3 percentages
Download as PPT, PDF0 likes431 views
A percent is a ratio comparing a number to 100. It is represented with the % symbol. To calculate a percentage increase or decrease, the percent is written as a fraction out of 100. This fraction is then used as a multiplier for the original quantity. For a percentage increase, the multiplier is 1 + the percentage as a decimal. For a percentage decrease, the multiplier is 1 - the percentage as a decimal. Several examples are provided calculating percentage increases and decreases using this method.
3 percentages
- 1. Percentages A percent is a ratio of a number to 100. The symbol % is used to indicate a percent. The word percent means “per hundred.” So 6% means “6 out of 100.”
- 2. 6 100 = 6% Example Notice the 10 x 10 square grid. There are 100 total squares. Six of the squares are colored. Six red squares of 100 total squares can be shown like this:
- 3. Which of the following is an example of a percent? 32% A B 76
- 4. Additional Example 3: Writing Percents as Decimals Write 31% as a decimal. Method 1 Use pencil and paper. 31% = 31 100 = 0.31 Write the percent as a fraction with a denominator of 100. Divide 17 by 100. Method 2 Use mental math. 31% = 0.31 Move the decimal point two places to the left.
- 5. Percentages Percentage increase Find the percentage of the quantity and add it to the original Example 1: Increase 300 by 12% 12 × 300 100 3 = 36 cancel common factors 200 + 36 = 236 Example 2: Increase 170 by 30% cancel common factors 170 + 51 = 221 30 × 170 100 3 10 ≡ = 51
- 6. Percentages Percentage increase Find the percentage of the quantity and add it to the original Example 1: Increase 300 by 12% 12 × 300 100 3 = 36 cancel common factors 200 -36 = 164 Example 2: Increase 170 by 30% cancel common factors 170 -51 = 119 30 × 170 100 3 10 ≡ = 51
- 7. Percentages Percentage increase When calculating a percentage increase of a quantity we are starting with 100% and then we add the percentage asked for. e.g. Increase a quantity by 23% 100 % + 23 % = 123 % 100 % + 23 % = 123 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 + 23 = 123 100 100 100 Now 123 = 1.23 100 This is called the percentage multiplier for a percentage increase
- 8. Percentages Example : Increase 345 by 56% the percentage multiplier is 1.56 100 % + 56 % = 156 % 156 = 1.56 100 345 × 1.56 = 538.2
- 9. Percentages Now do these: 1. Increase 125 by 16% 2. Increase 340 by 9% 3. Increase 575 by 22% 4. Increase 84 by 1.3% 5. Increase £6.30 by 17.5% Percentage multiplier is 1.16 125 × 1.16 = 145 Percentage multiplier is 1.09 340 × 1.09 = 370.6 Percentage multiplier is 1.22 575 × 1.22 = 701.5 Percentage multiplier is 1.013 80 × 1.013 = 81.04 Percentage multiplier is 1.175 6.30 × 1.175 = £7.40
- 10. Percentages Percentage decrease When calculating a percentage decrease of a quantity we are starting with 100% and then we subtract the percentage asked for. e.g. decrease a quantity by 23% 100 % - 23 % = 77 % 100 % - 23 % = 77 % In order to do this calculation we write the percent as a fraction in hundredths. So this becomes: 100 - 23 = 77 100 100 100 Now 77 = 0.77 100 This is called the percentage multiplier for a percentage decrease
- 11. Percentages Example : Decrease 345 by 56% the percentage multiplier is 0.44 100 % - 56 % = 44 % 44 = 0.44 100 345 × 0.44 = 151.8
- 12. Percentages To summarise percentage calculations Original quantity × percentage multiplier = new quantity By understanding how to rearrange equations you can find any of the three if you know the other two.