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Ratio
Proportion
Proportion - Solve for variables
Rate
Unit Rate
Scenario Application
Real World Application
Quick Recap
Quiz
What is a ratio?
Ratios are expressions that compare two or more quantities.
Represents quantity of one entity for
every amount of another entity.

wikihow.com
Ratio – Expression Representation
Example

Ratio of length of tennis court to its
width can be expressed in 3 ways as:

Fraction 24/12

www.clipartsfree.net

Width=12m

Two quantities separated by
colon
Two quantities separated by
“to”

24:12
24 to 12
Ratio – How to Simplify?
Find highest common factor for all the
entities.
Example
Ratio for previous example was written as

24:12
How to further simplify?
1

2

Width=12m
www.clipartsfree.net

3

H.C.F for 24 and 12 = 12

Divide both numbers by 12
24/12: 12/12 = 2:1
Quick Question

Note : Click on the checkbox
Find the ratio of width of tennis court
to its length in its simplest form?
24:12
1:2
Width=12m
www.clipartsfree.net

2:1
12:24
Solution
Find the ratio of width of tennis court
to its length in its simplest form?

Width=12m
www.clipartsfree.net






24:12

Notice that the order of the entities listed
has changed.

1:2
2:1
12:24

Notice that the order of the entities listed
has changed.
Ratio must be simplified
Proportion
Two equal ratios form a proportion.

20

en.wikipedia.org
10

Width of swimming pool(plan) = Width of swimming pool(actual)
Length of swimming
pool(plan)
10 *2
20 *2

=

Length of swimming
pool(actual)

20
40

en.wikipedia.org
Proportion - How to check if ratios are proportional?
1

Reduce to lowest terms
(Taking the previous example.)

20

10

en.wikipedia.org

en.wikipedia.org

Width of swimming pool(plan)
Length of swimming
pool(plan)

10
20
1
2

=
=

20
40
1
2

=

Width of swimming pool(actual)
Length of swimming
pool(actual)

Reducing to lowest
terms on both sides
Hence ratios are
proportional.
Proportion -

How to check if ratios are proportional?(Continued)

2

Find Cross Products

Extreme

=

=

=
Means

Hence ratios are
proportional.
Proportion – Quick Quiz

8
15

=

4
8

Proportional
Not Proportional
Proportion – Quick Quiz

8
15




=

4
8

Proportional
Not Proportional
Proportion – Quick Quiz(Continued)

5
4

=

25
20

Proportional
Not Proportional
Proportion – Quick Quiz(Solution)

5
4




=

25
20

Proportional
Not Proportional
Proportion – Solve for variables
Proportion – Work out
Now watch the following video carefully and answer
questions 1 and 2.
Proportion - Application

Choose the correct formula to solve this problem:
Height of fence/Length of fence shadow = Height of tree/Length of
tree shadow
Height of fence/Length of fence shadow = Length of tree
shadow/Height of tree
Height of fence*Length of fence shadow = Height of tree *Length of
tree shadow
Height of tree= Height of fence *Length of fence shadow
Proportion - Application

Choose the correct formula to solve this problem:




Height of fence/Length of fence shadow = Height of tree/Length of
tree shadow




Height of fence*Length of fence shadow = Height of tree *Length of
tree shadow

Height of fence/Length of fence shadow = Length of tree
shadow/Height of tree

Height of tree= Height of fence *Length of fence shadow
Proportion - Application

The height of the tree in Keona’s garden is :
12 ft.
24 ft.
44 ft.
6 ft.
Proportion - Application

The height of the tree in Keona’s garden is :






12 ft.
24 ft.
44 ft.
6 ft.
Ratios and Proportions – Word Problem Game
Solve ratio word problems
with Thinking Block game.
http://www.thinkingblocks.com/thinkingblocks_r
atios/tb_ratio_main.html

en.wikipedia.org
Rate
Compare quantities of different units.

If 2 kg apples cost
7$.

commons.wikimedia.org

Cost to Weight rate is
written as : 7$/2kg.
Unit Rate
Unit Rates have a denominator of 1.

www.flickr.com
land8.com
Unit Rates - Example

Paul takes 3 hours to cover 270km.
Unit rate is written as :
1 Set up
a rate

270km
3 hours

2 Divide by
denominator
3

en.wikipedia.org

90km per hour

270km/3
3 hours/3

=

90km
1 hour
Unit Rates – Work out
Test your knowledge on unit rates.
Solve questions on unit rate with Braining Camp
http://www.brainingcamp.com/content/rates/questions.php

www.forbes.com
Ratios and Proportions – Scenario application
Ratios and Proportions – Real world application
Quick Recap
Recall and memorize various
terms used, with StudyStack
http://www.studystack.com/flashcard-201074

caseywhite.hubpages.com
Are you prepared to take a Quiz?

www.flickr.com
Here you go!

Test your knowledge with Quia.
http://www.quia.com/cb/407619.html

en.wikipedia.org

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Ratios and proportions

  • 1.
  • 2. Ratio Proportion Proportion - Solve for variables Rate Unit Rate Scenario Application Real World Application Quick Recap Quiz
  • 3. What is a ratio? Ratios are expressions that compare two or more quantities. Represents quantity of one entity for every amount of another entity. wikihow.com
  • 4. Ratio – Expression Representation Example Ratio of length of tennis court to its width can be expressed in 3 ways as: Fraction 24/12 www.clipartsfree.net Width=12m Two quantities separated by colon Two quantities separated by “to” 24:12 24 to 12
  • 5. Ratio – How to Simplify? Find highest common factor for all the entities. Example Ratio for previous example was written as 24:12 How to further simplify? 1 2 Width=12m www.clipartsfree.net 3 H.C.F for 24 and 12 = 12 Divide both numbers by 12 24/12: 12/12 = 2:1
  • 6. Quick Question Note : Click on the checkbox Find the ratio of width of tennis court to its length in its simplest form? 24:12 1:2 Width=12m www.clipartsfree.net 2:1 12:24
  • 7. Solution Find the ratio of width of tennis court to its length in its simplest form? Width=12m www.clipartsfree.net     24:12 Notice that the order of the entities listed has changed. 1:2 2:1 12:24 Notice that the order of the entities listed has changed. Ratio must be simplified
  • 8. Proportion Two equal ratios form a proportion. 20 en.wikipedia.org 10 Width of swimming pool(plan) = Width of swimming pool(actual) Length of swimming pool(plan) 10 *2 20 *2 = Length of swimming pool(actual) 20 40 en.wikipedia.org
  • 9. Proportion - How to check if ratios are proportional? 1 Reduce to lowest terms (Taking the previous example.) 20 10 en.wikipedia.org en.wikipedia.org Width of swimming pool(plan) Length of swimming pool(plan) 10 20 1 2 = = 20 40 1 2 = Width of swimming pool(actual) Length of swimming pool(actual) Reducing to lowest terms on both sides Hence ratios are proportional.
  • 10. Proportion - How to check if ratios are proportional?(Continued) 2 Find Cross Products Extreme = = = Means Hence ratios are proportional.
  • 11. Proportion – Quick Quiz 8 15 = 4 8 Proportional Not Proportional
  • 12. Proportion – Quick Quiz 8 15   = 4 8 Proportional Not Proportional
  • 13. Proportion – Quick Quiz(Continued) 5 4 = 25 20 Proportional Not Proportional
  • 14. Proportion – Quick Quiz(Solution) 5 4   = 25 20 Proportional Not Proportional
  • 15. Proportion – Solve for variables
  • 16. Proportion – Work out Now watch the following video carefully and answer questions 1 and 2.
  • 17. Proportion - Application Choose the correct formula to solve this problem: Height of fence/Length of fence shadow = Height of tree/Length of tree shadow Height of fence/Length of fence shadow = Length of tree shadow/Height of tree Height of fence*Length of fence shadow = Height of tree *Length of tree shadow Height of tree= Height of fence *Length of fence shadow
  • 18. Proportion - Application Choose the correct formula to solve this problem:   Height of fence/Length of fence shadow = Height of tree/Length of tree shadow   Height of fence*Length of fence shadow = Height of tree *Length of tree shadow Height of fence/Length of fence shadow = Length of tree shadow/Height of tree Height of tree= Height of fence *Length of fence shadow
  • 19. Proportion - Application The height of the tree in Keona’s garden is : 12 ft. 24 ft. 44 ft. 6 ft.
  • 20. Proportion - Application The height of the tree in Keona’s garden is :     12 ft. 24 ft. 44 ft. 6 ft.
  • 21. Ratios and Proportions – Word Problem Game Solve ratio word problems with Thinking Block game. http://www.thinkingblocks.com/thinkingblocks_r atios/tb_ratio_main.html en.wikipedia.org
  • 22. Rate Compare quantities of different units. If 2 kg apples cost 7$. commons.wikimedia.org Cost to Weight rate is written as : 7$/2kg.
  • 23. Unit Rate Unit Rates have a denominator of 1. www.flickr.com land8.com
  • 24. Unit Rates - Example Paul takes 3 hours to cover 270km. Unit rate is written as : 1 Set up a rate 270km 3 hours 2 Divide by denominator 3 en.wikipedia.org 90km per hour 270km/3 3 hours/3 = 90km 1 hour
  • 25. Unit Rates – Work out Test your knowledge on unit rates. Solve questions on unit rate with Braining Camp http://www.brainingcamp.com/content/rates/questions.php www.forbes.com
  • 26. Ratios and Proportions – Scenario application
  • 27. Ratios and Proportions – Real world application
  • 28. Quick Recap Recall and memorize various terms used, with StudyStack http://www.studystack.com/flashcard-201074 caseywhite.hubpages.com
  • 29. Are you prepared to take a Quiz? www.flickr.com
  • 30. Here you go! Test your knowledge with Quia. http://www.quia.com/cb/407619.html en.wikipedia.org