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Ratio Proportion

Simplifying Ratios

Ratio Calculations

Proportional Division

Proportion

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Direct Proportion

Graph of Direct Proportion

Inverse Proportion

Starter Questions

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Ratio Proportion

What is a ratio ?

Learning Intention

Success Criteria

- Understand the term ratio. .

1. To understand what a ratio is and explain

how we can sometimes simplify them.

2. Calculate and simplify basic ratios.

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Ratio Proportion

What is a ratio ?

Ratios can be used to compare different quantities

Example There are 2 triangles and 3 rectangles.

The ratio of triangles to rectangles is said to

be 2 3

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Note The ratio of rectangles to triangles is

said to be 3 2

Ratio Proportion

Simplifying a ratio ?

Simplifying a ratio is like simplifying fractions

Fraction

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Ratio

Ratio Proportion

Simplifying a ratio ?

Sometimes we need to multiply to simplify

Ratio

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Ratio Proportion

Simplifying a ratio ?

When working with ratios, the two units MUST be

the same

Ratio

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Ratio Proportion

Simplifying a ratio ?

Now try Exercise 12 Ch41 (page 158)

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Starter Questions

9

8

6

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Ratio Proportion

Ratio Calculations

Learning Intention

Success Criteria

- Use tabulating method to work out ratios.

1. To show how to do ratio calculations.

2. Show appropriate working.

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Ratio Proportion

Ratio Calculations

Example The ratio of boys to girls is 45.

If there are 16 boys, how many girls are

there.

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4

5

x 4

x 4

16

20

Ratio Proportion

Ratio Calculations

Example The ratio of cars to buses is 37.

If there are 49 buses, how many cars are

there.

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3

7

x 7

x 7

21

49

Ratio Proportion

Ratio Calculations

Now try Exercise 3 Ch41 (page 160)

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Starter Questions

9

8

6

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Ratio Proportion

Proportional Division

Learning Intention

Success Criteria

1. Work out equal number of shares for a ratio.

1. Explain how to work out proportional

division by using shares.

2. Solve problems using shares.

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3. Show appropriate working.

Ratio Proportion

Proportional Division

Example Bill and Ben share a raffle win of

400 in the ratio 35. How much does each get ?

Step 1 Since the ratio is 35, there are

35 8 shares

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Step 2 Each share is worth

Check ! 150 250 400

Step 3 Bill gets 3 x 50 150

Ben gets 5 x 50 250

Ratio Proportion

Proportional Division

Example Ryan and Ross share 24 cakes in the

ratio 31. How many cakes does each get ?

Step 1 Since the ratio is 31, there are

31 4 shares

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Step 2 Each share is worth

Check ! 18 6 24

Step 3 Ryan gets 3 x 6 18

Ross gets 1 x 6 6

Ratio Proportion

Proportional Division

Now try Exercise 4 Ch41 (page 161)

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Starter Questions

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Ratio Proportion

Proportion

Learning Intention

Success Criteria

1. Understand the idea of proportion.

1. To explain the term proportion.

2. Solve simple proportional problems.

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Ratio Proportion

Proportion

If you know the total cost of several items, you

can easily find the cost per item.

Example The cost of 5 cakes is 4.00. Find

the cost of one.

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Cost of one is simply

Ratio Proportion

Proportion

Now try Exercise 5 Ch41 (page 163)

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Starter Questions

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Ratio Proportion

Direct Proportion

Learning Intention

Success Criteria

1. Understand the idea of Direct Proportion.

1. To explain the term Direct Proportion.

2. Solve simple proportional problems.

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Ratio Proportion

Direct Proportion

Two quantities, (for example, number of cakes and

total cost) are said to be in DIRECT PROPORTION,

if

Are we expecting more or less

.. When you double the number of cakes you

double the cost.

Easier method Cakes Pence 6 ? 420 5

Example The cost of 6 cakes is 4.20. Find

the cost of 5 cakes.

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Cakes Cost

6 ? 4.20

(less)

1 ? 4.20 6 0.70

5 ? 0.70 x 5 3.50

Ratio Proportion

Direct Proportion

Example On holiday I exchanged 30 for

45. How many will I get for 50.

Are we expecting more or less

What name do we give to this value

Exchange rate

Easier method 30 ? 45 50

30 ? 45

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1 ? 45 30 1.5

50 ? 1.5 x 50 75

(more)

Ratio Proportion

Direct Proportion

Sometimes it is easier to find the cost of 10,100

or 1000 items rather than 1.

Are we expecting more or less

Example 300 pencils cost 6. How much will 200

cost.

Easier method Pencil Pence 300 ? 600

200

Pencils Cost

300 ? 6.00

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100 ? 6.00 3 2.00

200 ? 2.00 x 2 4.00

(less)

Ratio Proportion

Direct Proportion

Now try Exercise 6 Ch41 (page 164)

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Starter Questions

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Ratio Proportion

Direct Proportion Graphs

Learning Intention

Success Criteria

1. Understand that Direct Proportion Graph is a

straight line.

1. To explain how Direct Proportion Graph is

always a straight line.

2. Construct Direct Proportion Graphs.

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Ratio Proportion

Direct Proportion Graphs

The table below shows the cost of packets of

Biscuits.

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We can construct a graph to represent this data.

What type of graph do we expect ?

Notice that the points lie on a straight line

passing through the origin

Direct Proportion Graphs

This is true for any two quantities which are in

Direct Proportion.

Ratio Proportion

Direct Proportion Graphs

KeyPoint

Two quantities which are in DIRECT

PROPORTION always lie on a straight line passing

through the origin.

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Ratio Proportion

Direct Proportion Graphs

Example Plot the points in the table below.

Are they in direct proportion?

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We plot the points (1,3) , (2,6) , (3,19) , (4,12)

Ratio Proportion

Direct Proportion Graphs

12

Plotting the points (1,3) , (2,6) , (3,9) ,

(4,12)

11

10

9

8

7

Since we have a straight line passing through the

origin x and y are in direct proportion.

6

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5

4

3

2

1

0

1

2

3

4

Ratio Proportion

Direct Proportion

Now try Exercise 7 Ch41 (page 166)

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Starter Questions

y

x

x

x

x

x

x

x

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x

Ratio Proportion

Inverse Proportion

Learning Intention

Success Criteria

1. Understand the idea of Inverse Proportion.

1. To explain the term Inverse Proportion.

2. Solve simple inverse proportion problems.

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Ratio Proportion

Inverse Proportion

Inverse proportion is when one quantity

doubles and the other halves. The two quantities

are said to be INVERSELY PROPORTIONAL or

(INDIRECTLY PROPORTIONAL) to each other.

Are we expecting more or less

Easier method Workers Hours 3 ? 8 4

Example If it takes 3 workers 8 hours to build

a wall. How long will it take 4 men.

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Men Hours

3 ? 8

(less)

1 ? 3 x 8 24 hours

4 ? 24 4 6 hours

Ratio Proportion

Inverse Proportion

Example It takes 10 workers 12 months to build

a house. How long should it take 8 men.

Are we expecting more or less

Men Months

Easier method Workers months 10 ? 12

8

10 ? 12

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1 ? 12 x 10 120

8 ? 120 8 15 months

(more)

Ratio Proportion

Direct Proportion

Now try Exercise 8 Ch41 (page 168)

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Ratio Proportion

Mixed Problems Exercise 9 Ch41 (page 168)

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