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Reverse percentage calculations therefore reconstruct the original by dividing the final amount by the appropriate multiplier."},{"text":"The new amount.","correct":false,"explanation":"Using the new amount as the percentage base reverses the relationship incorrectly. The percentage change is based on the original amount, before any increase or decrease occurs."},{"text":"The amount of change.","correct":false,"explanation":"The amount of change is found from the percentage and the original value; it is not the base itself. The percentage change is based on the original amount."},{"text":"The percentage multiplier.","correct":false,"explanation":"The multiplier represents the combined original proportion and change, rather than the amount used as the percentage base. Percentage change is always based on the original amount."}]},{"id":"8d739cb0-2bc0-7626-c285-f24e39345a09","cardType":"basic","points":1,"front":"A price increases by 8%. What multiplier is used?","back":"1.08","mcqOptions":[{"text":"1.08","correct":true,"explanation":"An 8% increase means the new price is 108% of the original. Converting 108% to a decimal gives the multiplier $1.08$."},{"text":"1.8","correct":false,"explanation":"This treats 8% as 80%, producing an 80% increase. An 8% increase leaves 108% of the original, so the correct multiplier is $1.08$."},{"text":"0.92","correct":false,"explanation":"Subtracting 8% from 100% gives the multiplier for an 8% decrease. An increase requires adding 8%, giving 108% or $1.08$."},{"text":"1.008","correct":false,"explanation":"This converts 8% as though it were 0.8%, placing the decimal one position too far left. Adding $0.08$ to 1 gives $1.08$."}]},{"id":"63a4d9c1-05e0-b8ed-b7b8-e318e150deb7","cardType":"basic","points":1,"front":"A price decreases by 20%. What multiplier is used?","back":"0.80","mcqOptions":[{"text":"0.80","correct":true,"explanation":"A 20% decrease leaves 80% of the original price. Converting 80% to a decimal gives the multiplier $0.80$."},{"text":"1.20","correct":false,"explanation":"Adding 20% to 100% gives the multiplier for an increase, not a decrease. A 20% decrease leaves 80%, so the multiplier is $0.80$."},{"text":"0.20","correct":false,"explanation":"This uses the proportion removed rather than the proportion remaining. After a 20% decrease, 80% remains, so the required multiplier is $0.80$."},{"text":"0.98","correct":false,"explanation":"This treats 20% as 2%, a decimal-place conversion error. Subtracting $0.20$ from 1 gives the correct decrease multiplier of $0.80$."}]},{"id":"6ca61bd5-bff1-3c73-f116-6c464ba1ebac","cardType":"cloze","points":null,"front":"For a percentage increase, the multiplier is [ ].","back":"For a percentage increase, the multiplier is bigger than 1.","mcqOptions":[{"text":"bigger than 1","correct":true,"explanation":"An increase leaves more than 100% of the original amount. Since 100% corresponds to 1, any percentage increase has a multiplier bigger than 1."},{"text":"smaller than 1","correct":false,"explanation":"A multiplier smaller than 1 leaves less than the original and therefore represents a percentage decrease. An increase requires a multiplier bigger than 1."},{"text":"equal to 1","correct":false,"explanation":"A multiplier equal to 1 leaves the amount unchanged because it represents exactly 100%. A percentage increase needs a multiplier bigger than 1."},{"text":"smaller than 0","correct":false,"explanation":"A negative multiplier would generally produce a negative result, not an ordinary percentage increase. An increase produces more than 100% of the original, so its multiplier is bigger than 1."}]},{"id":"73ef09b3-1fdc-50ae-2d5f-93cdd9d2b530","cardType":"cloze","points":null,"front":"For a percentage decrease, the multiplier is [ ].","back":"For a percentage decrease, the multiplier is smaller than 1.","mcqOptions":[{"text":"smaller than 1","correct":true,"explanation":"A decrease leaves less than 100% of the original amount. Since 100% corresponds to 1, the multiplier for a percentage decrease is smaller than 1."},{"text":"bigger than 1","correct":false,"explanation":"A multiplier bigger than 1 produces more than the original amount and therefore represents an increase. A decrease requires a multiplier smaller than 1."},{"text":"equal to 1","correct":false,"explanation":"Multiplying by 1 leaves the amount unchanged, so it represents neither an increase nor a decrease. A percentage decrease uses a multiplier smaller than 1."},{"text":"smaller than 0","correct":false,"explanation":"A standard percentage decrease leaves a non-negative proportion of the original, not a negative amount. Its multiplier is smaller than 1 but normally at least 0."}]},{"id":"d4f2b94b-616c-af5f-6dd9-a8a13532172a","cardType":"basic","points":1,"front":"What is the multiplier for a 5% increase?","back":"1.05","mcqOptions":[{"text":"1.05","correct":true,"explanation":"A 5% increase makes the new amount 105% of the original. Dividing 105 by 100 converts this to the multiplier $1.05$."},{"text":"0.95","correct":false,"explanation":"Subtracting 5% from 100% gives the multiplier for a 5% decrease. For an increase, add 5% to obtain 105%, or $1.05$."},{"text":"1.50","correct":false,"explanation":"This treats 5% as 50%, making the increase ten times too large. Five percent is $0.05$, so the correct multiplier is $1.05$."},{"text":"1.005","correct":false,"explanation":"This converts 5% as 0.5%, placing the decimal one position too far left. Five percent is $0.05$, giving a multiplier of $1.05$."}]},{"id":"bfa8e020-fd3f-1450-1df6-55cfdb76323f","cardType":"basic","points":1,"front":"What is the multiplier for a 30% decrease?","back":"0.70","mcqOptions":[{"text":"0.70","correct":true,"explanation":"A 30% decrease leaves 70% of the original amount. Converting 70% to a decimal gives the multiplier $0.70$."},{"text":"1.30","correct":false,"explanation":"Adding 30% to 100% gives the multiplier for a 30% increase. A 30% decrease leaves 70%, so the correct multiplier is $0.70$."},{"text":"0.30","correct":false,"explanation":"This uses the proportion removed instead of the proportion remaining. Subtracting 30% from 100% leaves 70%, giving the multiplier $0.70$."},{"text":"0.97","correct":false,"explanation":"This treats 30% as 3%, a decimal-place conversion error. Thirty percent is $0.30$, so subtracting it from 1 gives $0.70$."}]},{"id":"cd49fe91-6986-0a17-74bf-435ef02e863b","cardType":"basic","points":1,"front":"A 25% discount leaves what percentage of the original price?","back":"75%","mcqOptions":[{"text":"75%","correct":true,"explanation":"A 25% discount removes 25% of the original price. Subtracting this from 100% leaves 75% of the original price."},{"text":"25%","correct":false,"explanation":"This is the percentage removed by the discount, not the percentage remaining. Subtracting 25% from 100% shows that 75% of the original price is left."},{"text":"80%","correct":false,"explanation":"This would be the proportion remaining after a 20% discount, confusing 25% with one fifth. A 25% discount leaves $100\\%-25\\%=75\\%$."},{"text":"125%","correct":false,"explanation":"Adding 25% gives the result of a 25% increase rather than a discount. A discount subtracts 25% from 100%, leaving 75%."}]},{"id":"40b5e19e-3963-5ace-e890-bb80c107471c","cardType":"cloze","points":null,"front":"The forward percentage formula is [ ].","back":"The forward percentage formula is final = original × multiplier.","mcqOptions":[{"text":"final = original × multiplier","correct":true,"explanation":"A percentage multiplier converts the original amount directly into the final amount, so multiplying the original by the appropriate multiplier gives the value after the percentage change."},{"text":"final = original ÷ multiplier","correct":false,"explanation":"Dividing reverses a percentage change rather than applying it forwards. The forward formula is final = original × multiplier because the multiplier represents the proportion of the original remaining."},{"text":"original = final × multiplier","correct":false,"explanation":"This incorrectly multiplies the final amount when trying to identify the original. The forward relationship starts with the original: final = original × multiplier."},{"text":"final = multiplier ÷ original","correct":false,"explanation":"This reverses the division and does not produce an amount with meaningful units. The correct forward formula is final = original × multiplier."}]},{"id":"6f2d417d-0fd0-52b1-e14e-2ed472e421c5","cardType":"cloze","points":null,"front":"To find the original from a final amount, use [ ].","back":"To find the original from a final amount, use original = final ÷ multiplier.","mcqOptions":[{"text":"original = final ÷ multiplier","correct":true,"explanation":"The forward calculation multiplies the original by the multiplier, so its inverse divides the final amount by that same multiplier to recover the original."},{"text":"original = final × multiplier","correct":false,"explanation":"Multiplying repeats the percentage change instead of reversing it. To recover the starting value, use original = final ÷ multiplier."},{"text":"original = multiplier ÷ final","correct":false,"explanation":"This reverses the order of the division, producing a small ratio rather than the original amount. The final amount must be divided by the multiplier."},{"text":"original = final ÷ percentage","correct":false,"explanation":"Dividing by the stated percentage confuses the percentage change with the multiplier. Reverse percentages require original = final ÷ multiplier."}]},{"id":"84d41faa-a00f-2b7c-0e8a-bd92d67ac00b","cardType":"basic","points":1,"front":"If a final amount is given after a percentage change, what do you divide by?","back":"Divide by the multiplier.","mcqOptions":[{"text":"Divide by the multiplier.","correct":true,"explanation":"The final amount equals the original multiplied by the percentage multiplier, so dividing the final amount by that multiplier reverses the change and finds the original."},{"text":"Divide by the percentage change.","correct":false,"explanation":"The percentage change alone represents only the increase or decrease, not the final proportion. Divide by the multiplier, such as 1.05 or 0.80, to find the original."},{"text":"Divide by the original amount.","correct":false,"explanation":"The original amount is the unknown being calculated, so it cannot be the divisor. Divide the given final amount by the multiplier to recover the original."},{"text":"Divide by the final amount.","correct":false,"explanation":"Dividing by the final amount would produce a ratio rather than the original value. The final amount must instead be divided by the percentage multiplier."}]},{"id":"412506ba-5880-5b16-7887-f094976b43e4","cardType":"basic","points":2,"front":"A flat increases by 5% and is now £210,000. What was the original value?","back":"£200,000","mcqOptions":[{"text":"£200,000","correct":true,"explanation":"A 5% increase uses the multiplier 1.05. Dividing £210,000 by 1.05 gives £200,000, which is correctly smaller than the increased final value."},{"text":"£199,500","correct":false,"explanation":"Subtracting 5% of £210,000 treats the final value as the base, producing £199,500. Reverse the increase by calculating £210,000 ÷ 1.05 = £200,000."},{"text":"£220,500","correct":false,"explanation":"Adding another 5% applies a second increase and makes the value larger. The original is found by dividing £210,000 by 1.05, giving £200,000."},{"text":"£210,000","correct":false,"explanation":"This simply repeats the final value and ignores the 5% increase. Dividing £210,000 by the multiplier 1.05 gives the original value of £200,000."}]},{"id":"320abaf1-2ae0-c54f-88e8-ad9a67d07376","cardType":"basic","points":2,"front":"A game is reduced by 20% to £28. What was the normal price?","back":"£35","mcqOptions":[{"text":"£35","correct":true,"explanation":"A 20% reduction leaves 80% of the normal price, giving a multiplier of 0.8. Therefore, £28 ÷ 0.8 = £35."},{"text":"£33.60","correct":false,"explanation":"Adding 20% of £28 uses the reduced price as the percentage base. Since £28 represents 80% of the normal price, calculate £28 ÷ 0.8 = £35."},{"text":"£22.40","correct":false,"explanation":"Taking 20% off £28 applies the discount a second time rather than reversing it. Divide £28 by 0.8 to obtain the normal price of £35."},{"text":"£140","correct":false,"explanation":"Dividing by 0.2 treats £28 as the 20% discount rather than the remaining 80%. The correct calculation is £28 ÷ 0.8 = £35."}]},{"id":"d7019cd1-166b-ad32-ae33-fc51acb99ff0","cardType":"basic","points":1,"front":"After an increase, should the original be smaller or bigger than the final amount?","back":"Smaller than the final amount.","mcqOptions":[{"text":"Smaller than the final amount.","correct":true,"explanation":"An increase raises the original value to produce the final value. Therefore, the amount before the increase must be smaller than the amount afterwards."},{"text":"Bigger than the final amount.","correct":false,"explanation":"This reverses the direction of an increase. Because the final amount has grown from the original, the original must be smaller than the final amount."},{"text":"Equal to the final amount.","correct":false,"explanation":"Equal values would mean no change had occurred. After a genuine percentage increase, the original must be smaller than the final amount."},{"text":"Double the final amount.","correct":false,"explanation":"An increase does not generally imply that the starting value was double the result. The original must simply be smaller than the increased final amount."}]},{"id":"d13fb7b7-6502-fb7a-a78d-a44743f1c98f","cardType":"basic","points":1,"front":"After a decrease, should the original be smaller or bigger than the final amount?","back":"Bigger than the final amount.","mcqOptions":[{"text":"Bigger than the final amount.","correct":true,"explanation":"A decrease lowers the original value to produce the final value. Therefore, the amount before the decrease must be bigger than the amount afterwards."},{"text":"Smaller than the final amount.","correct":false,"explanation":"This reverses the direction of a decrease. Since the final amount has fallen from the original, the original must be bigger than the final amount."},{"text":"Equal to the final amount.","correct":false,"explanation":"Equal values would indicate that no decrease occurred. After a genuine percentage decrease, the original amount must be bigger than the final amount."},{"text":"Half the final amount.","correct":false,"explanation":"A decrease does not generally mean that the original was half the resulting amount. The original must instead be bigger than the decreased final amount."}]},{"id":"26afd194-21e8-7131-b9a6-bf0b2bf30bb2","cardType":"cloze","points":null,"front":"If the amount of change is given, use [ ].","back":"If the amount of change is given, use original = change ÷ percentage as a decimal.","mcqOptions":[{"text":"original = change ÷ percentage as a decimal","correct":true,"explanation":"The change equals the original multiplied by the percentage written as a decimal. Reversing this relationship means dividing the change by the decimal percentage."},{"text":"original = change × percentage as a decimal","correct":false,"explanation":"Multiplying calculates a percentage of the change rather than recovering the original. Since change = original × decimal percentage, use original = change ÷ percentage as a decimal."},{"text":"original = percentage as a decimal ÷ change","correct":false,"explanation":"This reverses the order of division and produces a ratio rather than an original amount. Divide the amount of change by the percentage written as a decimal."},{"text":"original = change ÷ percentage multiplier","correct":false,"explanation":"The multiplier represents the final proportion after a change, not the change itself. When the change amount is given, divide it by the percentage as a decimal."}]},{"id":"1de99a28-f3c6-8d42-b06c-426b116f6970","cardType":"basic","points":1,"front":"If a bill increased by 4% and the increase was £32, what is £32 as a percentage of the original?","back":"4% of the original.","mcqOptions":[{"text":"4% of the original.","correct":true,"explanation":"The stated 4% increase equals £32, so £32 represents 4% of the original bill. The original amount would therefore be £32 divided by 0.04."},{"text":"96% of the original.","correct":false,"explanation":"This confuses the remaining proportion with the increase. The £32 is the 4% increase itself, so it represents 4% of the original bill, not 96%."},{"text":"104% of the original.","correct":false,"explanation":"This treats the increase as the whole new bill. The new bill is 104% of the original, but £32 is only the increase, equal to 4% of the original."},{"text":"0.04% of the original.","correct":false,"explanation":"This converts 4% to the decimal 0.04 but incorrectly retains the percent sign. The £32 increase is 4% of the original bill."}]},{"id":"3e5d0551-68ed-bf32-c6eb-9354d1a39a31","cardType":"basic","points":2,"front":"A subscription increased by 6%, and the increase was £18. What was the original cost?","back":"£300","mcqOptions":[{"text":"£300","correct":true,"explanation":"The £18 increase represents 6% of the original cost. Dividing £18 by 0.06 gives an original subscription cost of £300."},{"text":"£318","correct":false,"explanation":"Adding the £18 increase to an assumed £300 original reverses the calculation incorrectly. Since £18 is 6% of the original, the original cost is £18 divided by 0.06, or £300."},{"text":"£30","correct":false,"explanation":"This treats £18 as though it were 60% rather than 6% of the original cost. Dividing £18 by 0.06 gives the correct original cost of £300."},{"text":"£108","correct":false,"explanation":"This result comes from using an incorrect percentage multiplier. Because £18 equals 6% of the original, one percent is £3 and 100% is £300."}]},{"id":"fd50a7f5-ada1-91d9-b4b1-a6a3cba6d205","cardType":"basic","points":2,"front":"A bag is reduced by 15%, and the discount is £9. What was the normal price?","back":"£60","mcqOptions":[{"text":"£60","correct":true,"explanation":"The £9 discount represents 15% of the normal price. Dividing £9 by 0.15 gives a normal price of £60."},{"text":"£51","correct":false,"explanation":"This is the sale price obtained after subtracting £9 from the normal price, not the normal price itself. Since £9 is 15%, the normal price is £60."},{"text":"£69","correct":false,"explanation":"This adds the discount to the correct normal price, producing neither the normal price nor the sale price. Dividing £9 by 0.15 gives the normal price of £60."},{"text":"£6","correct":false,"explanation":"This treats 15% as 1.5 when dividing, making the result ten times too small. Using 0.15 gives £9 divided by 0.15, which is £60."}]},{"id":"0407c61e-d95f-d090-5cf0-0c131169967c","cardType":"cloze","points":null,"front":"It is wrong to add 20% of the sale price after a 20% reduction because the 20% was taken from the [ ].","back":"It is wrong to add 20% of the sale price after a 20% reduction because the 20% was taken from the original price.","mcqOptions":[{"text":"original price","correct":true,"explanation":"A percentage reduction is calculated from the price before the reduction. Therefore, the removed 20% is 20% of the original price, not of the lower sale price."},{"text":"sale price","correct":false,"explanation":"The sale price is the amount remaining after the reduction, so it is only 80% of the starting amount. The 20% reduction was calculated from the original price."},{"text":"discount amount","correct":false,"explanation":"The discount amount is the value removed, not the base from which the percentage was calculated. The 20% reduction was taken from the original price."},{"text":"increased price","correct":false,"explanation":"There is no increased price in a reduction calculation; the price falls from its initial value. The 20% was calculated using the original price as the base."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Reverse Percentages","title":"Reverse Percentages Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L36"}]}],"topicId":"67d32641-fc77-4c13-b52f-063ce151af36","walled":"$L37"}],"$L38","$L39"]