Www.mathsrevision.com Created by Mr. Lafferty @ Rate and Proportion Rates and Finding Rates...
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Transcript of Www.mathsrevision.com Created by Mr. Lafferty @ Rate and Proportion Rates and Finding Rates...
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Rate and Rate and ProportionProportion
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Rates and Finding Rates
Friday, April 21, 2023Friday, April 21, 2023 11
Direct Proportion
S4
Direct Proportion graphs
Inverse Proportion
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Starter QuestionsStarter Questionsw
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72 of 81
4.
pay. weekly total my is What hour. per £8 is
pay of rate my and week a hours 20 work I 3.
2.35 (b) 1.24 (a)
place decimal 1 to Round 2.
140 of 5% Find 1.
Friday, April 21, 2023Friday, April 21, 2023 22
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Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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1.1. To understand the term To understand the term ‘rate’ and calculate it.‘rate’ and calculate it.
1. To explain the term ‘rate’ is and how to find the rate.
Rates
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Friday, April 21, 2023Friday, April 21, 2023 33
Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Per means for each. A phrase that contains the word
‘per’ is called a RATE.
Example : Sean walks at 5 km per hour (km/hr)
This means that if Sean walked at this speed forone hour he would travel 5km.
RatesRatesS4
www.mathsrevision.comwww.mathsrevision.com
We are often interested in rates
•Miles per gallon•Goals per game•£’s spent per day•Calories per day•Words per minute
Rates
Why are we interested in rates?
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Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Example : Sean walks at 5 km per hour (km/hr)
How far would he walk in :
(a) 4 hours (b) Half an hour
(a) 4 x 5 =
(b) 5 x 0.5 =
20km
2.5 km
RatesRatesS4
Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Finding the Rate
Example : For 5 hours’ work Jennifer is paid £30.Calculate her rate of pay per hour.
Answer :
5 hours £30
1 hour £30 ÷ 5 =£6
This means that Jennifer is paid a ‘rate’ of£6 per hour
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Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Finding the Rate
Example : 3 litres of paint covers a fence area of 36 m2 How much will 1 litre cover.
Answer :
3 litres 361 litre 36 ÷ 3 =12m2
This means that 12m2 requires 1 litre of paint.
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Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
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Finding the Rate
Example : Nicola gets paid £48 000 pounds a year. What is her monthly rate of pay.
Answer :
12 months £48 0001 month £48 000 ÷ 12 =£4 000
This means Nicola gets paid £4 000 per month
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Friday, April 21, 2023Friday, April 21, 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]
Now try Ex 1
Ch 2 (page 26)
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1010
Finding the Rate
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1. Calculate 3 + 5 4
Calculate 6% of 300
3. Find the mean, median and mode for
25, 20, 55, 20
2.
4. Calculate 4 55 8
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain the term Direct Proportion.
1. Understand the idea of Direct Proportion.
Direct Direct ProportionProportion
2. Solve simple proportional problems.
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
“ .. When you double the number of cakes you double the cost.”
Cakes Cost
Two quantities, (for example, number of cakes and total cost) are said to be in DIRECT PROPORTION, if :
Example : The cost of 6 cakes is £4.20. find the cost of 5 cakes.
6 4.20 1 4.20 ÷ 6 = 0.70 5 0.70 x 5 = £3.50
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Easier methodCakes Pence
6 420 5
Are we expecting more or
less
5
6420
(less)
350 £3.50
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
£ $
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 valueExchang
e rate
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Easier method£ $30 45
50
Are we expecting more or
less
50
3045
(more)
$75
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Direct Direct ProportionProportion
Pencils Cost
Sometimes it is easier to find the cost of 10,100 or 1000 items rather than 1.
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
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Easier methodPencil Pence300 600
200
Are we expecting more or
less
200
300600
(less)
400 £4
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try Ex 2Ch2 (page 28)
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Direct Direct ProportionProportion
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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
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain how Direct Proportion Graph is always a straight line.
1. Understand that Direct Proportion Graph is a straight line.
ProportionProportion
2. Construct Direct Proportion Graphs.
Direct Proportion GraphsS4
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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 ?
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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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ProportionProportionDirect Proportion Graphs
KeyPoint
Two quantities which are in DIRECT PROPORTION
always lie on a straight linepassing through the origin.
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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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
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
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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
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ Extension booklet
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ProportionProportionDirect ProportionS4
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Starter QuestionsStarter Questionsw
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1. Simplfy the ratio 95 : 35
Calculate 0.5 + 1.45 + 0.062.
4. Calculate 1 1 2 6
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21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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1. To explain the term Inverse Proportion.
1. Understand the idea of Inverse Proportion.
ProportionProportion
2. Solve simple inverse proportion problems.
Inverse ProportionS4
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
Men Hours
Inverse proportion is when one quantity increasesand the other decreases. The two quantities are said
to be INVERSELY PROPORTIONAL or (INDIRECTLY PROPORTIONAL) to each other.
Example : If it takes 3 men 8 hours to build a wall.How long will it take 4 men. (Less time !!)
3 8 1 3 x 8 = 24 hours
4 24 ÷ 4 = 6 hours
Inverse ProportionS4
Easier methodWorkers Hours
3 8 4
Are we expecting more or
less
3
48
(less)
6 hours
1 12 x 10 = 120
8 120 ÷ 8 = 15 months
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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ProportionProportion
Men Months
Example : It takes 10 men 12 months to build a house.How long should it take 8 men.
10 12
Inverse ProportionS4
Easier methodWorkers months
10 12 8
Are we expecting more or
less
10
812
(more)
15 months
21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ ExtensionBooklet
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ProportionProportionInverse ProportionS4