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23:[["$","$L32",null,{"feature":"flashcards"}],"$L33",["$","$L34",null,{"href":"/gcse/maths/ocr/grade-3-3-7-percentages/flashcards","label":"Percentages","subjectCode":"gcse_maths__ocr","surface":"flashcards"}],["$","$L35",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L36",null,{"decks":[{"id":"50917e10-d60a-881f-d5b2-55b90659f75e","title":"Percentages Flashcards","topicId":"77e84631-da25-4c98-9472-e2936a51205f","topicSlug":"grade-3-3-7-percentages","cards":[{"id":"6119106f-793a-9907-af29-a30c397c41b8","cardType":"cloze","points":null,"front":"A percentage means "out of [ ]".","back":"A percentage means "out of 100".","mcqOptions":[{"text":"100","correct":true,"explanation":"Percent means “per hundred”, so a percentage expresses a number of parts out of a total of 100 equal parts."},{"text":"10","correct":false,"explanation":"Confusing percentages with tenths makes 10 seem plausible. A percentage means “out of 100”, because the word percent means “per hundred”."},{"text":"1","correct":false,"explanation":"This confuses a percentage with a single part of a whole. Percentages are measured out of 100 equal parts, so the correct denominator is 100."},{"text":"1000","correct":false,"explanation":"This adds an unnecessary zero and would describe parts per thousand. A percentage is measured per hundred, so it means “out of 100”."}]},{"id":"555bc061-7009-dce5-96ab-4fe1c8c4568a","cardType":"cloze","points":null,"front":"100% represents the [ ].","back":"100% represents the whole amount.","mcqOptions":[{"text":"whole amount","correct":true,"explanation":"All 100 out of 100 equal parts make the complete quantity, so 100% represents the whole amount."},{"text":"half amount","correct":false,"explanation":"Half of an amount is 50%, not 100%. All 100 percentage parts together represent the whole amount."},{"text":"double amount","correct":false,"explanation":"Double the original amount is 200%, which is twice the whole. The original whole amount is represented by 100%."},{"text":"quarter amount","correct":false,"explanation":"A quarter of an amount is 25%, since one whole contains four quarters. The whole amount itself is represented by 100%."}]},{"id":"97c0b56c-3b3b-b316-a855-bcd6428b480a","cardType":"cloze","points":null,"front":"To find 10% of an amount, divide by [ ].","back":"To find 10% of an amount, divide by 10.","mcqOptions":[{"text":"10","correct":true,"explanation":"Ten equal groups of 10% make 100%, so dividing the whole amount by 10 gives one group worth 10%."},{"text":"100","correct":false,"explanation":"Dividing by 100 finds 1%, not 10%. Since 10% is one tenth of the whole, the amount must be divided by 10."},{"text":"5","correct":false,"explanation":"Dividing by 5 finds one fifth of the amount, which is 20%. To calculate 10%, divide the amount by 10."},{"text":"20","correct":false,"explanation":"Dividing by 20 finds one twentieth of the amount, which is 5%. To find one tenth, or 10%, divide by 10."}]},{"id":"ab489d4d-dd35-2e9d-0f64-045da63f38e0","cardType":"cloze","points":null,"front":"To find 1% of an amount, divide by [ ].","back":"To find 1% of an amount, divide by 100.","mcqOptions":[{"text":"100","correct":true,"explanation":"One percent is one part out of 100 equal parts, so dividing the whole amount by 100 finds 1%."},{"text":"10","correct":false,"explanation":"Dividing by 10 finds one tenth of the amount, which is 10%. To find 1%, divide the amount by 100."},{"text":"1","correct":false,"explanation":"Dividing by 1 leaves the amount unchanged and therefore gives 100%. One percent is one hundredth, so divide by 100."},{"text":"1000","correct":false,"explanation":"Dividing by 1000 finds 0.1%, which is one tenth of 1%. To calculate exactly 1%, divide by 100."}]},{"id":"71a002a1-401f-466f-bb3d-020897d579fe","cardType":"basic","points":1,"front":"If a question asks for 50% of an amount, what operation finds it?","back":"Halve the amount.","mcqOptions":[{"text":"Halve the amount.","correct":true,"explanation":"Fifty percent is one half of the whole because $50/100 = 1/2$. Therefore, halving the amount finds 50%."},{"text":"Double the amount.","correct":false,"explanation":"Doubling an amount gives 200%, not 50%. Since 50% is one half of the whole, the amount should be halved."},{"text":"Quarter the amount.","correct":false,"explanation":"Quartering finds 25%, because a quarter is $25/100$. Fifty percent is one half, so the amount should instead be halved."},{"text":"Divide by 50 the amount.","correct":false,"explanation":"Dividing by the percentage number does not generally find that percentage and here gives 2%. Since 50% equals one half, halve the amount."}]},{"id":"093e1bb4-0670-23ba-9b8b-6e4ff018355d","cardType":"basic","points":1,"front":"If a question asks for 25% of an amount, what operation finds it quickly?","back":"Divide by 4.","mcqOptions":[{"text":"Divide by 4.","correct":true,"explanation":"Twenty-five percent equals $25/100 = 1/4$, so dividing the amount by 4 quickly finds 25%."},{"text":"Multiply by 4.","correct":false,"explanation":"Multiplying by 4 gives 400% of the original amount, reversing the required operation. Since 25% is one quarter, divide by 4."},{"text":"Divide by 2.","correct":false,"explanation":"Dividing by 2 finds one half, which is 50%. Twenty-five percent is one quarter, so divide the amount by 4."},{"text":"Divide by 25.","correct":false,"explanation":"Dividing by the percentage number is a common misconception and gives 4% here. Since 25% equals one quarter, divide by 4."}]},{"id":"374e762c-e4e7-9efa-0cbb-67257f6dccbf","cardType":"basic","points":1,"front":"If you know 10% of an amount, how can you find 5%?","back":"Halve the 10% amount.","mcqOptions":[{"text":"Halve the 10% amount.","correct":true,"explanation":"Five percent is half of 10%, so halving the known 10% amount gives the value of 5%."},{"text":"Double the 10% amount.","correct":false,"explanation":"Doubling the 10% amount produces 20%, not 5%. Since 5% is half of 10%, the known amount should be halved."},{"text":"Divide by 5 the 10% amount.","correct":false,"explanation":"Dividing the 10% amount by 5 produces 2%, because $10\\% \\div 5 = 2\\%$. To find 5%, halve the 10% amount."},{"text":"Multiply by 5 the 10% amount.","correct":false,"explanation":"Multiplying the 10% amount by 5 produces 50%, not 5%. To reduce 10% to 5%, halve the known amount."}]},{"id":"00989d55-dbc4-50e2-1ecc-301412349a3b","cardType":"basic","points":2,"front":"Find 34% of 2500.","back":"850.","mcqOptions":[{"text":"850.","correct":true,"explanation":"Thirty percent of 2500 is 750 and 4% is 100. Adding these parts gives $750 + 100 = 850$."},{"text":"85.","correct":false,"explanation":"This answer is ten times too small, typically from mishandling the decimal percentage. Using $0.34 \\times 2500$ gives the correct value of 850."},{"text":"340.","correct":false,"explanation":"This treats the calculation as though the base amount were 1000. For 2500, $0.34 \\times 2500 = 850$."},{"text":"8500.","correct":false,"explanation":"This answer is ten times too large, usually because 34% was converted incorrectly. Since 34% is $0.34$, multiplying by 2500 gives 850."}]},{"id":"c42cda8c-5f37-d4b7-bb9e-960495d99e7c","cardType":"basic","points":1,"front":"If a percentage is greater than 100%, how does the answer compare with the original?","back":"It is bigger than the original.","mcqOptions":[{"text":"It is bigger than the original.","correct":true,"explanation":"A percentage greater than 100% represents more than the whole original amount. For example, 120% is 1.2 times the original, so it is bigger."},{"text":"It is smaller than the original.","correct":false,"explanation":"Confusing percentages above 100% with a percentage decrease reverses the comparison. More than 100% represents more than one whole, so the answer is bigger than the original."},{"text":"It is equal to the original.","correct":false,"explanation":"Only 100% is equal to the original amount. A percentage greater than 100% represents more than one whole, so the answer is bigger than the original."},{"text":"It is half of the original.","correct":false,"explanation":"Half of the original is 50%, not a percentage greater than 100%. More than 100% represents more than one whole, making the answer bigger than the original."}]},{"id":"486eecdd-9034-538d-36c4-a9b34fdadd22","cardType":"basic","points":2,"front":"Find 215% of 80.","back":"172.","mcqOptions":[{"text":"172.","correct":true,"explanation":"Convert 215% to 2.15, then calculate $2.15 \\times 80 = 172$. Since 215% exceeds 100%, the result is correctly greater than 80."},{"text":"17.2.","correct":false,"explanation":"Dividing by an extra factor of 10 gives 21.5% rather than 215%. The correct calculation is $2.15 \\times 80 = 172$."},{"text":"92.","correct":false,"explanation":"Adding 15% of 80 to the original finds 115%, not 215%. Since 215% is $2.15 \\times 80$, the correct answer is 172."},{"text":"215.","correct":false,"explanation":"Treating the percentage itself as the answer ignores the original amount of 80. Convert 215% to 2.15 and multiply by 80 to obtain 172."}]},{"id":"59e9d655-cd19-1af6-f967-1dead03b4ebb","cardType":"basic","points":2,"front":"Why should you not compare percentage amounts using the percentages alone?","back":"The wholes may be different.","mcqOptions":[{"text":"The wholes may be different.","correct":true,"explanation":"A percentage describes a proportion of a whole, so equal percentages can represent different amounts when their wholes differ. The whole must therefore be considered when comparing percentage amounts."},{"text":"The percentages may be different.","correct":false,"explanation":"The percentages are already known and can be compared directly, but they do not reveal the actual amounts. The wholes may differ, causing a smaller percentage to represent a larger amount."},{"text":"The units may be different.","correct":false,"explanation":"Different units can prevent a direct comparison, but that is not the key percentage issue here. Percentage amounts cannot be compared alone because their wholes may be different."},{"text":"The symbols may be different.","correct":false,"explanation":"The symbols used do not determine the size of a percentage amount. The important issue is that percentages are proportions of wholes, and those wholes may be different."}]},{"id":"87909e44-6db4-9670-fbb4-09ee66478cba","cardType":"basic","points":1,"front":"To find the difference between two amounts, what do you subtract?","back":"Subtract the smaller from the larger.","mcqOptions":[{"text":"Subtract the smaller from the larger.","correct":true,"explanation":"Difference means the positive distance between two amounts. Subtracting the smaller amount from the larger amount produces that distance without giving a negative answer."},{"text":"Subtract the larger from the smaller.","correct":false,"explanation":"Reversing the subtraction gives a negative result rather than the usual positive difference. To find the difference, subtract the smaller amount from the larger amount."},{"text":"Subtract the smaller from the smaller.","correct":false,"explanation":"Subtracting an amount from itself always gives zero, which does not measure the gap between two different amounts. Subtract the smaller amount from the larger amount instead."},{"text":"Subtract the larger from the total.","correct":false,"explanation":"Subtracting the larger amount from their total simply returns the smaller amount, not the gap between them. The difference is found by subtracting the smaller from the larger."}]},{"id":"a6803151-739f-8960-c31c-9ed1db61b89c","cardType":"basic","points":1,"front":"If 40% of people are children, what percentage are adults?","back":"60%.","mcqOptions":[{"text":"60%.","correct":true,"explanation":"Children and adults make up the full 100%. Subtracting the children's percentage gives $100\\% - 40\\% = 60\\%$, so 60% are adults."},{"text":"40%.","correct":false,"explanation":"This repeats the percentage of children rather than finding the remaining percentage. Adults account for $100\\% - 40\\% = 60\\%$ of the people."},{"text":"140%.","correct":false,"explanation":"Adding 40% to 100% incorrectly creates more than the entire group. Children and adults together total 100%, so adults make up $100\\% - 40\\% = 60\\%$."},{"text":"50%.","correct":false,"explanation":"Assuming the group is divided equally ignores the given 40% of children. The adult percentage is the remainder, calculated as $100\\% - 40\\% = 60\\%$."}]},{"id":"cb94e97c-b0f0-6997-e441-c4f369169847","cardType":"basic","points":2,"front":"If 60% of a total is 54, what is 100%?","back":"90.","mcqOptions":[{"text":"90.","correct":true,"explanation":"If 60% is 54, then 10% is $54 \\div 6 = 9$. Multiplying by 10 gives 100% as $9 \\times 10 = 90$."},{"text":"32.4.","correct":false,"explanation":"Calculating 60% of 54 treats 54 as the whole, although it is already the 60% amount. Scaling $54 \\div 60 \\times 100$ gives 90."},{"text":"60.","correct":false,"explanation":"Using the percentage number as the total ignores the value represented by 60%. Since 10% is $54 \\div 6 = 9$, the whole is 90."},{"text":"84.","correct":false,"explanation":"Adding 30 to 54 does not scale 60% up to 100% proportionally. Dividing 54 by 0.6 gives the correct total of 90."}]},{"id":"142ccea9-f986-2a3a-603e-28d8f79635e4","cardType":"basic","points":1,"front":"For a percentage increase, what happens to the percentage amount?","back":"It is added to the original.","mcqOptions":[{"text":"It is added to the original.","correct":true,"explanation":"A percentage increase first finds a percentage of the original amount, then adds that amount to the original. This produces a new value greater than the starting value."},{"text":"It is subtracted from the original.","correct":false,"explanation":"Subtracting the percentage amount describes a percentage decrease, not an increase. For an increase, the calculated percentage amount must be added to the original."},{"text":"It is divided by the original.","correct":false,"explanation":"Division can help compare two quantities, but it does not apply a percentage increase. The percentage amount is calculated and then added to the original value."},{"text":"It is replaced by the original.","correct":false,"explanation":"Replacing the percentage amount with the original does not change the value or represent an increase. The percentage amount must be added to the original."}]},{"id":"cfa80392-76a3-e00f-1648-17b850d2d32a","cardType":"basic","points":2,"front":"A coat costs £45 and is reduced by 20%. What is the sale price?","back":"£36.","mcqOptions":[{"text":"£36.","correct":true,"explanation":"The discount is $20\\% \\times £45 = £9$. Subtracting it from the original price gives the sale price: $£45 - £9 = £36$."},{"text":"£9.","correct":false,"explanation":"This is only the value of the 20% discount, not the sale price. Subtract the £9 discount from £45 to obtain a sale price of £36."},{"text":"£54.","correct":false,"explanation":"Adding £9 applies a 20% increase rather than a reduction. The £9 discount must be subtracted from £45, giving the correct sale price of £36."},{"text":"£25.","correct":false,"explanation":"Subtracting 20 directly from £45 confuses 20% with £20. The discount is 20% of £45, which is £9, so the sale price is £36."}]},{"id":"fdf65941-a373-6e62-3087-1e1a18e301ec","cardType":"basic","points":1,"front":"After paying a deposit, how do you find the amount left to pay?","back":"Subtract the deposit from the total cost.","mcqOptions":[{"text":"Subtract the deposit from the total cost.","correct":true,"explanation":"The deposit has already been paid towards the purchase, so deducting it from the total cost gives the remaining amount that still needs to be paid."},{"text":"Add the deposit to the total cost.","correct":false,"explanation":"Adding the deposit counts that payment on top of the full price. The amount left is found by subtracting the deposit from the total cost."},{"text":"Subtract the total cost from the deposit.","correct":false,"explanation":"This reverses the subtraction and would usually produce a negative value. Subtract the deposit from the total cost to find the outstanding amount."},{"text":"Divide the total cost by the deposit.","correct":false,"explanation":"Division would compare the total cost with the deposit rather than find a remaining balance. Subtract the deposit from the total cost instead."}]},{"id":"94a1d35b-51f1-fdda-2332-b2f362c8a307","cardType":"basic","points":1,"front":"For 6 cans in a "buy 2 get 1 free" offer, how many cans are paid for?","back":"4 cans.","mcqOptions":[{"text":"4 cans.","correct":true,"explanation":"Each group of three cans contains two paid cans and one free can. Six cans form two groups, so four cans are paid for."},{"text":"3 cans.","correct":false,"explanation":"This treats every second can as free, like a buy one get one free offer. Here, two of every three cans are paid for, giving four."},{"text":"5 cans.","correct":false,"explanation":"This counts only one free can across the whole purchase. Six cans make two groups of three, so two are free and four are paid for."},{"text":"6 cans.","correct":false,"explanation":"This ignores the offer and charges for every can. Two groups qualify for one free can each, leaving four cans to be paid for."}]},{"id":"59f04dbb-bbac-a2b7-9cab-6c3ffea2ea61","cardType":"cloze","points":null,"front":"Simple interest is worked out from the [ ] each year.","back":"Simple interest is worked out from the original amount each year.","mcqOptions":[{"text":"original amount","correct":true,"explanation":"Simple interest is calculated each year using the initial principal only. Previous interest is not added to the amount used in later interest calculations."},{"text":"current balance","correct":false,"explanation":"Using the current balance means interest is calculated on previously earned interest, which describes compound interest. Simple interest always uses the original amount."},{"text":"interest earned","correct":false,"explanation":"Interest is not calculated from the interest already earned. For simple interest, the same percentage of the original amount is added each year."},{"text":"final amount","correct":false,"explanation":"The final amount is only known after the interest has been calculated and added. Simple interest is worked out from the original amount each year."}]},{"id":"38aa1fda-7e49-f07e-b644-0220fe444702","cardType":"basic","points":2,"front":"£600 is invested for 4 years at 1.5% simple interest per year. What is the total interest?","back":"£36.","mcqOptions":[{"text":"£36.","correct":true,"explanation":"One year’s interest is $600\\times0.015=£9$. Simple interest adds the same £9 each year, so over four years the total is $4\\times£9=£36$."},{"text":"£9.","correct":false,"explanation":"This is only one year’s interest, found from $600\\times0.015$. Multiplying the annual £9 by four years gives the correct total interest of £36."},{"text":"£24.","correct":false,"explanation":"This effectively uses 1% per year instead of the stated 1.5%. At 1.5%, the annual interest is £9, giving £36 over four years."},{"text":"£360.","correct":false,"explanation":"This treats 1.5% as 15%, making the interest ten times too large. Using $1.5\\%=0.015$ gives £9 per year and £36 altogether."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Percentages","title":"Percentages Flashcards","topbar":{"backHref":"/gcse/maths/ocr/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"77e84631-da25-4c98-9472-e2936a51205f","walled":"$L38"}],"$L39","$L3a"]