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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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.


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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 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]

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44

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

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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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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


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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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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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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

S4


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.


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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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“ .. 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


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£ $

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

S4

Easier method£ $30 45

50


less

50

3045

(more)

$75


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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


less

200

300600

(less)

400 £4


Now try Ex 2Ch2 (page 28)

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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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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


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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 ?

S4


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.


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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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Example : Plot the points in the table below. Are they in direct proportion?


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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1

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Plotting the points

(1,3) , (2,6) , (3,9) , (4,12)


0 1 2 3 4

101112

23456789

Since we have a straight linepassing through the origin

x and y are in direct proportion.

x

yS4


Now try TJ Extension booklet

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ProportionProportionDirect ProportionS4



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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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1. To explain the term Inverse Proportion.

1. Understand the idea of Inverse Proportion.


2. Solve simple inverse proportion problems.

Inverse ProportionS4


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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


Easier methodWorkers Hours

3 8 4


less

3

48

(less)

6 hours

1 12 x 10 = 120

8 120 ÷ 8 = 15 months


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Men Months

Example : It takes 10 men 12 months to build a house.How long should it take 8 men.

10 12


Easier methodWorkers months

10 12 8


less

10

812

(more)

15 months


Now try TJ ExtensionBooklet

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ProportionProportionInverse ProportionS4

Www.mathsrevision.com Created by Mr. Lafferty @ Rate and Proportion Rates and Finding Rates...

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