another…

66 = = 12 12

n 24n 24

Correct! 12

ProportionsProportions

Recall that a  fraction is always used for part-to-Recall that a  fraction is always used for part-to-whole  comparison, but a ratio can be used for whole  comparison, but a ratio can be used for 

– part-to-part comparison part-to-part comparison – part-to-whole comparison part-to-whole comparison – other comparisons such as length-to-width.other comparisons such as length-to-width.

Practical Examples Practical Examples

A A proportionproportion is a statement that two given ratios are  is a statement that two given ratios are equal equal 

Practical examples:Practical examples:– If a punch If a punch reciperecipe calls for 1 part of 7-up and 2 parts of calls for 1 part of 7-up and 2 parts of

orange juice, then you need to use the same ratio (no orange juice, then you need to use the same ratio (no matter how much of punch you want) in order to keep matter how much of punch you want) in order to keep the taste consistent.  the taste consistent.  

– If you are If you are mixingmixing paint to paint your house, you need paint to paint your house, you need to keep the ratio (of color pigments to white paint) to keep the ratio (of color pigments to white paint) constant to ensure that the color will remain exactly constant to ensure that the color will remain exactly the same. the same.

Word ProblemsWord Problems A muffin A muffin reciperecipe calls for 7 cups calls for 7 cups

flour for every 2 cups milk. How flour for every 2 cups milk. How much flour will you need if you much flour will you need if you use 5 cups milk?use 5 cups milk?

–First set up a proportion then solve for your First set up a proportion then solve for your variable.variable.

–Remember proportions are two equivalent ratios Remember proportions are two equivalent ratios set equal to each other.set equal to each other.

–7 cups flour7 cups flour = = x cups flour x cups flour

2 cups milk 5 cups milk2 cups milk 5 cups milk

Solving the proportionSolving the proportion 7 cups flour7 cups flour = = x cups flourx cups flour

2 cups milk 5 cups milk2 cups milk 5 cups milk 7(5) = 2x7(5) = 2x 35 = 2x35 = 2x 3535 = = 2x2x

2 22 2 17.5 = x 17.5 = x You must use 17.5 cups of flour with 5 You must use 17.5 cups of flour with 5

cups of milk!cups of milk!

Mixture Word ProblemsMixture Word Problems– To make a certain concentration of a chemical, a To make a certain concentration of a chemical, a

scientist mixes 81 ml of the chemical with 180 scientist mixes 81 ml of the chemical with 180 ml of distilled water. To make more of this ml of distilled water. To make more of this chemical concentration, exactly how many chemical concentration, exactly how many milliliters of the chemical should the scientist milliliters of the chemical should the scientist mix with 260 ml of distilled water?mix with 260 ml of distilled water?

– 81ml chemical81ml chemical = = x ml chemicalx ml chemical

180 ml water 260 ml water180 ml water 260 ml water

– Remember proportions are two equivalent ratios set equal Remember proportions are two equivalent ratios set equal to each other.to each other.

– First set up a proportion, then solve for the variable. First set up a proportion, then solve for the variable.

Solving the proportionSolving the proportion

81ml chemical81ml chemical = = x ml chemicalx ml chemical

180 ml water 260 ml water180 ml water 260 ml water

81(260) = 180x81(260) = 180x

21060 = 180x21060 = 180x

2106021060 = = 180x180x

180 180180 180

117 ml chemical = x117 ml chemical = x

Try one on your own…Try one on your own… Sandy mixes 8 ounces of cream Sandy mixes 8 ounces of cream

cheese with 12 ounces of salsa to cheese with 12 ounces of salsa to make a dip for her party. She make a dip for her party. She wants to use this mixture to make wants to use this mixture to make 48 ounces of dip. Exactly how 48 ounces of dip. Exactly how many ounces of cream cheese many ounces of cream cheese should she use?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 Remember proportions are two equivalent ratios set equal to each other.set equal to each other.

And another…And another…

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

In your journals, explain in words how In your journals, explain in words how you would solve the following problem.you would solve the following problem. Joseph is mixing cleaning solution Joseph is mixing cleaning solution

with water to clean his kitchen floor. with water to clean his kitchen floor. He should use 1 fluid ounce of He should use 1 fluid ounce of cleaning solution for every ½ gallon cleaning solution for every ½ gallon of water. If Joseph fills a bucket of water. If Joseph fills a bucket with 4 ½ gallons of water, exactly with 4 ½ gallons of water, exactly how many fluid ounces of cleaning how many fluid ounces of cleaning solution should he use?solution should he use?

Now, let’s do some more practicing!