GCSE Maths(Higher Tier)

Inverse

Proportion

B

1

Direct proportion what does it mean?

£

10 20 30 40 50 60 70 80 90 100

Percentage

30 60 90 120 150 180 210 240 270 300

Both of the lines are travelling in the same direction. As the percentage values goes up so does the amount (£) go up.

Direct proportion what does it mean?

£

10 20 30 40 50 60 70 80 90 100

Percentage

30 60 90 120 150 180 210 240 270 300

This type of relationship when both lines are going in the same directions are said to be in DIRECT PROPORTION to each other. The sign for direct proportion is :

What type of proportion is this?What is our strategy to work it out?

We want to find the equivalent measurement in miles for 3 km.

KmMiles

8

5

3

?

Strategy

?

385

358 ?

Lines to extract information

Answer

There are 4.8 kilometres in 3 miles

Calculation

Lines to extract informationQuestion

How many kilometres are there in 3 miles?

Km

Miles8

53

?

The equivalent fractions are

84

358

.?

?

358 ?

Do you expect the time to be more, less or the same?

Why?

Time in mins.

mph

90

60

?

70

More Speed Less Speed

More TimeLess Time

They still have a relationship but this relationship is described as inverse proportion

Time in mins.

mph

90

60

?

70

More Speed Less Speed

More TimeLess Time

It takes one person 8 days to complete a job. How many days will it take 2 people? 4 people?

Why do you know this?

Time in days.

Number of people

8

1

2

4

More people Less people

More TimeLess Time

2

4

What else can you notice?

Time in days.

Number of people

8

1

2

4

More people Less people

More TimeLess Time

2

4

4 x 2 = 8 2 x 4 = 8 1 x 8 = 8

Equal products

Percentage

£

10 20 30 40 50 60 70 80 90 100

30 60 90 120 150 180 210 240 270 300

3

1300

100

3

1240

80

3

1180

60

3100

300

380

240

360

180

Direct proportion relationships have equivalent fractions.

Direct proportion relationships have equivalent fractions

We used this to solve questions relating to direct proportion.

We know that inverse proportion relationships have the same product, we can use this to solve questions that have

arrows going in different directions.

Time in days.

Number of people

8

1

2

4

More people Less people

More TimeLess Time

2

4

4 x 2 = 8 2 x 4 = 8 1 x 8 = 8

Equal products

Start by putting the sums equal to each other.Then divide both sides by what ever is multiplying

the ?

Time in mins.

mph

90

60

?

70

More Speed Less Speed

More TimeLess Time

609070? 7770

6090?

As always don’t forget to put the answer in context of the question.

Time in mins.

mph

90

60

?

70

609070? 7770

6090?

It takes approximately 77 minutes to get to my destination if I use the faster train.

Strategy

?

385

358 ?

Lines to extract information

Answer

It takes approximately 77 minutes to get to my destination if I use the faster train.

Calculation – to get method marks

Lines to extract informationQuestion – read it carefullyThere is a fast and a slow train to

get to my destination. One travels at a speed .of 60mph and takes 90 mins, the other train travels at 70mph. How long will my journey take if I choose the faster train.

mph

Time in min

60

90?

70

The equivalent products are

77?70

6090?

609070?

When you do some questions. Remember the strategy is:

?

385

358 ?

Lines to extract information

Answer

Put answer in context!

Calculation – to get method marks

Lines to extract informationQuestion – read it carefully

mph

Time in min A?The equivalent products are

DC

BA

?

?

BAC ?

C B