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Proportions

Proportions. 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

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  1. Proportions

  2. 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

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

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

  5. Proportions Determine if the following are proportions. 1) 2)

  6. Proportions 3 x 60 = 5 x 36 4 x 15 = 8 x 8 180 = 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… • 3 = 12 y 28

  10. And another… • 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. 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

  13. Solving the proportion • 1 can = x cans $2 $10 • 1(10) = 2x • 10 = 2x • 10 = 2x 2 2 • 5 = x: You can buy 5 cans with $10.

  14. 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

  15. Solving the proportion • 6 Tale = x Tala $2 $6 • 6(6) = 2x • 36 = 2x • 36 = 2x 2 2 • 18 = x: She would get 18 Tala.

  16. 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.

  17. 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?

  18. 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?

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