
PERCENTAGE PERCENTAGES A) Expressing Percentages as the Number of Parts in every 100 1. The symbol for percentage is %. 2. A percentage is a fraction in which the denominator is 100. For example : 9 = 9% 100 32 = 32% 100 3. Convercely, percentages can be expressed as fractions. For example : 24 = 24% 100 122 = 122% 100 Worked Example Express each of the following as a percentage. (a) 72 100 (b) 102 100 Solution (a) 72 = 72% 100 (b) 102 = 102% 100 Worked Example Convert the following to fraction with 100 as their denominators. (a) 6% (b) 75% Solution (a) 6% = 6 100 (b) 75% = 75 100 B) Changing a Fraction or Decimal to a Percentage and vice versa 1. We can change a fraction or a decimal to a percentage by multiplying it by 100. Worked Example Convert the following to percentages. (a) 1 (b) 1 3 2 200 Solution (a) 1 = 1 x 100 2 2 Worked Example Convert each of the following to a fraction. (a) 0. 6 (b) 1. 02 Solution (a) 0. 6 = 0. 6 x 100% = 60% (b) 1. 02 = 1. 02 x 100% = 102% When converting a percentage to a fraction or a decimal, first change the percentage to a fraction with 100 as its denominator. Worked Example Convert each of the following to a fraction. (a) 140% Solution Worked Example Convert the following to decimals. (a) 55% (b) 324% Solution (a) 55% = 55 100 = 0.55 (b) 324% = 324 100 = 3. 24 COMPUTATIONS AND PROBLEM SOLVING A) Finding the Percentage of a Quantity Worked Example Find (a) 5 1 % of 600, 2 (b) 36% of 50 buttons, (c) 120% of RM800. Solution B) Expressing One Number as a Percentage of Another In general, to express one number, y , as a percentage of another number, z, we (a) write y as a fraction of z, (b) multiply the fraction y by 100% to convert z it to a percentage. Worked Example Find the percentage of the following. (a) 8 of 10 (b) 50 sen of RM1 Solution C) Finding a Number when given the percentage Worked Example Find the original value if 30% of the original value is 12. Solution D) Finding Percentage of Increase or Decrease Worked Example Find the percentage of increase or decrease of the following. (a) 200 is increased by 50. (b) 25 is decreased to 10. Solution E) Problem Solving i  Finding the change in value and the final value 1.To find the increase in value, use the formula below : 2. To find the final value, use any one of the formula below : Worked Example The population of a villlage was 2 000. It has increased by 10% after 5 years. Find the new population of the village. Solution 1. Understand the problem Given information : Number of population = 2 000 Percentage of increase = 10% Find : The new population 2. Devise a plan Find the increase in population, then add to the number of population. 3. Carry out the plan Increase in population = 10% of 2 000 = 200 people Therefore, the new population of the village is 2 200 people. 4. Check 3. To find the decrease in value, use the formula: 4. Use any of the following formula to find the final value: Worked Example A vessel contained 80 liters of water. 30% of water was used. Find (a) the amount of water used, (b) the amount of water left. Solution (a) Amount of water used = 24 liters 4. Amount of water left = 80 liters  24 liters = 56 liters ii) Finding the original value when given the percentage change and the final value Worked Example After a 20% decrease in mass, a boy weights 40 kg. Find his mass before the decrease. Solution 1. Understand the problem Given information : Percentage of decrease = 20% Final value = 40 kg Find : The mass before the degrease 2. Devise a plan Use the unitary method. 3. Carry out the plan New mass is 80% of old mass = 40 kg 1% = 40 kg 80 = 50 kg 4. Check Percentage of decrease iii) Finding profit and loses 1. A profit occurs when the selling price is higher than the cost price. 2. When the selling price is lower than the cost price, a loss is incurred. 3. Profit and loss can be calculated by using the following formula : 4. Use one of the following formula to find the percentage of profit or percentage of loss. Worked Example The profit made on the sale of a camera is 12% of the cost price. If the cost price is RM50, find the profit. Solution 1. Understand the problem Given information : Percentage of profit = 12% Cost price = RM50 Find : The profit 2. Devise a plan Use profit formula. 3. Carry out the plan Profit = Percentage of profit x Cost price Therefore, the profit is RM6. 4. Check Percentage of profit 5. The unitary method can be used to find the cost price. Worked Example Adina sold his bicycle for RM270 at a loss of 40%. Find the cost price of the bicycle. Solution 60% of cost price = RM270 1% = RM270 60 Therefore, the cost price of the bicycle is RM450. Check : Selling price = 60% * RM450 iv) Finding simple interest 1. Simple interest ( I ) is the amount of money earned on savings or to be paid on loans with banks and finance companies at a fixed rate ( R ) over a period of time ( T ), in years. 2. The money deposited or loaned is called the principal ( P ). 3. Simple interest and the rate in percentage a year are calculated as follows : Worked Example Puan Asniza took a bank loan RM8 000. If the simple interest paid is RM1 280 for 2 years, calculate the simple interest rate. Solution 1. Understand the problem Given information : Principal = RM8 000 Simple interest = RM1 280 Time = 2 years Find : The simple interest rate 2. Devise a plan Use simple interest rate formula. 3. Carry out the plan Simple interest rate = Simple interest x 100% Principal x Time Therefore, the simple interest rate is 8% a year. 4. Check 4. The principal can be calculate by the formula : Worked Example Jacky put his money in a bank to earn a simple interest at a rate of 81% a year. 2 How much money did he put in if he gets an interest of RM765 in 3 years ? Solution Simple interest for 1 year Check : Simple interest v) Finding dividends 1. Dividend is a part of the profit that a company gives to its shareholders. 2. Dividend and percentage of dividend can be calculate by using the formulae: Worked Example A company pays 6% dividend. Find the dividend Chong receives for a RM7 000 investment. Solution 1. Understand the problem Given information : Percentage of dividend = 6% Amount invested = RM7 000 Find : The dividend 2. Devise a plan Use dividend formulae. 3. Carry out the plan Dividend Amount = Percentage of dividend x invested Therefore, Chong receives a dividend of RM420. 4. Check Percentage of dividend Worked Example Kasim receives a dividend of RM5 500 on his investment of RM50 000 in a company. Find the percentage of dividend declared by the company. Solution Percentage of dividend = Dividend __ x 100% Amount invested Therefore, the company gives a dividend of 11%. vi) Calculating commissions 1. A commission is an earning paid to an agent on his total sales of a product. 2. Commission and the percentage of commission can be calculated by using the formilae : Worked Example As a salesman, Dewi gets a commission of 5% on the sale value of a jewellery sold at price of RM6 000. What is the commission she gets ? Solution 1. Understand the problem Given information : Percentage of commission = 5% Total sales value RM6 000 Find : The commission 2. Devise a plan Use commission formulae. 3. Carry out the plan Commission = Percentage of x Total sales commission value Therefore, the commission she gets is RM300. 4. Check Worked Example Ah Wah received RM7 360 as commission for a RM92 000 house he sold. What is the percentage of his commission ? Solution Percentage of commission = Commission x 100% Total sales value vii) Calculating discount 1. Discount is the amount taken off from the list price or the original price. Discount = Original price  Selling price 2. The formulae for calculating discount and the percentage of discount are as follows : Worked Example The original price of a television set is RM2 000. It is sold for RM1 700 after a discount. Find the percentage of discount given. Solution 1. Understand the problem Given information : Original price = RM2 000 Selling price = RM1 700 Find : The persentage of discount 2. Devise a plan Find the discount, then use percentage of discount formulae. 3. Carry out the plan Discount = Original price  Selling price = RM2 000  RM1 700 = RM300 percentage of discount = Discount x 100% Original price Therefore, the percentage of discount given is 15%. 4. Check Discount = 15% * RM2 000 Worked Example Find the original price of a book if it is sold for RM48 after a 40% discount. Solution Therefore, the original price of the book is RM80. Worked Example The original price of a handbag is RM245. If a discount of 20% is given at a sale, find the discount given in RM. Solution Discount = Percentage of discount x Original price Therefore, the discount is RM49. 

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