Percentages Knowledge Organiser PDF

Knowledge Organiser: Percentages What you need to know: Key Terms: You need to be able to: Percentage of an amount – Non calculator...

Knowledge Organiser: Percentages What you need to know: Key Terms: You need to be able to: Percentage of an amount – Non calculator Percentage: Out of one Calculate a percentage To calculate any percentage it is useful to start with 10%. hundred. of an amount. To find 10% we divide by 10. Decimal: A decimal is a fraction 30% of 120: 10% = 120 ÷ 10 = 12 written in a special form e.g. 30% = 3 x 12 = 36 0.6. Use a multiplier to To find 30% we multiply 10% by 3. Multiplier: This is used to calculate a percentage 45% of 80: 10% = 80 ÷ 10 = 8 5% = 8 ÷ 2 = 4 calculate percentages when we of an amount. 40% = 4 x 8 = 32 5% is half of 10% have a calculator. 45% = 40% + 5% = 32 + 4 = 36 so we divide by 2. Increase: When an amount Calculate a percentage To find 1% we divide the starting amount by 100. goes up. increase. 1% of 30 = 30 ÷ 100 = 0.3. Decrease: When an amount goes down. Percentage of an amount – Calculator Simple interest: The amount of Calculate a percentage interest is fixed over period of decrease. When we have a calculator we can use a multiplier; this is the decimal equivalent of the percentage. Change the time. 80% of 120: 80% = 0.80 percentage to Compound interest: The Calculate simple 80% of 120 = 0.80 x 120 = 96 a decimal and interest earned over time will then multiply. interest. continue to increase. 33% of 90: 33% = 0.33 Calculate compound Be careful if 33% of 90 = 0.33 x 90 = 29.7 the percentage is less than 10. Hegarty maths clip numbers interest. 4% of 88: 4% = 0.04 Percentage of Amount: 84 – 87 4% of 88 = 0.04 x 88 = 3.52 Take care using Percentage Increase/Decrease: decimal percentages, 88 – 90 still divide by 100. 12.5% of 42: 12.5% = 0.125 Simple and Compound Interest: 12.5% of 42 = 0.125 x 42 = 5.25 91 – 94  Knowledge Organiser: Percentages What you need to know: Simple interest Percentage increase and decrease Increase: To calculate a percentage increase we calculate the To calculate simple interest we start by calculating the percentage and percentage and add the value on to the original amount. multiplying it by the period of time. Non Calculator: Increase 70 by 65% Calculate 65% by splitting into 10% and Example: £250 is in a bank account which is paying 5% simple interest per 10% = 70 ÷ 10 = 7 5% = 7 ÷ 2 = 3.5 5% and then add the year. How much will be in the bank account at the end of 3 years? 60% = 6 x 7 = 42 answer on to the 65% = 60% + 5% = 42 + 3.5 = 45.5 original amount. 5% = 0.05 Multiply by 3 because 0.05 x 250 = £12.50 the question asks for 70 + 45.5 = 115.5 3 years. Calculator: Increase 130 by 26% 3 x £12.50 = £37.50. Add your answer to Calculate 26% using a multiplier and add this answer the original amount in 26% of 130 = 0.26 x 10 = 33.8 the question. onto the original amount. £250 + £37.50 = £287.50 130 + 33.8 = 163.8 Compound interest Decrease: To calculate a percentage decrease we calculate the To calculate compound interest we use powers as the amount percentage and subtract the value off the original amount. changes at the end of each year. Non Calculator: Decrease 20 by 35% Calculate 35% by 10% = 20 ÷ 10 = 2 5% = 2 ÷ 2 = 1 splitting into 10% and Example: £250 is in a bank account which is paying 4% compound 5% and then subtract interest per year. How much will be in the bank account at the 30% = 3 x 2 = 6 the answer off the 35% = 30% + 5% = 6 + 1 = 7 end of 5 years? Interest means an increase original amount. so 100% + 4% = 104% which as a multiplier is 1.04 20 - 7 = 13 4% increase = 1.04 Calculator: Decrease 65 by 14% Power of 5 because the Calculate 14% using a multiplier 14% of 65 = 0.14 x 65 = 9.1 1.045 x 250 = £304.16 questions asks for 5 years. and subtract this answer off the original amount. This is the final answer 65 – 9.1 = 55.9