direct proportionality

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Direct ProportionalityMonday 4 January 2010

Understand the idea

Know how to checkthat two quantities aredirectly proportional

Find a missing number

Level 7

Why am I

doing this?

It is an important idea thathas many real life

applications

A favourite SAT and

GCSE question



Here is an example of direct proportionality

Some DIY stores sell electrical wire by the

metre.Suppose that one store sells it at 25pper metre. The cost for different lengths isshown on this table.

Length (m) 0 1 2 3

Cost (p) 0 25 50 75

If I want to make an electricallead that is 4 metres long, whatwill be the cost of the wire?

Answer

100p

£1

The relationshipbetween the

length and the

cost is directly

proportional.



Checking if a relationshipis directly proportional

You need to be able todecide if a relationship isdirectly proportional



When are quantities are DIRECTLY PRPORTINAL?

Hours 4 7 9

Wages 25 43.75 56.25

Here is a tableshowing the wagesearned for thenumber of hoursworked.

You would expect this to be a directlyproportional relationship. You can checkwhether or not it is directly proportional bydividing like this:

25 ÷ 4 = 6.25

43.75 ÷ 7 = 6.25

56.25 ÷ 9 = 6.25

If you always get the sameanswer when you divide, therelationship is directlyproportional.



When are quantities are DIRECTLY PROPORTINAL?

Hours 4 6 9

Wages 28 42 72

Here is another tableshowing the wagesearned for thenumber of hoursworked.

Are the wages directly proportional to thehours worked?

28 ÷ 4 = 7

42 ÷ 6 = 772 ÷ 9 = 8

If even one result does not give

the same answer, the relationshipis NOT directly proportional.



Which of the relationships shown beloware directly proportional?

Length 3 4 10

Weight 15 21 50

Cost 2 5 9

Length 7.4 18.5 33.3

Base 2 5 9

Height 12.4 31 55.8

15 ÷ 3 = 5

21 ÷ 3 = 5.25

15 ÷ 3 = 5

7.4 ÷ 2 = 3.7

18.5 ÷ 5 = 3.7

33.3 ÷ 9 = 3.7

12.4 ÷ 2 = 6.2

31 ÷ 5 = 6.2

55.8 ÷ 9 = 6.2

NO

YES

YES



Solving Direct

ProportionalityProblems

Monday 4 January 2010



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 thistable.

Length 12 15 21 40

Cost 42 52.5 73.5 60

The next two slides will help you

understand how to do this



Length (m) 0 1 2 3 4 5

Cost (p) 0 25 50 75 100

How to find amissing number

First choose any of thenumbers on the top row.

I’ve chosen 2

Find the number that youhave 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

x 2.5

x 2.5

125



Length (m) 0 1 2 3 4

Cost (p)

0 25 50 75 100 525

Missing numbers on thetop row can be found

by a similar method

First choose any of thenumbers on the bottom

row. I’ve chosen 50

Find the number that you have tomultiply 50 by to get 525.

(525 ÷ 50 =10..5) 50 x 10.5 = 525 Multiply 2 by 10.5 to

get the missing number

x 10.5

x 10.5

21



Direct Proportionality – Test

1) The relationship between A and L is directly proportional.

Copy and complete this table:

A 1.4 1.6 1.72 3.2

L 12 18 1.60 114

2) The relationship between K and V is directly proportional.

Copy and complete this table:

K 7.2 1.18 1.6 1.9

V 0.2 0.5 0.48 0.25



Direct Proportionality

Getting the Idea

Model Plane Real Plane

When there is direct proportionality betweentwo things, it means that the relationship is the

same as the model’s lengths and the real plane’slengths.



A scale for model planes is 1/72. This means thatthe real plane’s lengths are 72 time bigger than

the model’s.Complete the numbers in this chart,

Model Plane 1 3 4 10 12 10

Real Plane 72 144 576 504 936

Model Plane 1 3 2 4 10 8 7 12 10 13

Real Plane 72 216 144 288 720 576 504 864 720 936

direct proportionality

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