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Proportion

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Proportion

What is a Proportion?
Calculating proportional values
Direct proportion and Inverse Proportion

Khan Video Tutorial: Video 1 | Video 2 | Video 3 | Video 4

Link to powerpoint with a really good explanation of ratio vs proportion vs fraction and also scaling recipes up or down

 

Class notes | pdf

p371 Ex 25.03

p51 Ex 4.01, p60 Ex 4.04

NuLake p30, 31, 32, 33

 

 

Direct Proportion: As one quantity increases so does the other
Example 1
eg. It takes a person 6 minutes to harvest the apples from a tree
How long will it take to harvest 20 trees? (assume trees similar)
 
 
(multiply)
More trees = More time
1 person = 1 tree = 6 minutes
1 person = 20 trees = 6 x 20 = 120 minutes (2hr)
Answer = 120 minutes (2hr)
 
As one value Increases the other value Increases also.
 
Inverse Proportion: As one quantity increases the other decreases
Example 2
eg. It takes a person 48 minutes to harvest a row of apple trees
How long will it take 4 people to harvest a row? (assume rows similar)
 
 
Information given
1 person = 1 row = 48 minutes
(divide)
More people = Less time
4 people = 1 row = 48 ÷ 4 = 12 minutes
Answer = 12 minutes
 
As one value Increases the other value Decreases.
 
 
 
 
Combined Problems
Example 3
eg. It takes 4 people 32 minutes to harvest 5 rows of pear trees
How long will it take 2 people to harvest 4 rows? (assume rows similar)
 
 
Information given
4 people = 5 rows = 32 minutes
Less people = More time
2 people = 5 rows = 64 minutes
Less rows = Less time
2 people = 1 row = 12.8 minutes
More rows = More time
2 people = 4 rows = 51.2 minutes
 
Answer = 51.2 minutes
 
 
 
 
Example 4
eg. It takes 8 people 35 minutes to harvest a 6 rows of apricot trees.
5 people have 2hr or time available.
How many rows can they harvest? (assume rows similar)
 
 
Information given
8 people = 6 rows = 35 minutes
Less people = More time
1 person = 6 rows = 280 minutes
More people = Less time
5 people = 6 rows = 56 minutes
Less time = Less rows
5 people = 6/56 rows = 1 minute
More time = More rows
5 people = 12.857 rows = 120 minutes
 
Answer = 12.9 rows (almost thirteen)

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