11. [Percentages] 60% Write the number followed by the percent symbol % Hint: Percentage means per hundred or of each hundred.

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1 . [Percentages] Skill. Writing a number out of 00 as a percentage. Write the number followed by the percent symbol % Hint: Percentage means per hundred or of each hundred. Q. Write as a percentage: 84 out of 00. A. 84 out of 00 84% a) Write as a percentage: 60 out of % b) Write as a percentage: out of 00. c) Write as a percentage: 46 out of 00. d) Write as a percentage: out of 00. e) Write as a percentage: 5 out of 00. f) Write as a percentage: 9 out of 00. g) Write as a percentage: 6 out of 00. h) Write as a percentage: 5 out of 00. i) Write as a percentage: 4 out of 00. j) Write as a percentage: 7 out of 00. k) Write as a percentage: 59 out of 00. l) Write as a percentage: 9 out of 00. m) Write as a percentage: 8 out of 00. n) Write as a percentage: 79 out of 00. page 67 Maths Mate 4./5. kill Builder

2 Skill. Finding the remaining percentage. Subtract the given percentages from 00%, to find the remaining percentage. Q. According to a projection for 00, 9% of the population of the USA will be aged between 0-9 and 5% between What percentage of the population will be aged 60 or more? a) Approximately 59% of the athletes at the 000 Sydney Olympics were male. What percentage of the athletes were female? 00% 59% c) The green-yellow 8-carat gold is 75% gold and the rest is silver. What percentage is silver? e) If 78% of the Supreme Court justices are male, what percentage are females? g) In Mali 7% of people earn less than a day. What percentage of people earn more than a day? 4% A. 00% 9% 5% 00% 74% 6% b) School is approximately 60% of the calendar year in the Russian Federation. What percentage do holidays account for? 00% 60% d) If 89% of the West Point military academy graduates are male, what percentage are females? f) If the cucumber is 96% water, what percentage do the other components equal? h) If 7.5% of the adult teeth are incisors and canines, what percentage is formed by molars and pre-molars? i) Approximately 60.5% of the world population lives in Asia and.5% lives in North and South America. What percentage of the population lives in the rest of the world? 00% 60.5%.5% k) If England occupies 57% and Scotland occupies 4% of Great Britain (the main island of the United Kingdom), what percentage is occupied by Wales? j) Approximately 7.% of the world population is aged between 0 and 4 years and 65.% between 5 and 64 years. What percentage of the population is aged 65 years and over? l) At the 0 London Olympics, 0% of the medals won by Australia were gold, and 46% were silver. What percentage of the medals were bronze? page 68 Maths Mate 4./5. Skill Builder

3 Skill. Finding a percentage of multiples of 00 (). EITHER Change the percentage to a fraction out of 00. To find 0% divide by 0 0 Example: 40% 40 5% half of 0% 00 Rewrite the question as a multiplication (change of to ). 0% divide by 5 5 Change the whole number to a fraction over. 5% divide by 4 Example: Cross simplify the fractions before multiplying. 50% divide by (see skill 0.4, page 60) OR First find 0%. Then multiply by the amount needed to make the required percentage, i.e. multiply by to get 0%. Q. 40% of 6.00 A. 40% of % of cents.40 Convert to cents Simplify: 00 OR A cents cents.40 Find 0% Multiply by 4 to get 40% a) 4% of Divide by 00 4 b) 85% of 00 c) 69% of 00 d) 9% of 00 e) 7% of 00 f) 50% of g) 75% of h) 0% of Divide 00 by 0 i) 0% of Find 0% first j) 60% of 00 k) 5% of 800 l) 70% of page 69 Maths Mate 4./5. Skill Builder...

4 Skill. Finding a percentage of multiples of 00 (). m) 5% of % is half of 0% n) 5% of Find 0% o) 5% of p) 50% of 700 q) 0% of 00 r) 40% of s) 80% of 400 t) 90% of 00 u) 5% of v) 50% of 5.00 w) 0% of.00 x) 75% of y) 5% of 4.00 z) 40% of.50 A) 0% of page 70 Maths Mate 4./5. Skill Builder

5 Skill.4 Finding a percentage of any number (). EITHER Change the percentage to a fraction out of 00. To find % divide by Example: 40% 40.5% divide by Rewrite the question as a multiplication (change of to ). % divide by Change the whole number to a fraction over % divide by Example: 7 multiply by Cross simplify the fractions before multiplying. (see skill 0.4, page 60) OR First find 0%. Then multiply by the amount needed to make the required percentage, i.e. multiply by to get 0%. Q. 66 % of 70 A. 66 of 70 % Simplify: Substitute 66 % with Change of to 70 Change 70 to 70 Multiply by a) 0% of Simplify: 0, twice 0 b) 70% of Multiply by 7 to get 70% 4 7 Find 0% first c) 80% of 0... d) 40% of g) 70% of 0... j) 5% of 60 0% % is half of 0%... 5% 6 5% 6 + Find 0% first e) 60% of h) 5% of k) 5% of 80 0% 5% % f) 0% of i) 5% of 0... l) 45% of 0 0% 5% % page 7 Maths Mate 4./5. Skill Builder

6 Skill.4 Finding a percentage of any number (). m) 5% of Divide by Simplify: 5 n) 75% of o) 75% of 0... p) 5% of Simplify: q) 6% of 0... r) 8% of s) % of t) % of u) % of v).5% of Simplify: 8... w).5% of x).5% of y) % of Simplify:... z) % of A) % of B) 66 % of C) 66 % of D) 66 % of 0... page 7 Maths Mate 4./5. Skill Builder

7 Skill.5 Working with percentages to find discounts and sale prices (). To find the discount on an item Calculate the percentage of the given amount. (see skill., page 69 and skill.4, page 7) Discount is associated with words like: discounted, reduced, off, save, cash back Q. In a store a 00 jacket is marked 0% off. What is the sale price of the jacket? To find the sale price if a discount is applied Calculate the percentage of the given amount. Subtract this result from the given amount. A. Discount: 0% of Sale price: Divide by 00 a) If a 0 T-shirt is reduced by 5%, what is the discount? 5% of b) If a 0 bike is reduced by 5%, what is the discount? c) If a 500 computer is reduced by 5%, what is the discount? 5% of d) If an 80 game is reduced by 40%, what is the discount? e) If a 000 laptop is reduced by 0%, what is the sale price? 0% of Divide by sale price: f) If a 500 dress is discounted by 40%, what is the sale price? sale price:... g) In a store a 5 skirt is marked 50% off. What is the sale price of the skirt? sale price:... h) In a store a 40 suitcase is marked 0% off. What is the sale price of the suitcase? sale price:... page 7 Maths Mate 4./5. Skill Builder

8 Skill.5 Working with percentages to find discounts and sale prices (). i) If a 400 gold bracelet is discounted by 0%, what is the sale price? sale price:... j) If a car is reduced by 0%, what is the sale price? sale price:... k) In a store a 900 canoe is labelled Save 60%. What is the sale price of the canoe? sale price:... l) In a store a 00 pram is labelled Save 5%. What is the sale price of the pram? sale price:... m) A printer is priced at 00. Which is the better deal? A ) 0% off B ) 50 cash back sale price A: sale price B: n) A watch is priced at 450. Which is the better deal? A ) Save 0% B ) Take 00 off sale price A: sale price B: o) A utility is priced at Which is the better deal? A ) 0% discount B ) Reduce by 5 sale price A: sale price B: p) A lounge suite is priced at Which is the better deal? A ) Save 5% B ) Reduce by sale price A: sale price B: page 74 Maths Mate 4./5. Skill Builder

9 Skill.6 Working with percentages greater than 00%. EITHER Change the percentage to a fraction out of 00. Example: 50% Rewrite the question as a multiplication (change of to ). Change the whole number to a fraction over. 7 Example: 7 Cross simplify the fractions before multiplying. (see skill 0.4, page 60) OR First find 00% or other multiples of 00%. Then find the remaining percentage. Add the results. To find 00% multiply by 00% multiply by Q. 50% of 40 A. 50% of Simplify: 0, twice OR A. 00% of 40 is 40 So 00% is triple that, or 0 50% of 40 is 0 So 50% of 40 is a) 00% of d) 0% of 80 00% of Find 0% 0% of Add the results g) 50% of j) 0% of 60 Simplify: 0, twice 0 Find 00% b) 00% of e) 0% of h) 40% of k) 0% of 70 c) 400% of f) 50% of i) 0% of l) 50% of page 75 Maths Mate 4./5. Skill Builder

10 Skill.7 Writing one number as a percentage of another number. Form a fraction using the two numbers. EITHER Multiply this fraction by 00%. Simplify the resulting fraction and/or change it to a mixed number if necessary. (see skill 9., page 4) OR Find an equivalent fraction with the denominator 00, by Multiplying by 00% 00% Multiplying by or 00% does not change the value. multiplying or dividing both the numerator and denominator by the same number. Write this fraction as a percentage. (see skill., page 9) Hint: Both numbers must represent the same unit of measurement. Q. Write as a percentage: out of 50. A. out of 50 00% % 50 46% Simplify: 50 OR A. out of % a) Write as a percentage: out of Simplify: Find equivalent fraction.... 0% c) At the 00 Delhi Commonwealth Games, out of the 4 medals won by Samoa were gold. What percentage is this? b) In Australia 88 out of every 00 people live in an urban area. What percentage is this?.... d) For every 0 Skype calls made, 8 calls are video to video. What percentage is this? e) A male lion weighs 5 kg. It eats 9 kg of food each day. What percentage of its own weight does a lion eat each day? f) Of the billion cattle in the world, 00 million are in India. What percentage of the world s cattle are in India? page 76 Maths Mate 4./5. Skill Builder

11 Skill.8 Calculating profit or loss as a percentage of the cost price. Calculate the profit or the loss, as the difference between the selling and the cost price. Express the profit or the loss as a percentage of the cost price. (see skill.7, page 76) Q. A shop buys jackets in bulk for 50 each, then sells them for 95 each. Calculate the profit on each jacket as a percentage of the cost price. a) Lorien lost 40 on a ring costing 400. What was her loss as a percentage of the cost price? loss: loss out of cost: 40 out of % 40 4 % 0%. c) John made 0 profit on a tool box costing 00. What was his profit as a percentage of the cost price? profit:... profit out of cost:.... e) Serena bought a car for If she later sold it for 500, find the loss as a percentage of the cost price g) Amelia bought a table for 400. If she later sold it for 50, find the loss as a percentage of the cost price. A. profit: profit out of cost price: 45 out of % % 90% b) The Cycle Centre made 0 profit on a bicycle costing 50. What was the profit as a percentage of the cost price? profit:... profit out of cost:.... d) Jason lost 5 on a book costing 0. What was his loss as a percentage of the cost price? loss:... loss out of cost:.... f) A shop buys school uniforms in bulk for 75 each, then sells them for 00 each. Find the profit as a percentage of the cost price h) A painting was bought for If it was later sold for 7500, find the profit as a percentage of the cost price page 77 Maths Mate 4./5. Skill Builder

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4 Percentages Chapter notes

4 Percentages Chapter notes GCSE Specification concepts and skills Find a percentage of a quantity (N o): 4. Use percentages to solve problems (N m): 4., 4.2, 4., 4.4 Use percentages in real-life situations: