16-aug-15compiled by mr. lafferty maths dept. fractions egyptian fractions using a to find...
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
FractionsFractionsw
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Using a to Find Fractions
Using a to Finding a Percentage
Percentage Increase and Decrease
Percentages
Rates and Working out Rates
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
1. Calculate 35.7 - 19.8
2. Calculate
(a) 24.5 1000 (b) 83.4 100
(c) 45.3 1000 (d) 0.087 100
3 Find the volume of the cuboid.
4. I get paid £45 for 5 hours work. What is my hourly rate.
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10cm3cm
2cm
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Egyptian Egyptian FractionsFractions
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1.1. To understand the term To understand the term Egyptian Fraction. Egyptian Fraction.
1. To understand what an Egyptian Fraction is and how to solve problems.
2.2. Be able to solve Be able to solve Egyptian Fraction Egyptian Fraction problems .problems .
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Egyptian Fractions were invented in 3000 BC
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Egyptian Egyptian FractionsFractions
How long ago is this?
A Egyptian Fraction consists of 2 parts.
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Top number ALWAYS 1 is called the numerator
Bottom number is called the denominator
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Egyptian Fractions were invented in 3000 BCS4
Egyptian Egyptian FractionsFractions
It was a 25 year old Scotsman, Henry Rhind who brought the first evidence of Egyptian Fractions to Britain.
Rhind Mathematical Papyrus
He bought at a market in Luxor, Egypt, in 1858 papyrus scrolls that contained evidence of fractions. These are called the
Stored in the British Museum in
London
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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81
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Egyptian Egyptian FractionsFractions
51
17
23
13
501001
21
100
24
34
Write down all the Egyptian Fractions you can see below:
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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How to calculate a fraction of a quantity.
12
of 12014 of 120
Simply divide the quantity by the bottom number
2 120 4 120
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Egyptian Egyptian FractionsFractions
60 30
=12
x 120 x 12014
=
‘of’ means ‘x’
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1 of 150
2
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Egyptian Egyptian FractionsFractions
1 of 360
9
1 of 450
5
1 of 210
3
1 of 30.36
6
1 of 50.5
5
75
40
90
70
5.06
10.1
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 2.1Ch5 Page 72
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Egyptian Egyptian FractionsFractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
1. Calculate 24.3 - 12.5
2. Calculate
(a) 0.07 100 (b) 0.4 100
(c) 45.3 1000 (d) 1.087 100
3 Find the volume of the cuboid.
4. I get paid £6.50 for 40 hours work. What is my hourly rate.
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20cm
2cm5cm
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Calculator FractionsCalculator Fractions
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Calculator Keys
1 0 = 308 0 6
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Fractions of a Fractions of a quantityquantity
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1.1. To know the 2 step for To know the 2 step for finding a fraction of a finding a fraction of a quantity.quantity.
1. To show how to use a calculator to calculate a fraction of a quantity.
2.2. Be able to calculate the Be able to calculate the fraction of a quantity.fraction of a quantity.
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Calculator FractionsCalculator Fractions
119
Calculator Keys
1 2 = 7.54 . 1
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Q. Of 3500 people surveyed believed that Globe Warming was not a serious problem.
How many people believed it was not a problem.
Calculator FractionsCalculator Fractions
125
Calculator Keys
3 0 = 1405 0 2
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 2.2Ch5 Page 74
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Calculator FractionsCalculator Fractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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1.
2. What is my hourly rate if I earn £40 for 8 hours work.
3. Calculate 24.4 - 15.9
4. 690 1000
1 of 1563
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
PercentagesPercentagesw
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1.1. To understand the term To understand the term percentage.percentage.
1. To explain what the term percentage means and how it is connected to Egyptian Fractions.
2.2. Understand connection Understand connection between percentage, and between percentage, and Egyptian Fractions.Egyptian Fractions.
3.3. Find a percentage of a Find a percentage of a quantity.quantity.
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PercentagesPercentages
When a shape is divided into100 ‘bits’ each bit is called
“ 1 percent” = 1%
31 % means31
=0.31100
7 % means7
=0.07100
31 out of a 100
7 out of a 100
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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are connected with the Egyptian Fractions.
PercentagesPercentagesS4
You have 1 minute to write downthe basic percentages and there
equivalent fraction
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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PercentagesPercentagesS4
Answers
110%
10
120%
5
125%
4
1 133 %
3 3
150%
2
11%
100
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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70%60100
PercentagesPercentages
60%
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70100
Q. Change these fractions to percentages
=90%30100
=30%90100
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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30%= 50 ÷ 100 = 0.5
PercentagesPercentages
50%
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30 100 =0.3
Q. Change these decimals to percentages
0.75 =0.75 x 100 =75%
0.1 =0.1 x 100 =10%
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1=
2
PercentagesPercentages
50%
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Q. Find 25% of 180
= 2 7035
1=
425% = 4 180
45
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 3.1Ch5 Page 76
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PercentagesPercentagesS4
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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1. Find the area and perimter of a square with length 3 cm.
2. Calculate 20% of £300
3. Find the volume of the cuboid.
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1cm3cm
6cm
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Use a calculator to find Use a calculator to find a percentage of a a percentage of a quantity.quantity.
1. To understand how to calculate a percentage of a quantity using a calculator. 2.2. Show all working.Show all working.
PercentagesPercentages(Calculator)(Calculator)
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PercentagesPercentages
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Remember money is always 2
decimal places
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450 100 x 17 = £76.50
Calculator Keys
4 0 x =5 1 0 1 7
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PercentagesPercentages
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Remember money is always 2
decimal places
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70 100 x 4 = £2.80
Calculator Keys
0 x =7 1 0 4
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Q. 73% of 3600 people in a survey have brown eyes. How many people have brown eyes.
Calculator FractionsCalculator FractionsS4
Calculator Keys
6 0 x =5 1 0 7 33
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 3.2Ch5 Page 78
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PercentagesPercentagesS4
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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15
100
1. Calculate 45.6 x 7
2. Write the fraction as a percentage
3. Find 20% of 700
4. 4 jars of sweets cost £2.40.
How much for 3 jars.
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
PercentagePercentageIncrease / DecreaseIncrease / Decrease
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1.1. Understand terms increase Understand terms increase /decrease for percentages./decrease for percentages.
1. To explain some simple increases and decreases in percentages using shop prices.
2.2. Calculate simple increases Calculate simple increases / decreases in / decreases in percentages.percentages.
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Example 1Example 1
In a sale the cost of a jumper is reduced by 10%.In a sale the cost of a jumper is reduced by 10%.What is the sale price of the jumper.What is the sale price of the jumper.
35 100 10 = £3.50
PercentagePercentageIncrease / DecreaseIncrease / Decrease
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Original Price£3535 3 50 = £31.50.Sale Price =
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Example 2Example 2
The total hours of sunshine in June was 260.The total hours of sunshine in June was 260.The total for July was 5% higher than June..The total for July was 5% higher than June..What is the total hours of sunshine in July.What is the total hours of sunshine in July.
260 100 5 = 13
PercentagePercentageIncrease / DecreaseIncrease / Decrease
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260 13 = 273July Total Hours =
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 4.1
Ch5 Page 80
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Simple Simple PercentagesPercentages
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75200
1. Calculate 1200 300
2. Simplify
3. Find 10% of 65
4. Find LCM and HCF for 7 and 35
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. To know the basic To know the basic percentages.percentages.
1. To explain some more basic percentages.
2.2. Calculate basic percentage Calculate basic percentage without a calculator.without a calculator.
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RatesRates
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
£6.50 x 5 = £32.50£6.50 x 5 = £32.50Pay is = Pay is =
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Mick the mechanic hourly rate of pay is £6.50.Last week he worked 5 hours. What is his basic pay?
RatesRates
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
£10.50 x 40 = £420.00£10.50 x 40 = £420.00Pay is = Pay is =
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Jim is a joiner his hourly rate of pay is £10.50.He works 40 hours a week. What is his basic pay?
RatesRates
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
300 300 ÷÷ 6 = 50 words 6 = 50 words
Words per minuteWords per minute
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Example 3 :
Wendy can type 300 words in 6 minutes.How many words does she type per minute.
RatesRates
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£2.10 ÷ 6 = £0.35£2.10 ÷ 6 = £0.351 bag = 1 bag =
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Example 4 :
Six bags of crisps were bought for £2.10.How much for 1 bag of crisps.
RatesRates
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 5.1 & 5.2
Ch5 Page 82
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