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Mathematics

Learn how to calculate percentages, find percentage increases and decreases, and solve reverse percentage problems in mathematics.

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Mathematics

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  1. Mathematics Percentages

  2. One number as a percentage of another 3 7 4 4 35 35 80% = 4 × 100% 11 % 7 = × 100% = 35 There are 35 sweets in a bag. Four of the sweets are orange flavour. What percentage of sweets are orange flavour? Start by writing the proportion of orange sweets as a fraction. 4 out of 35 = Then convert the fraction to a percentage. 20 7

  3. Calculating percentages

  4. Finding a percentage increase or decrease actual increase Percentage increase = × 100% original amount actual decrease Percentage decrease = × 100% original amount Sometimes, we are given an original value and a new value and we are asked to find the percentage increase or decrease. We can do this using the following formulae:

  5. Finding a percentage increase 0.7 The percentage increase = × 100% 3.5 A baby weighs 3.5 kg at birth. After 6 weeks the baby’s weight has increased to 4.2 kg. What is the baby’s percentage increase in weight? The actual increase = 4.2 kg – 3.5 kg = 0.7 kg = 20%

  6. Finding a percentage loss 0.46 Her percentage loss = × 100% 3.68 A share dealer buys a number of shares at £3.68 each. After a week the price of the shares has dropped to £3.22. What is her percentage loss? Her actual loss = £3.68 – £3.22 = 46p Make sure the units are the same. = 12.5%

  7. Finding a percentage change

  8. Percentage increase Method 1 We can work out 20% of £150 000 and then add this to the original amount. The value of Bob’s house has gone up by 20% in three years. If the house was worth £150 000 three years ago, how much is it worth now? There are two methods to increase an amount by a given percentage. The amount of the increase = 20% of £150 000 = 0.2 × £150 000 = £30 000 The new value = £150 000 + £30 000 = £180 000

  9. Percentage decrease Method 1 We can work out 30% of £75 and then subtract this from the original amount. The amount taken off = 30% of £75 A CD walkman originally costing £75 is reduced by 30% in a sale. What is the sale price? There are two methods to decrease an amount by a given percentage. = 0.3 × £75 = £22.50 The sale price = £75 – £22.50 = £52.50

  10. Reverse percentages I bought some jeans in a sale. They had 15% off and I only paid £25.50 for them. What is the original price of the jeans? Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount. The original price had 15% taken off so £25.50 represents 85% 85% = £25.50 1% = £25.50 ÷85 = £0.30 100% = £0.30 ×100 = £30

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