ratios and proportions
TRANSCRIPT
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.
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Width=12m
Ratio of length of tennis court to its width can be expressed in 3 ways as:
Fraction
Two quantities separated by colon Two quantities separated by “to”
24/12
24 to 12
24:12
Ratio – Expression Representation
Example
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Ratio – How to Simplify?
Find highest common factor for all the entities.
Ratio for previous example was written as
Width=12m
24:12
H.C.F for 24 and 12 = 12
How to further simplify?
1
Divide both numbers by 12 2
24/12: 12/12 = 2:1 3
Example
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Width=12m
Find the ratio of width of tennis court to its length in its simplest form?
Quick Question
24:12
1:2
2:1
12:24
Note : Click on the checkbox
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Width=12m
Find the ratio of width of tennis court to its length in its simplest form?
Notice that the order of the entities listed has changed.
24:12
1:2
2:1
12:24 Ratio must be simplified
Notice that the order of the entities listed has changed.
Solution
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Proportion
Two equal ratios form a proportion.
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20
10
Width of swimming pool(plan)
Length of swimming pool(plan)
= Width of swimming pool(actual)
Length of swimming pool(actual)
10
20
= 20
40
*2
*2
Proportion - How to check if ratios are proportional?
Reduce to lowest terms 1
(Taking the previous example.) 20
10
Width of swimming pool(plan)
Length of swimming pool(plan)
= Width of swimming pool(actual)
Length of swimming pool(actual)
10 20
= 20
40 Reducing to lowest terms on both sides
1 2
= 1 2 Hence ratios are
proportional.
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Proportion - How to check if ratios are proportional?(Continued)
=
Means
Extreme
=
=
Hence ratios are proportional.
Find Cross Products 2
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 = 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
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_ratios/tb_ratio_main.html
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Rate
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If 2 kg apples cost 7$.
Cost to Weight rate is written as : 7$/2kg.
Compare quantities of different units.
Unit Rate
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Unit Rates have a denominator of 1.
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Paul takes 3 hours to cover 270km.
270km/3
3 hours/3 =
90km
270km 3 hours
1 hour
Unit rate is written as :
90km per hour
Unit Rates - Example
1 Set up a rate
2 Divide by denominator
3
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
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Ratios and Proportions – Scenario application
Ratios and Proportions – Real world application
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Quick Recap
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Recall and memorize various terms used, with StudyStack
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