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PROPORTIONS

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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__ = _ c__

b d

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Proportions

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

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3 : 5 = 6 : 10

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Means

Extremes

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Proportions

Means

Extremes

6 x 5 = 3 x 10

30 = 30

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Proportions

Determine if the following are proportions.

1)

2)

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Proportions

3 x 60 = 5 x 36

180 = 180

Yes, it is a proportion.

4 x 15 = 8 x 8

60

64

No, it is not a proportion.

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Solving Proportions

  • 4 = 24

y 30

4(30) = 24y

120 = 24y

120 = 24y

24 24

5 = y

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  • 1. Cross Multiply

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  • 2. Solve for the variable.

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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

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Try one on your own…

  • 3 = 12

y 28

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And another…

  • 6 = 12

n 24

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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.

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Practical Examples

  • A proportion is a statement that two given ratios are equal 
  • Practical examples:
    • If a cocktail 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 cocktail 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. �

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Practical Examples

  • If city tax rate is $7.75 to every $100 of purchase, then you have to use the same ratio no matter how much your purchase is (because it is the law).

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  • Why babies can crawl on their knees for a long time?
    • If a baby is only 1/3 of our height, then the pressure on its knees will only be 1/3 of ours, and such small pressure will not cause pain in the knees.� 

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Proportion Word Problems

  • If you can buy one can of pineapple chunks

for $2 then how many can you buy with $10?

    • First set up a proportion then solve for your variable.
    • Remember proportions are two equivalent ratios set equal to each other.
    • 1 can = x

$2 $10

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Solving the proportion

  • 1 can = x cans

$2 $10

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  • 1(10) = 2x
  • 10 = 2x
  • 10 = 2x

2 2

  • 5 = x: You can buy 5 cans with $10.

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Proportion Word Problems

  • Ming was planning a trip to Western Samoa. Before going, she did some research and learned that the exchange rate is 6 Tala for $2. How many Tala would she get if she exchanged $6?
    • First set up a proportion then solve for your variable.
    • Remember proportions are two equivalent ratios set equal to each other.
    • 6 Tala = x Tala

$2 $6

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Solving the proportion

  • 6 Tale = x Tala

$2 $6

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  • 6(6) = 2x
  • 36 = 2x
  • 36 = 2x

2 2

  • 18 = x: She would get 18 Tala.

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Try one on your own…

  • Jasmine bought 32 kiwi fruit for $16. How many kiwi can Jasmine buy if she only had $4?
    • First set up a proportion then solve for your variable.
    • Remember proportions are two equivalent ratios set equal to each other.

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And another…

  • Jenny was planning a trip to the United Arab Emirates. Before going, she did some research and learned that the exchange rate is 4 Dirhams for every $1. How many Dirhams would she get if she exchanged $5?

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And one more…

  • Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall?