Mathematics Percentages
One number as a percentage of another 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 4 out of 35 = 35 Then convert the fraction to a percentage. 20 4 × 100% 4 80% = × 100% = = 35 35 7 7 3 7 11 %
Calculating percentages
Finding a percentage increase or decrease 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: Percentage increase = actual increase original amount × 100% actual decrease Percentage decrease = × 100% original amount
Finding a percentage increase 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 0. 7 The percentage increase = × 100% 3. 5 = 20%
Finding a percentage loss 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 = 46 p Make sure the units are the same. 0. 46 Her percentage loss = × 100% 3. 68 = 12. 5%
Finding a percentage change
Percentage increase 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. Method 1 We can work out 20% of £ 150 000 and then add this to the original amount. The amount of the increase = 20% of £ 150 000 = 0. 2 × £ 150 000 = £ 30 000 The new value = £ 150 000 + £ 30 000 = £ 180 000
Percentage decrease 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. Method 1 We can work out 30% of £ 75 and then subtract this from the original amount. The amount taken off = 30% of £ 75 = 0. 3 × £ 75 = £ 22. 50 The sale price = £ 75 – £ 22. 50 = £ 52. 50
Reverse percentages Sometimes, we are given the result of a given percentage increase or decrease and we have to find the original amount. 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? The original price had 15% taken off so £ 25. 50 represents 85% = £ 25. 50 1% = £ 25. 50 ÷ 85 = £ 0. 30 100% = £ 0. 30 × 100 = £ 30
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