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
6 x 5 = 3 x 10
30 = 30

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

5. 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.

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

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

8. Try one on your own…
3 = 12 y

9. And another…
6 = 12 n

10. 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.

11. 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
$ $10

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

13. 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
$ $6

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

15. 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.

16. 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?

17. 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?