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**Solving Reverse Fraction Problems**

Mathematics Solving Reverse Fraction Problems

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**Lesson Objectives The aim of this powerpoint is to help you…**

to find the original value when you have been given the increased or decreased value to revise dividing by fractions

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**Reversing Fractional Changes**

You MUST use ‘method 2’ of fractional change Writing this method as a formula we have… New fraction × Original quantity = Changed Quantity To work backwards to find the original quantity we must do the opposite… Changed Quantity ÷ New fraction = Original quantity You will need to remember the method for dividing by fractions!

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Example 1 In a sale, all the prices are marked down by 3 10 If the sale price of some jeans is £56, what was their original price? 1 – 3 10 £56 ÷ 7 10 × original = £56 56 1 × = 56×10 1×7 560 7 = 560 ÷ 7 = £80

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**Reversing Fractional Changes**

Watch out for the increase or decrease being quoted rather than the new value. Writing this as a formula we have… Fraction × Original quantity = Increase or decrease To work backwards to find the original quantity we must do the opposite… Increase or Decrease ÷ Fraction = Original quantity You will still need to remember the method for dividing by fractions!

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Example 2 Rosemary’s weekly wage increases by 2 5 This equates to an increase of £40. What did she originally earn each week? 2 5 × original = £40 £40 ÷ 2 5 40 1 × = 40×5 1×2 200 2 = 200 ÷ 2 = £100

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**Quick Practice A Increase 36 by 4 9 B Decrease 50 by 3 10**

C A hat usually costs £36.99. In a sale a third is knocked off the price. What is the dale price of the hat? D Sarah earns £7.50 per hour. If this increases by 2 5 , what is her new hourly rate of pay? Work out your answers before clicking on to the next slide.

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**Answers A 4 9 of 36 = B 1 – 3 10 C 1 – 1 3 D 1 + 2 5 **

(36 ÷ 9) x 4 = 16 = 52 Using Method 1 Using Method 2… of 50 = (50 ÷ 10) x 7 = 35 2 3 of = (36.99 ÷ 3) x 2 = £24.66 7 5 of = (7.5 ÷ 5) x 7 = £10.50

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What next? Print out the notes called Frac10. Read them and make sure you answer any questions If you need more practice, try the worksheet called RevFrac-S1.xlsx. You have now completed all the work in the Fractions Module, though you will come across FDP conversions in the Percentages module. Please attempt the Fractions Assessment.

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