S4_Foundation_Fractions_MIA

# S4_Foundation_Fractions_MIA - Fractions Egyptian Fractions...

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Unformatted text preview: Fractions Egyptian Fractions www.mathsrevision.com Using a Percentages Using a to Find Fractions to Finding a Percentage Percentage Increase and Decrease Rates and Working out Rates 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions 1. Calculat e 35. 7 - 19. 8 Calculat e (a) (c) 3 4. 24. 5 45. 3 1000 1000 (b) 83. 4 (d) 0. 087 100 100 www.mathsrevision.com 2. Find t he volume of t he cuboid. I get paid 45 f or 5 hours work. W hat is my hourly rat e. Compiled by Mr. Lafferty Maths Dept. 2cm 10cm 3cm 13 Feb 2012 Egyptian Fractions S4 Learning Intention Success Criteria 1. To understand the term Egyptian Fraction. 2. Be able to solve Egyptian Fraction problems . www.mathsrevision.com 1. To understand what an Egyptian Fraction is and how to solve problems. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Egyptian Fractions S4 How long ago is this? Egyptian Fractions were invented in 3000 BC www.mathsrevision.com A Egyptian Fraction consists of 2 parts. 1 5 Top number ALWAYS 1 is called the numerator Bottom number is called the denominator 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Egyptian Fractions S4 Stored in the British Museum in London Egyptian Fractions were invented in 3000 BC www.mathsrevision.com It was a 25 year old Scotsman, Henry Rhind who brought the first evidence of Egyptian Fractions to Britain. He bought at a market in Luxor, Egypt, in 1858 papyrus scrolls that contained evidence of fractions. These are called the Rhind Mathematical Papyrus 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Egyptian Fractions S4 Write down all the Egyptian Fractions you can see below: www.mathsrevision.com 1 3 2 4 8 1 1 7 2 3 5 1 1 2 50 10 0 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 1 10 0 3 4 S4 `of' means `x' Egyptian Fractions 1 4 1 = 4 How to calculate a fraction of a quantity. www.mathsrevision.com 1 2 1 = 2 of 120 x 120 2 12 0 60 of 120 x 120 4 12 0 30 Simply divide the quantity by the bottom number 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Egyptian Fractions S4 Try these www.mathsrevision.com 1 o f 15 0 2 75 40 90 1 o f 2 10 3 70 5.06 10.1 1 o f 3 6 0 9 1 o f 4 5 0 5 13 Feb 2012 1 o f 3 0 .3 6 6 1 o f 5 0 .5 5 Compiled by Mr. Lafferty Maths Dept. Egyptian Fractions S4 www.mathsrevision.com Now try Ex 2.1 Ch5 Page 72 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions 1. Calculat e 24. 3 - 12. 5 Calculat e (a) (c) 3 4. 0. 07 45. 3 100 1000 (b) 0. 4 100 100 www.mathsrevision.com 2. (d) 1. 087 20cm Find t he volume of t he cuboid. I get paid 6. 50 f or 40 hours work. W hat is my hourly rat e. Compiled by Mr. Lafferty Maths Dept. 5cm 2cm 13 Feb 2012 Calculator Fractions S4 Q. www.mathsrevision.com 1 Find of 1800 60 Calculator Keys 1 8 0 0 6 = 30 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions of a quantity S4 Learning Intention Success Criteria 1. To know the 2 step for finding a fraction of a quantity. 2. Be able to calculate the fraction of a quantity. www.mathsrevision.com 1. To show how to use a calculator to calculate a fraction of a quantity. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Calculator Fractions S4 Q. www.mathsrevision.com 1 Find of 142.50 19 Calculator Keys 1 4 2 . 5 1 = 7.5 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Calculator Fractions S4 1 Q. Of 3500 people surveyed believed that Globe Warming 25 was not a serious problem. www.mathsrevision.com How many people believed it was not a problem. Calculator Keys 3 5 0 0 2 = 140 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Calculator Fractions S4 www.mathsrevision.com Now try Ex 2.2 Ch5 Page 74 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Starter Questions 1. www.mathsrevision.com 1 of 156 3 W hat is my hourly rat e if I earn 40 f or 8 hours work. Calculat e 24. 4 - 15. 9 690 13 Feb 2012 2. 3. 4. 1000 Compiled by Mr. Lafferty Maths Dept. Percentages S4 Learning Intention Success Criteria 1. To understand the term percentage. www.mathsrevision.com 1. To explain what the term percentage means and how it is connected to Egyptian Fractions. 2. Understand connection between percentage, and Egyptian Fractions. 3. Find a percentage of a quantity. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 31 out of a 100 Percentages S4 www.mathsrevision.com When a shape is divided into 100 `bits' each bit is called " 1 percent" = 1% 31 % means 7 % means 31 = 0 .3 1 10 0 7 = 0 .0 7 10 0 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 7 out of a 100 Percentages S4 www.mathsrevision.com The basic Percentages (%) are connected with the Egyptian Fractions. You have 1 minute to write down the basic percentages and there equivalent fraction 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages S4 www.mathsrevision.com 1 10% = 10 1 1% = 100 1 50% = 2 Answers 1 20% = 5 1 25% = 4 Compiled by Mr. Lafferty Maths Dept. 1 1 33 % = 3 3 13 Feb 2012 Percentages S4 Q. Change these percentages to fractions out of a 100 www.mathsrevision.com 60 60% = 10 0 30 =30% 10 0 13 Feb 2012 70 70% = 10 0 90 =90% 10 0 Compiled by Mr. Lafferty Maths Dept. Q. Change these fractions to percentages Percentages S4 Q. Change these percentages to decimals. www.mathsrevision.com 5 0 % = 5 0 10 0 = 0 .5 30% =30 10 0 = 0 .3 Q. Change these decimals to percentages 0 .7 5 = 0 .7 5 x 10 0 = 7 5 % 0 .1 13 Feb 2012 = 0 .1 x 10 0 = 10 % Compiled by Mr. Lafferty Maths Dept. Percentages S4 Q. Find 50% of 70 www.mathsrevision.com 1 5 0 % = 2 Q. Find 25% of 180 = 2 7 0 35 1 2 5 % = 4 13 Feb 2012 = 4 18 0 45 Compiled by Mr. Lafferty Maths Dept. Percentages S4 www.mathsrevision.com Now try Ex 3.1 Ch5 Page 76 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 www.mathsrevision.com 1. Find t he area and perimt er of a square wit h lengt h 3 cm. Calculat e 20% of 300 Find t he volume of t he cuboid. 3cm 6cm 1cm 2. 3. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages S4 (Calculator) Learning Intention Success Criteria 1. Use a calculator to find a percentage of a quantity. 2. Show all working. www.mathsrevision.com 1. To understand how to calculate a percentage of a quantity using a calculator. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages S4 Remember money is always 2 decimal places Q. www.mathsrevision.com Find 17% of 450 450 4 5 0 10 0 x 17 Calculator Keys 1 0 = 76.50 x 1 7 = 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages S4 Remember money is always 2 decimal places Q. www.mathsrevision.com Find 4% of 70 70 7 0 10 0 x 4 Calculator Keys 1 0 = 2.80 x 4 = 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Calculator Fractions S4 Q. www.mathsrevision.com 73% of 3600 people in a survey have How many people have brown eyes. brown eyes. Calculator Keys 3 6 5 0 1 0 x 7 3 = 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages S4 www.mathsrevision.com Now try Ex 3.2 Ch5 Page 78 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 1. www.mathsrevision.com Calculat e 45. 6 x 7 2. 3. 4. 13 Feb 2012 15 W rit e t he f ract ion as a percent age 100 Find 20% of 700 4 j ars of sweet s cost 2. 40. How much f or 3 j ars. Compiled by Mr. Lafferty Maths Dept. S4 Percentage Increase / Decrease Learning Intention Success Criteria 1. Understand terms increase /decrease for percentages. 2. Calculate simple increases / decreases in percentages. www.mathsrevision.com 1. To explain some simple increases and decreases in percentages using shop prices. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. S4 Percentage Increase / Decrease Example 1 www.mathsrevision.com In a sale the cost of a jumper is reduced by 10%. What is the sale price of the jumper. 35 100 Sale Price = 10 = 3.50 Original Price 35 35 - 3.50 = 31.50 Created by Mr. Lafferty Maths Dept S4 Percentage Increase / Decrease Example 2 www.mathsrevision.com The total hours of sunshine in June was 260. The total for July was 5% higher than June.. What is the total hours of sunshine in July. 260 100 July Total Hours = 5 = 13 260 + 13 = 273 Created by Mr. Lafferty Maths Dept Simple Percentages S4 www.mathsrevision.com Now try Exercise 4.1 Ch5 Page 80 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions S4 1. www.mathsrevision.com Calculat e 1200 Simplif y 300 2. 3. 4. 13 Feb 2012 75 200 Find 10% of 65 Find LCM and HCF f or 7 and 35 Compiled by Mr. Lafferty Maths Dept. Rates S4 Learning Intention Success Criteria 1. To know the basic percentages. www.mathsrevision.com 1. To explain some more basic percentages. 2. Calculate basic percentage without a calculator. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Rates Example 1 : www.mathsrevision.com Mick the mechanic hourly rate of pay is 6.50. Last week he worked 5 hours. What is his basic pay? Pay is = 6.50 x 5 = 32.50 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Rates Example 2 : www.mathsrevision.com Jim is a joiner his hourly rate of pay is 10.50. He works 40 hours a week. What is his basic pay? Pay is = 10.50 x 40 = 420.00 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Rates Example 3 : www.mathsrevision.com Wendy can type 300 words in 6 minutes. How many words does she type per minute. Words per minute 300 6 = 50 words 13 Feb 2012 Created by Mr. Lafferty Maths Dept. Rates Example 4 : www.mathsrevision.com Six bags of crisps were bought for 2.10. How much for 1 bag of crisps. 1 bag = 2.10 6 = 0.35 13 Feb 2012 Created by Mr. Lafferty Maths Dept. S4 Rates Now try Ex 5.1 & 5.2 Ch5 Page 82 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. ...
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