Ratios and Proportions

Unit 4, Lesson 7

peer.tamu.edu/NSF_Files/Ratios%20and%20Proportions.ppt

Ratios:

• http://www.brainpop.com/math/ratioproportionandpercent/ratios/preview.weml

What is a Ratio?

• A ratio is a comparison of two numbers.• Ratios can be written in three different ways:

a to b

a:b

b

a

Ratios are expressed in simplest form

How to Use Ratios?

• The ratio of boys and girls in the class is 12 to11.

4cm

1cm

• The ratio of length and width of this rectangle is 4 to 1.

. • The ratio of cats and dogs at my home is 2 to 1

How to simplify ratios?

• Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1?

6

12=1

2

More examples…

24

8

9

27

200

40=

=

=

5

1

3

150

12= 25

6

18

27=

2

3

1

3

Proportions:

• http://www.brainpop.com/math/ratioproportionandpercent/proportions/

Now, on to proportions!

d

c

b

a

What is a proportion?

A proportion is an equation that equates two ratios

Properties of a proportion?

4

6

2

3

2x6=12 3x4 = 12

Cross Product Property

How about an example?

62

7 x Solve for x:

7(6) = 2x

42 = 2x

21 = x

How about another example?

x

12

2

7 Solve for x:

7x = 2(12)

7x = 24

x =7

24

Define: Let t = time needed to ride 295 km.

In 2000, Lance Armstrong completed the 3630-km Tour de France course in 92.5 hours. Traveling at his average speed, how long would it take Lance Armstrong to ride 295 km?

3630t = 92.5(295) 3630

t ≈ 7.5

363092.5

295

tkilometershours

Write: =

Applications of Proportions

3630