Post on 15-Jan-2016
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Simplifying Ratios
Ratio Calculations
Ratio & Ratio & ProportionProportion
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Direct Proportion
Graph of Direct Proportion
Inverse Proportion
Proportional Division
Proportion
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2. Calculate 20% of 220
(a) 123 (b) 202 (c) 0.09
1. 3x + 5 = 17
3. How many significant numbers
4. Car depreciates by 20% in its first year. I f it was bought new for £10 000. How much is it worth now.
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1.1. Understand the term ratio. Understand the term ratio. ..
1. We are learning what a ratio is and explain how we can sometimes simplify them.
Ratio & Ratio & ProportionProportion
2.2. Calculate and simplify Calculate and simplify basic ratios showing basic ratios showing appropriate working.appropriate working.
What is a ratio ?
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Ratios can be used to compare different quantitiesRatios can be used to compare different quantities
What is a ratio ?
Example : There are 2 triangles and 3 rectangles.
The ratio of triangles to rectangles is said to be 2 : 3
Note: The ratio of rectangles to triangles is said to be 3 : 2
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Simplifying a ratio is like simplifying fractionsSimplifying a ratio is like simplifying fractions
Simplifying a ratio ?
Fraction :÷2
÷2
6 6 3= =
8 8 4
Ratio : ÷2 ÷26 : 8 = 6 : 8 = 3 : 4
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Sometimes we need to multiply to simplifySometimes we need to multiply to simplify
Simplifying a ratio ?
Ratio :1 : 5 =
31
×3 : 5×3 = 3
1 : 15
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
When working with ratios, When working with ratios, the two units the two units MUSTMUST be the same be the same
Simplifying a ratio ?
Ratio :1 hour : 40 minutes
4
= 15 minutes : 40 minutes
= 3 minutes : 8 minutes
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 1&2
Ch41 (page 158)
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Ratio & Ratio & ProportionProportionSimplifying a ratio ?
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2. Calculate the area of the shape.
3 2+4 3
(a) 0.13 (b) 0.02 (c) 1.09
1. 3x + 5 = 17
3. How many significant numbers
4.
9
6
8
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1.1. Remember and apply Remember and apply tabular method to work tabular method to work out ratios.out ratios.
1 We are learning to do ratio calculations.
Ratio & Ratio & ProportionProportion
2.2. Show appropriate Show appropriate working.working.
Ratio Calculations
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportionRatio Calculations
Example : The ratio of boys to girls is 4:5. If there are 16 boys, how many girls are there.
boys girls
4 5
16 20x 4 x 4
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportionRatio Calculations
Example : The ratio of cars to buses is 3:7. If there are 49 buses, how many cars are there.
cars buses
3 7
21 49x 7 x 7
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch41 (page 160)
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Ratio & Ratio & ProportionProportionRatio CalculationsMNU 3-08a
MNU 4-08a
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2. Calculate the area of the shape.
5 1+2 4
(a) 0.853 (b) 0.356 (c) 1.995
1. 6x + 5 = 59
3. Round to 2 decimal places.
4.
9
6
8
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning to calculate proportional division by using shares.
1. Calculate one share.
Ratio & Ratio & ProportionProportionProportional Division
2. Solve problems using shares.
3. Show appropriate working.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Example : Bill and Ben share a raffle win of £400 in the ratio 3:5. How much does each get ?
Proportional Division
Step 1 : Since the ratio is 3:5, there are :
3+5 = 8 shares
Step 2 : Each share is worth : 50
8 400
Step 3 : Bill gets 3 x 50 = £150
Ben gets 5 x 50 = £250Check !150 + 250 = 400
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Example : Ryan and Ross share 24 cakes in the ratio3:1. How many cakes does each get ?
Proportional Division
Step 1 : Since the ratio is 3:1, there are :
3+1 = 4 shares
Step 2 : Each share is worth : 6
4 24
Step 3 : Ryan gets 3 x 6 = 18
Ross gets 1 x 6 = 6Check !18 + 6
= 24
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 4Ch41 (page 161)
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Ratio & Ratio & ProportionProportionProportional DivisionMNU 3-08a
MNU 4-08a
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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1. Simplfy the ratio 13 : 52
Calculate 2.5
3. I got $650 for £100. How much would I get for £2.
4. Put in order, smallest first.
0.25, 0.19, 0.01, 0.026
5. Find the value
% of 4002.
of x 7x +2.5 = 20
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1 We are learning the term proportion.
1. Understand the idea of proportion.
Ratio & Ratio & ProportionProportion
2. Solve simple proportional problems.
Proportion
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Example : The cost of 5 cakes is £4.00. Find the cost of one.
Cost of one is simply :
If you know the total cost of several items, you caneasily find the cost per item.
0.805 4.00 = 80p
ProportionMNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 5Ch41 (page 163)
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Ratio & Ratio & ProportionProportion
ProportionMNU 3-08aMNU 4-08a
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2.
4. Calculate 4 5×5 8
1. Simplfy the ratio 85 : 25
Calculate 6.5% of 300
3. Find the mean, median and mode for
25, 20, 55, 20
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning the term Direct Proportion.
1. Understand the idea of Direct Proportion.
Ratio & Ratio & ProportionProportion
2. Solve simple proportional problems.
Direct Proportion
Example : The cost of 6 cakes is £4.20. Find the cost of 5 cakes.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
“ .. When you double the number of cakes you double the cost.”
Cakes Cost
Two quantities, (for example, number of cakes and totalcost) are said to be in DIRECT PROPORTION, if :
Direct Proportion
6 4.20 1 4.20 ÷ 6 = 0.70 5 0.70 x 5 = £3.50
Easier methodCakes Pence
6 420 5
Are we expecting more or
less
5
6420
(less)
350 £3.50
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
£ $
Direct Proportion
Example : On holiday I exchanged £30 for $45.How many $ will I get for £50.
30 45 1 45 ÷ 30 = 1.5 50 1.5 x 50 = $75
What name do we give to
this valueExchange
rateEasier method£ $30 45
50
Are we expecting more or
less
50
3045
(more)
$75
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Pencils Cost
Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1.
Direct Proportion
Example : 300 pencils cost £6. How much will 200 cost.
300 £6.00 100 £6.00 ÷ 3 = £2.00200 £2.00 x 2 = £4.00
Easier methodPencil Pence300 600
200
Are we expecting more or
less
200
300600
(less)
400 £4
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 6Ch41 (page 164)
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Ratio & Ratio & ProportionProportion
Direct ProportionMNU 3-08aMNU 4-08a
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2.
4. Calculate 31 1 × 12 2
1. Simplfy the ratio 95 : 35
Calculate 2.5% of 500
3. Find the mean, median and mode for
5, 2, 5, 8
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning how Direct Proportion Graph is always a straight line.
1. Understand that Direct Proportion Graph is a straight line.
Ratio & Ratio & ProportionProportion
2. Construct Direct Proportion Graphs.
Direct Proportion Graphs
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
The table below shows the cost of packets of “Biscuits”.
Direct Proportion Graphs
No. of Pkts 1 2 3 4 5 6
Cost (p) 20 40 60 80 100 120
We can construct a graph to represent this data.
What type of graph do we expect ?
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Direct Proportion
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6
No. of Packets
Cos
t (p
)
Direct Proportion GraphsNotice that the points lie on a straight line
passing through the origin
This is true for any two quantities
which are in Direct Proportion.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Direct Proportion Graphs
KeyPoint
Two quantities which are in DIRECT PROPORTION
always lie on a straight linepassing through the origin.
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Example : Plot the points in the table below. Are they in direct proportion?
Direct Proportion Graphs
We plot the points (1,3) , (2,6) , (3,19) , (4,12)
XX 11 22 33 44
yy 33 66 99 1212
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
1
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Ratio & Ratio & ProportionProportion
Plotting the points
(1,3) , (2,6) , (3,9) , (4,12)
Direct Proportion Graphs
0 1 2 3 4
101112
23456789
Since we have a straight linepassing through the origin
x and y are in direct proportion.
x
yMNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 7Ch41 (page 166)
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Ratio & Ratio & ProportionProportion
Direct ProportionMNU 3-08aMNU 4-08a
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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2.
4. Calculate 1 1 2 4
1. Simplfy the ratio 95 : 35
Calculate 0.5 + 1.45 + 0.06
3. I s there a correlation between the two quanities. I f so describe it.
xx
x
x
xx
x
x
y
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. We are learning the term Inverse Proportion.
1. Understand the idea of Inverse Proportion.
Ratio & Ratio & ProportionProportion
2. Solve simple inverse proportion problems.
Inverse Proportion
Example : If it takes 3 workers 8 hours to build a wall.How long will it take 4 men.
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Ratio & Ratio & ProportionProportion
Men Hours
Inverse proportion is when one quantity doublesand the other halves. The two quantities are said
to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other.
3 8 1 3 x 8 = 24 hours
4 24 ÷ 4 = 6 hours
Inverse Proportion
Easier methodWorkers Hours
3 8 4
Are we expecting more or
less
3
48
(less)
6 hours
MNU 3-08aMNU 4-08a
8 120 ÷ 8 = 15 months
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Ratio & Ratio & ProportionProportion
Men Months
Example : It takes 10 workers 12 months to build a house. How long should it take 8 men.
10 12 1 12 x 10 = 120
Inverse Proportion
Easier methodWorkers months
10 12 8
Are we expecting more or
less
10
812
(more)
15 months
MNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Exercise 8Ch41 (page 168)
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Ratio & Ratio & ProportionProportion
Direct ProportionMNU 3-08aMNU 4-08a
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Mixed ProblemsExercise 9
Ch41 (page 168)
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Ratio & Ratio & ProportionProportion
MNU 3-08aMNU 4-08a