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PERCENTAGES Percentage (written %) means "out of one hundred" i.e. % means "twelve out of a hundred" or 00 50 50% means "50 out of a hundred" or 00 Fractions and decimals can easily be changed into percentages and vice-versa.

1 PERCENTAGES Percentage (written %) means "out of one hundred" i.e. % means "twelve out of a hundred" or % means "50 out of a hundred" or 00 Fractions and decimals can easily be changed into percentages and vice-versa. CHANGING FRACTIONS TO PERCENTAGES RULE To change a fraction into a %age, multiply the fraction by 00 = 60% 5 Remember to use your rules of fractions, and to cancel where possible. Example 00 e.g. to a percentage becomes 5 Change 7 to a percentage = = Example 6 % 7 Change to a percentage 5 First change the mixed number to an improper fraction, then multiply by (cancel where possible) 5 = 0% Exercise Change these fractions to percentages: Page of 5

2 CHANGING DECIMALS TO PERCENTAGES RULE To change a decimal to a percentage, multiply the decimal by 00. Example Example Change 0.8 to a percentage 0.8 x 00 = 8% Change 0.75 to a percentage x 00 = 7.5% Example Change 0.7 to a percentage 0. 7 x 00 = 70% (Remember that a 0.7 can be written as 0.70) Example Change.67 to a percentage. 67 x 00 = 67% Exercise Change these decimals to percentages: Page of 5

3 CHANGING PERCENTAGES TO FRACTIONS RULE To change a percentage to a fraction divide by 00. Example Change 75% to a fraction 75% = 75 (Cancel where possible) 00 Example Change % to a fraction First change the mixed number to an improper fraction, 5 Example then divide by 00 5 (Cancel where possible) 00 8 Change 0% to a fraction i.e. Exercise Change these to fractions:. 5%. 0%. 0%. % 5. 7 % Page of 5

4 CHANGING PERCENTAGES TO DECIMALS (DECIMAL FRACTIONS) RULE To change a percentage to a decimal (decimal fraction) divide the percentage by 00. Example Change 5% to a decimal fraction 5 5% = = Example Example Change.% to a decimal fraction..% = 00 = 0.0 Change.7% to a decimal fraction.7% = = 0.7 Example Change 6% to a decimal fraction 6 6% = = Exercise. Convert these to decimals a) 6% b).7% c) 5.65% d).% e) 7%. Copy out this table, then fill in the gaps fraction decimal %age.0 00% % Page of 5

5 PERCENTAGE CHANGE A number can be increased or decreased by a given percentage, e.g., shoes in a sale, may be decreased (or reduced) by 0%, you may have to pay a deposit of 0% if you are buying a video. Example Example What is 0% of 50? Remember that 'of means multiply. 0% means 0 divided by 00, so 0% of 50 is now written 0 50 = 0 (Cancel where possible) 00 So, 0% of 50 is 0 What is % of 60? 60 Multiply 5 00 Exercise 5 00 and 00 by, so we now get 60 0 (Remember to cancel where possible). 0% of 50. 0% of 70. 5% of 00. % of % of 0 INCREASING A NUMBER BY A GIVEN PERCENTAGE There are several methods which can be used, one of which is shown here. Increase 50 by 6% If we find 6% of 50, this gives the actual amount of the increase. This increase must be then added to 50 to give the final price So, 00 The increase of must now be added to 50, giving the answer 5. Page 5 of 5

6 DECREASING A NUMBER BY A GIVEN PERCENTAGE Using the same figures as in the example above, we know that 6% of 50 is. However, because we are looking for a decrease, the must be subtracted from 50, giving the answer of 7. Exercise 6. Increase 00 by %. Decrease 00 by %. Increase 0 by 0%. Decrease 0 by 0% MAKING A NUMBER A PERCENTAGE OF ANOTHER NUMBER Example What is out of 86 as a percentage? This is written as 00 = 50% 86 Example What percentage is 50 of 50? =.ǯ% 50 Exercise 7 What percentage is:. out of8. 0 out of out of out of out of 8000 COMMISSION This is another way of using percentages. Salesmen, representatives, etc, are sometimes paid commission on top of their basic pay. The commission is a percentage of the total value of the goods they have sold, Example A double-glazing salesman is paid commission of % on the goods that he sold. If he sells double-glazing to the value of 900 find the amount of commission. Page 6 of 5

7 Commission = % of 900 (of means x) = Example = 8 This would then be added to his basic wage. A woman is paid a basic wage of 6 per week and a commission of.5% on the goods she sells. How much commission will she be paid if the sells 500 of goods and what will be her pay for that week? Commission =.5% of 500 = = = = 7.50 Commission Pay for that week = = 7.50 Exercise 8. A car saleswoman sells a car for 600. If she is paid a commission of %, what is total amount of commission she receives?. The basic wage of a sales rep for baby goods is per week. In addition to this he is paid a commission of.5%. Calculate - a) commission on 960 b) his wage for that week, assuming he sells 960 of baby goods. Page 7 of 5

8 HIRE PURCHASE If we buy goods and pay for them by instalments, over a certain period of time, this is called buying goods on hire purchase. Usually, a deposit is required first, and the difference or balance and any interest must be repaid in a number of instalments. "Interest free credit" means that no interest is charged on the balance. Example A couple buy a three-piece suite for 500. They have to pay a deposit of 0% and the amount outstanding is charged at % per annum. The amount owing is then paid off in monthly instalments. How much will each instalment be? Price of suite = 500 Deposit of 0% = = 50 Outstanding balance = = 50 Interest charged at % on this amount 50 = 00 = 6 Total amount to be repaid = = 5 Monthly Instalments 5 = 6 Exercise 9. A man buys a car for 500 and puts down a deposit of 0%, Interest is charged at.5% per annum on the outstanding balance. He repays this balance over months. How much are the monthly instalment to the nearest pence?. An article can be purchased for I0. If bought on hire purchase, a deposit of 0% has to be paid first, then an interest rate of % is added to the outstanding balance. What is the difference between paying cash and buying the article on hire purchase if the balance is repaid in one year. BANK LOANS It is possible to borrow money from the bank on a 'personal loan'. The bank gives a rate of interest for the loan, and the loan plus the interest, is usually repaid over equal monthly instarnents: Example A couple borrows 000 from the bank. The interest rate is %. If the loan is repaid over months, calculate the amount of each payment to the nearest pence. Loan = 000 Interest rate = % Page 8 of 5

9 = = 0 So, the total amount to be repaid = loan + interest = 0 Monthly Instalments = 0 = 0. Exercise 0. A man borrows 00 from the bank. Interest is charged at 5% and the loan plus interest is to be repaid over months, what is his monthly repayment?. A bank lends a customer 650. Interest is charged at % per annum. If the loan is repaid, in equal monthly instalments, over years, calculate the amount of each instalment to the nearest pence. (HINT! Loan to be repaid over two years.) PROFIT AND LOSS When a shopkeeper buys goods, he buys them at Cost Price (CP). When he sells the goods, this is called the Selling Price (SP). Profit or Gain is made when the selling price is bigger than the cost price. Loss is made when the selling price is smaller than the cost price. So, to find profit (gain) or loss PROFIT (GAIN) = SP - CP LOSS = CP - SP If SP is 0 and the CP is 5 find the actual profit. Profit = SP - CP = 0-5 = 5 If the selling price is and cost price is 6, find the actual loss. Loss = CP - SP = 6 - = Page 9 of 5

10 FINDING THE PERCENTAGE GAIN AND LOSS You are often asked to find the percentage gain (profit) or loss. You simply use the formula given here. Percentage profit = Percentage profit = Gain 00 CP Loss 00 CP Example A woman buys a T-shirt for and sells it at 5. What percentage profit does she make? CP =, SP = 5 Percentage profit = Gain 00 CP 5 00 Percentage profit = 00 = Example A man buys a computer for 00 and sells it for 50. Calculate his %age loss. Percentage loss = CP - SP x 00 CP. Exercise = x = 6 %. A car is bought for 00. and sold for 800. Calculate the percentage loss.. A shopkeeper buys 0 articles costing p each and sells them at p each. What is her percentage profit?. kg of potatoes were bought at 0p and sold at p. What is the percentage profit?. A man weighed 00 kg. After a diet he then weighed 90 kg. What was his percentage loss in weight? 5. A plant was bought when it was cm high. It grew to a height of 6 cm. Calculate the percentage growth of the plant. Page 0 of 5

11 DISCOUNT In some shops, if you pay cash for an article, you may ask for a discount. This is a percentage of the selling price. A television is priced in a shop at 00. For cash, a discount of 0% is offered. What would the price of the TV be with 0% off? First of all find the actual discount, then, subtract it from the original price. Find 0% of Take this 0 from the original price: 00-0 = 70 So, you would pay 70 for the television. VAT This is the abbreviation used for Value Added Tax. At the time of writing, this stood at 7.5%. You pay VAT on many things, such as electrical goods, food in restaurants, clothes etc. To calculate VAT simply work out 7.5% of the amount given. Find the VAT on a meal costing 0, and give the cost of the meal when VAT is added. 7.5% of This amount, 5.5 must be added to the bill, so your final bill should be: = 5.5 COST PRICE AND SELLING PRICE Sometimes, you are asked to calculate the SP if you are given the CP and gain or loss, or the CP if you are given the SP and the gain or loss. Questions of this type are straight forward and the least complicated method of finding what is needed, is given here. Example An item was bought for 0 and had to sold so that a profit of 0% was made. What should be the selling price be? ' First find 0% of 0 Page of 5

12 0 0 This is the actual profit made The selling price is, therefore, the cost price plus the profit: 0 + = Example A car was bought for 000 and a loss of 5% was made on the sale. What was the car sold for? First find 5% of to give the actual loss Then take away this amount from the cost price: = 550 Example If the selling price of an item is and the profit made was 0%, what was the cost price? The cost price is 00%, so the selling price will be 00% + 0%. Example Cost price = 00 0 = 0 If the selling price is 90 and a loss of 5% is made, what is the cost price? Cost price = 00% Selling price = 00% - 5% = -95% So, CP = Exercise = 00. A mirror has 0% discount off the marked price of 5, what is the actual discount?. A shop offers a discount of 6p in the. How much will be allowed on an item costing 00.. CP = 0, Gain = 5% What is SP? Page of 5

13 . CP = 0, Loss =.5% What is SP? 5. SP = 5, Profit = 0% What is the CP? 6. SP = 00, Loss = 5% What is CP to the nearest pence? Page of 5

14 ANSWERS Exercise. 80%. %. 75%. Exercise 7 8 % 5. 0% 7. 65%. 7.5%. 89%. 60% 5..% Exercise Exercise. a) 0.6 b) 0.07 c) d) 0.0 e) fraction decimal %age.0 00% % % 0.5 5% 0.5 % 8 0. % % Exercise Exercise Exercise 7. 5%. 0%. 8 %. 0% 5. 7 % Page of 5

15 Exercise a).60 b) 5.60 Exercise Exercise Exercise. 5%. 50%. 0%. 0% 5. % Exercise Page 5 of 5

Chapter 5 Financial Maths

Chapter 5 Financial Maths (Usually Q1/Q2 Paper 1) This revision guide covers Ordinary level notes Miss McDonnell 1 o Ratio and proportions o Currency transactions o Converting between decimal, percent