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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
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Starter Questions
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Ratio Proportion
What is a ratio ?
Learning Intention
Success Criteria

1. Understand the term ratio. .

1. We are learning what a ratio is and explain
how we can sometimes simplify them.
2. Calculate and simplify basic ratios showing
appropriate working.
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Ratio Proportion
What is a ratio ?
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Simplifying a ratio ?
MNU 3-08a MNU 4-08a
Simplifying a ratio is like simplifying fractions
Fraction
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Ratio
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Ratio Proportion
Simplifying a ratio ?
MNU 3-08a MNU 4-08a
Sometimes we need to multiply to simplify
Ratio
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Ratio Proportion
Simplifying a ratio ?
MNU 3-08a MNU 4-08a
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
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8
6
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Ratio Proportion
Ratio Calculations
Learning Intention
Success Criteria

1. Remember and apply tabular method to work out
   ratios.

1 We are learning to do ratio calculations.
2. Show appropriate working.
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Ratio Proportion
Ratio Calculations
MNU 3-08a MNU 4-08a
Example The ratio of boys to girls is 45.
If there are 16 boys, how many girls are
there.
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5
x 4
x 4
16
20
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Ratio Proportion
Ratio Calculations
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Ratio Calculations
MNU 3-08a MNU 4-08a
Now try Exercise 3 Ch41 (page 160)
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Starter Questions
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8
6
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Ratio Proportion
Proportional Division
Learning Intention
Success Criteria
1. Calculate one share.
1. We are learning to calculate proportional
division by using shares.
2. Solve problems using shares.
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3. Show appropriate working.
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Ratio Proportion
Proportional Division
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Proportional Division
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Proportional Division
MNU 3-08a MNU 4-08a
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 We are learning the term proportion.
2. Solve simple proportional problems.
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Ratio Proportion
Proportion
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Proportion
MNU 3-08a MNU 4-08a
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. We are learning the term Direct Proportion.
2. Solve simple proportional problems.
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
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)
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
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)
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
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. We are learning how Direct Proportion Graph
is always a straight line.
2. Construct Direct Proportion Graphs.
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Ratio Proportion
Direct Proportion Graphs
MNU 3-08a MNU 4-08a
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 ?
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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.
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Ratio Proportion
Direct Proportion Graphs
MNU 3-08a MNU 4-08a
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
MNU 3-08a MNU 4-08a
Example Plot the points in the table below.
Are they in direct proportion?
X 1 2 3 4
y 3 6 9 12
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We plot the points (1,3) , (2,6) , (3,19) , (4,12)
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Ratio Proportion
Direct Proportion Graphs
MNU 3-08a MNU 4-08a
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Plotting the points (1,3) , (2,6) , (3,9) ,
(4,12)
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10
9
8
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Since we have a straight line passing through the
origin x and y are in direct proportion.
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5
4
3
2
1
0
1
2
3
4
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Inverse Proportion
Learning Intention
Success Criteria
1. Understand the idea of Inverse Proportion.
1. We are learning the term Inverse Proportion.
2. Solve simple inverse proportion problems.
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Ratio Proportion
Inverse Proportion
MNU 3-08a MNU 4-08a
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
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Ratio Proportion
Inverse Proportion
MNU 3-08a MNU 4-08a
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)
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Ratio Proportion
Direct Proportion
MNU 3-08a MNU 4-08a
Now try Exercise 8 Ch41 (page 168)
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Ratio Proportion
MNU 3-08a MNU 4-08a
Mixed Problems Exercise 9 Ch41 (page 168)
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