GCSE: Fractions & Percentages Dr J Frost Last modified: 24 th August 2013

Fractions Recap ? ? ? ? ? ?

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Multiplication/Division of Decimals ? ? ? ? ? ?

Exercises Edexcel GCSE Mathematics Textbook Page 93 – Exercise 7A Q6, 10

Manipulation of decimals What would be the effect on the result of multiplying the numerator by 10? What would be the effect on the result of multiplying the denominator by 10?

Manipulation of decimals 1 2 ? ?

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Exercises Edexcel GCSE Mathematics Textbook Page 96 – Exercise 7B Q5, 7, 11, 12, 13

Converting between decimals and fractions ? ?

? ? ?? ? ? When will it not be a recurring decimal? It the fraction in its simplest form only has prime factors of 2 and 5 in its denominator. ?

Exercises Edexcel GCSE Mathematics Textbook Page 99 – Exercise 7C Q7, 8 (but no calculator!)

Converting recurring decimals to fractions

? ? A* question alert! ?

Exercises Edexcel GCSE Mathematics Textbook Page 101 – Exercise 7D Q1-15

GCSE: Percentages Dr J Frost Last modified: 24 th August 2013

Overview 27% of 420 (using a calculator and without using a calculator) The cost of car originally worth £15,000 but after losing 15% of its value. The value of saving account BEFORE it increased by 35% to £16,000 The value of an ISA with a principal of £1000, after accruing 5 years of interest at 3% p.a

The Key to Percentages It’s all about identifying a decimal multiplier! What would you multiply by in order to: ? ? ? ? ?

Questions (use multipliers and a calculator) ? ? ? ?

WITHOUT a calculator 35% of £64

Exercises 1a 1b 1c ? ? ? For Q1, work out the following with a calculator, showing what multiplication you used to get the answer. For Q2, work out the following without a calculator. 2a 2b 2c ? ? ?

Finding the percentage change Formula: ? ? ? ? ? ?

Compound changes I put £1000 into an account with 3% interest p.a. How much is there in the account after 7 years? (Hint: again, it’s all about the appropriate multiplier!) ? My house is worth £250,000. However, due to the economic crisis, the value depreciates by 10% each year. How much is it worth 5 years later ?

Compound vs ‘Simple’ interest This rarely comes up in GCSE exams, but you should appreciate the difference between compound and simple interest. If the principal of a bond is £1000, and the interest rate 10% p.a., find the value after 5 years using: Compound interest: Simple interest: ? ?

Exercises Edexcel GCSE Mathematics Textbook, Page 186 – Exercise 12D Q3, 5, 6, ? ? ? ?

Reverse Percentages We’ve so far always multiplied by the multiplier in order to find the new value. But what if we wanted to find the original value before the percentage change? ?

Reverse Percentages After a bloody fight with George, Fareed lost 30% of his body’s blood. He now only had 5 pints of blood left. How much blood did he originally have? ?

To reverse or not to reverse? Shakespeare bought 375 quills this year. This was 25% less than last year. How many did he previously buy? Last year a performance of The Merchant of Venice took in 60 farthings. This year it took in 15% less. How much was made this year? A cutlass with 20% VAT costs £162. What was the cost without VAT? Mecrutio sues Romeo for 150 farthings for mortal injuries inflicted. However, after realising he’s being a bit of a douche, he decides to lower this amount by 36%. How much did he sue Romeo for?  Don’t Reverse Reverse  Don’t Reverse Reverse  Don’t Reverse Reverse  Don’t Reverse Reverse

More examples ? ? ? ?

Exercises Edexcel GCSE Mathematics Textbook, Page 188 – Exercise 12E Q1, 3, 5, 7, ? ? ? ? ?