Percentages Vocabulary: percentage terminating hundredth Theory book Percentages Vocabulary: percentage terminating hundredth fraction recurring increase decimal order discount convert quantity loss numerator decrease profit

Theory book Literacy activity: Put the vocabulary words in alphabetical order percentage terminating hundredth fraction recurring increase decimal order discount convert quantity loss numerator decrease profit Sort out the anagrams of the list words slos cernisea ceeaesdr citsdoun rctgenpeea

Which vocabulary word means: Theory book Which vocabulary word means: one of a hundred parts _____________ a part of something _____________ taking a given percentage off a price is called a ___________ when you make money on a transaction _____________

Percentages as Fractions Theory book Percentages as Fractions A percentage is a fraction out of 100. So, a percentage can be written as a fraction with a denominator of 100. This fraction can sometimes be simplified. So 45% means 45 out of 100

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Converting percentages Theory book Converting percentages To change a percentage to a decimal or fraction we simply divide by 100. This means that 75% is the same as 0.75 and ¾...

WORKBOOK CONVERSIONS The most important thing for you to remember is that a percentage is a fraction over 100. In year 7 you would have completed conversions between fractions, decimals and percentages. Try these as revision:

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RECURRING DECIMALS Let x = 0.643434343..... x = 637 990 Theory book RECURRING DECIMALS Some decimals go on infinitely. These are called 'recurring'. Consider the fraction 1 3 . It is the decimal 0. 3 , and also the percentage 33 1 3 %. If a number starts repeating itself after 1 decimal place, the denominator of the fraction is 9 (so 0.1111111 = 1 9 ). If a number repeats itself every two decimal places the denominator is 99 ( 0.31313131... = 31 99 ) ADVANCED: Change 0.643434343... to a fraction Let x = 0.643434343..... Then 100x = 64.34343..... 100x - x = 64.34343... - 0.6434343... 99x = 63.7 x = 63.7 99 x = 637 990

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Finding a percentage of a quantity Theory book Finding a percentage of a quantity To find a percentage of a quantity, 1) write the percentage as a fraction 2) multiply the fraction by the quantity, ensuring you consider the units e.g. find 30% of $200 = 30 100 x 200 = $60 A bar model can be very helpful here.

WORKBOOK 1. 72% of 350 = 252 2. 40% of 340 = 136 3. 80% of 175 = 140 4. 20% of 140 = 28 5. 30% of 380 = 114 6. 70% of 450 = 31 7. 10% of 470 = 47 8. 180% of 140 = 252 9. 170% of 80 = 136 10. 50% of 140 = 70 11. 84% of 250 = 210 12. 43% of 28 = 12.04 13. 65% of 360 = 234 14. 277% of 3030 = 8393.1 15. 164% of 3042 = 4988.88 16. 93% of 64 = 59.52 17. 5% of 771 = 38.55 18. 110% of 50 = 55 19. 3% of 945 = 28.35 20. 380% of 42 = 159.6

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Increasing or decreasing by a given percentage Sometimes we are asked to increase or decrease a quantity by a given percentage. Find the given percentage of the original number ADD (for ‘increase’) or SUBTRACT (for ‘decrease’) this amount to the original quantity CHECK to see your answer makes sense

Theory book discounts Stores will often sell items for a discounted sales price. The store will discount an item by a percent of the original price. For example, an item that originally cost $20 may be discounted by 25%. To find the amount of discount calculate 25% of $20. (25/100 x $20 = $5.00) Subtract the discount from the original price to find the sale price. ($20.00-$5.00=$15.00 sales price). Terms you may see for discounted items are: 50% Off Save 50% Discounted by 50%

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Theory book Harder percentages Sometimes you will be asked to find a profit or loss as a percentage of either sale price or cost price. Always read the question carefully! e.g. A CD is discounted by 20%. It's original price was $30. a) Find the discount as a percentage of the original price. b) Find the discounted price as a percentage of the original price a) 20 100 x $30 = $6. This is the profit. The discount as a percentage of original price is 6 30 x 100% = 20% b) The discounted price is $30 - $6 = $24 The discounted price as a percentage of the original price is 24 30 x 100% = 80%

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Word problems 1. Christian collects aluminum cans and takes them to the recycling centre every week. He put recycling boxes in all the classrooms, the cafeteria, and the teachers' lounge. He put a sign on each box asking people not to put anything but aluminum cans in them. Every week, though, Christian finds objects other than aluminum cans in the recycling boxes. He estimates that twenty-five percent of the weight of the material in the boxes is non- recyclable junk. The total weight of all the items collected in the recycling boxes this week was one hundred thirty- two kilograms. What was the weight of the aluminum cans, rounded to the nearest tenth of a kilogram?

Word problems 2. There were 13,179 weddings in Springs City last year. According to state records, notaries public performed 18% of the weddings. How many weddings were not performed by notaries public? 3. The local store is having a sale. All floopers are 29% off. If a flooper normally costs $15.52 plus 10% GST, how much will it cost to buy a flooper during the sale? 4. When our teacher handed out our math test, she told us to omit problems 4, 7, 9, 11, and 15. There were forty problems on the test. What percent of the problems did we have to solve (to the nearest percent)?

Extreme percentages… 11. 90% of what number is 279? 310 12. What number is 30% of 350? 105 13. 13298.04 is 189% of what number? 7036 14. What number is 90% of 170? 153 15. 275% of what number is 261.25? 95 16. 20% of 500 is what number? 100 17. 96 is 128% of what number? 75 18. What percent of 480 is 48? 10% 19. 195% of what number is 195? 100 20. What number is 344% of 392? 1348.48 1. 35 is 70% of what number? 50 2. 10 is 10% of what number? 100 3. 132% of what number is 660? 500 4. What percent of 300 is 420? 140% 5. 152 is what percent of 100? 152% 6. What number is 90% of 10? 9 7. What percent of 155 is 279? 180% 8. 30% of 270 is what number? 81 9. 105 is what percent of 105? 100% 10. 26% of 100 is what number? 26