Direct Proportionality

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Monday, 04 January 2010
Direct Proportionality
Why am I doing this?
Understand the idea Know how to check that two
quantities are directly proportional Find a
missing number
It is an important idea that has many real life
applications A favourite SAT and GCSE question
Level 7
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Here is an example of direct proportionality
Some DIY stores sell electrical wire by the
metre.Suppose that one store sells it at 25p per
metre. The cost for different lengths is shown on
this table.
The relationship between the length and the cost
is directly proportional.
If I want to make an electrical lead that is 4
metres long, what will be the cost of the wire?
Answer 100p ? 1
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Checking if a relationship is directly
proportional You need to be able to decide if a
relationship is directly proportional
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When are quantities are DIRECTLY PRPORTINAL?
Here is a table showing the wages earned for the
number of hours worked.
You would expect this to be a directly
proportional relationship. You can check whether
or not it is directly proportional by dividing
like this 25 4 6.25 43.75 7 6.25
56.25 9 6.25
If you always get the same answer when you
divide, the relationship is directly proportional.
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When are quantities are DIRECTLY PROPORTINAL?
Here is another table showing the wages earned
for the number of hours worked.
Are the wages directly proportional to the hours
worked? 28 4 7 42 6 7 72 9 8
If even one result does not give the same answer,
the relationship is NOT directly proportional.
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Which of the relationships shown below are
directly proportional?
15 3 5 21 3 5.25 15 3 5
NO
7.4 2 3.7 18.5 5 3.7 33.3 9 3.7
YES
12.4 2 6.2 31 5 6.2 55.8 9 6.2
YES
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Monday, 04 January 2010
Solving Direct Proportionality Problems
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Finding Missing Numbers
A common question is to give you a table showing
two quantities. Unfortunately, the table has some
missing numbers and you are asked to find these
values. Here is an example The table shows a
directly proportional relationship between LENGTH
and COST. Calculate the two missing values in
this table.
The next two slides will help you understand how
to do this ?
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How to find a missing number
x 2.5
125
x 2.5
First choose any of the numbers on the top row.
Ive chosen 2
Find the number that you have to multiply 2 by to
get 5. (5 2 2.5) 2 x 2.5 5
Multiply 50 by 2.5 to get the missing number
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Missing numbers on the top row can be found by a
similar method
x 10.5
21
x 10.5
First choose any of the numbers on the bottom
row. Ive chosen 50
Find the number that you have to multiply 50 by
to get 525. (525 50 10..5) 50 x 10.5 525
Multiply 2 by 10.5 to get the missing number
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Direct Proportionality Test 1) The
relationship between A and L is directly
proportional. Copy and complete this table
2) The relationship between K and V is directly
proportional. Copy and complete this table

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Direct Proportionality
Getting the Idea
When there is direct proportionality between two
things, it means that the relationship is the
same as the models lengths and the real planes
lengths.
Model Plane
Real Plane
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A scale for model planes is 1/72. This means that
the real planes lengths are 72 time bigger than
the models. Complete the numbers in this chart,