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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/aqa/grade-3-3-8-percentage-change/flashcards","label":"Percentage Change","subjectCode":"gcse_maths__aqa","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"621e95f2-a8da-0331-ba41-00fdf35ba74c","title":"Percentage Change Flashcards","topicId":"e52e88e1-2e3e-4067-a30a-f6ab93d24a52","topicSlug":"grade-3-3-8-percentage-change","cards":[{"id":"bf38058f-c12f-51e4-ea33-c36337045079","cardType":"basic","points":1,"front":"What does the term percentage literally mean?","back":"Out of 100.","mcqOptions":[{"text":"Out of 100.","correct":true,"explanation":"Percentage means “per hundred”, so a percentage expresses an amount as a number of parts out of 100."},{"text":"Out of 10.","correct":false,"explanation":"This confuses percentages with tenths. The word percentage means “per hundred”, so it describes an amount out of 100."},{"text":"Out of 1000.","correct":false,"explanation":"An amount out of 1000 is expressed in thousandths, not as a percentage. Percentage literally means an amount out of 100."},{"text":"Out of 1.","correct":false,"explanation":"An amount out of 1 is a decimal proportion. A percentage rescales that proportion so that it is expressed out of 100."}]},{"id":"2caadf05-3a5b-753d-b17f-1a889c0772f3","cardType":"cloze","points":null,"front":"The formula for percentage change is: $$\\text{percentage change} = \\frac{\\text{[...]}}{\\text{original value}} \\times 100$$","back":"The formula for percentage change is: $$\\text{percentage change} = \\frac{\\boxed{\\text{change}}}{\\text{original value}} \\times 100$$","mcqOptions":[{"text":"$$\\text{change}$","correct":true,"explanation":"Percentage change compares the amount of change with the original value, so the change must be placed in the numerator."},{"text":"$$\\text{new value}$","correct":false,"explanation":"Using the new value gives its size relative to the original, not the percentage change. The numerator must be the change between the two values."},{"text":"$$\\text{original value}$","correct":false,"explanation":"Putting the original value in both numerator and denominator would always produce 100%. The numerator must instead be the change."},{"text":"$$\\text{sum of values}$","correct":false,"explanation":"Adding the original and new values does not measure how much the value changed. The numerator must be the difference, called the change."}]},{"id":"f0005d33-43e1-26a8-5338-bdccb83510a7","cardType":"cloze","points":null,"front":"The formula for percentage change is: $$\\text{percentage change} = \\frac{\\text{change}}{\\text{[...]}} \\times 100$$","back":"The formula for percentage change is: $$\\text{percentage change} = \\frac{\\text{change}}{\\boxed{\\text{original value}}} \\times 100$$","mcqOptions":[{"text":"$$\\text{original value}$","correct":true,"explanation":"The original value is the comparison base, so percentage change is calculated by dividing the change by the original value and multiplying by 100."},{"text":"$$\\text{new value}$","correct":false,"explanation":"Using the new value as the denominator compares the change with the final amount. Percentage change must use the original value as its base."},{"text":"$$\\text{change}$","correct":false,"explanation":"Dividing the change by itself would give 1 and therefore 100%, regardless of the values. The denominator must be the original value."},{"text":"$$\\text{average value}$","correct":false,"explanation":"Using the average of the original and new values calculates a different type of relative difference. Standard percentage change uses the original value."}]},{"id":"0c84ecc8-513f-6fd9-aea7-2120da17c16b","cardType":"basic","points":1,"front":"When calculating percentage change, which value is used as the denominator (base)?","back":"The original value.","mcqOptions":[{"text":"The original value.","correct":true,"explanation":"Percentage change measures the change relative to the starting amount, so the original value is always used as the denominator."},{"text":"The new value.","correct":false,"explanation":"The new value is the final amount, not the comparison base. Percentage change divides by the original value from before the change occurred."},{"text":"The difference value.","correct":false,"explanation":"The difference is the change and belongs in the numerator. The denominator is the original value because it provides the comparison base."},{"text":"The average value.","correct":false,"explanation":"Averaging the original and new values gives a different relative-change measure. GCSE percentage change uses the original value as the denominator."}]},{"id":"ade67fd2-3894-6716-dcb9-fc1b1822289c","cardType":"basic","points":1,"front":"How do you calculate the change in a percentage change problem?","back":"The difference between the original and new values.","mcqOptions":[{"text":"The difference between the original and new values.","correct":true,"explanation":"The change is the amount separating the original and new values, found by subtracting one from the other and taking the appropriate increase or decrease."},{"text":"The sum of the original and new values.","correct":false,"explanation":"Adding the values finds their combined total, not how much one changed into the other. The change is their difference."},{"text":"The ratio between the original and new values.","correct":false,"explanation":"A ratio compares the relative sizes of the values but does not directly give the amount of change. The change is their difference."},{"text":"The average of the original and new values.","correct":false,"explanation":"The average gives a midpoint between the two values, not the distance between them. The change is found from their difference."}]},{"id":"190b7189-d1fb-d2a7-af1a-98b0a9807587","cardType":"basic","points":2,"front":"How can you determine if a change is a percentage increase or decrease?","back":"

Increase: new value is bigger than original.
Decrease: new value is smaller than original.

","mcqOptions":[{"text":"

Increase: new value is bigger than original.
Decrease: new value is smaller than original.

","correct":true,"explanation":"An increase moves from a smaller original value to a larger new value, while a decrease moves from a larger original value to a smaller new value."},{"text":"

Increase: new value is smaller than original.
Decrease: new value is bigger than original.

","correct":false,"explanation":"This reverses the two directions. A larger new value means an increase, while a smaller new value means a decrease."},{"text":"

Increase: new value is equal to original.
Decrease: new value is smaller than original.

","correct":false,"explanation":"Equal original and new values represent no change, not an increase. An increase requires the new value to be bigger than the original."},{"text":"

Increase: new value is bigger than original.
Decrease: new value is equal to original.

","correct":false,"explanation":"Equal values represent no change, not a decrease. A decrease occurs only when the new value is smaller than the original."}]},{"id":"5ab8ac88-db23-050a-6b10-476d376d382e","cardType":"basic","points":1,"front":"What is the common mistake made when selecting the denominator for percentage change?","back":"Dividing by the new value instead of the original.","mcqOptions":[{"text":"Dividing by the new value instead of the original.","correct":true,"explanation":"Students often use the final value as the comparison base. Percentage change must instead compare the change with the original value."},{"text":"Dividing by the original value instead of the new.","correct":false,"explanation":"This incorrectly labels the correct method as a mistake. The original value is the required denominator, while using the new value is the common error."},{"text":"Dividing by the change value instead of the original.","correct":false,"explanation":"The change belongs in the numerator, so using it as the denominator is structurally wrong. The commonly tested denominator error is using the new value."},{"text":"Dividing by the larger value instead of the original.","correct":false,"explanation":"The denominator is not chosen according to which value is larger. The specific common mistake is automatically using the new value rather than the original."}]},{"id":"a64b0ab1-a3ba-04c3-1e72-6f76a5b347cf","cardType":"cloze","points":null,"front":"In profit and loss questions, the original value is always the [ ].","back":"In profit and loss questions, the original value is always the cost price.","mcqOptions":[{"text":"cost price","correct":true,"explanation":"Profit or loss is measured relative to what the item originally cost, so the cost price is the original value used as the denominator."},{"text":"selling price","correct":false,"explanation":"The selling price is the new value received after the transaction. The original value is the cost price paid for the item."},{"text":"profit amount","correct":false,"explanation":"Profit is the positive difference between selling price and cost price, not the original value. The original value is the cost price."},{"text":"loss amount","correct":false,"explanation":"Loss is the difference when the selling price is below the cost price, not the starting value. The original value is the cost price."}]},{"id":"5609baee-6e9b-d91d-4bb6-14773aa96dfe","cardType":"basic","points":2,"front":"In business terms, what is the difference between cost price and selling price?","back":"

Cost price: amount paid to buy/make an item.
Selling price: amount received when selling the item.

","mcqOptions":[{"text":"

Cost price: amount paid to buy/make an item.
Selling price: amount received when selling the item.

","correct":true,"explanation":"Cost price records what the item costs the business, while selling price records the amount paid by the customer when the business sells it."},{"text":"

Cost price: amount received when selling an item.
Selling price: amount paid to buy/make the item.

","correct":false,"explanation":"This reverses the two definitions. Cost price is the amount paid to obtain or make the item, while selling price is the amount received from its sale."},{"text":"

Cost price: amount of profit made on an item.
Selling price: amount lost when selling the item.

","correct":false,"explanation":"Profit and loss are differences between prices, not definitions of the prices themselves. Cost price is paid to obtain the item, and selling price is received from selling it."},{"text":"

Cost price: amount shown on an item’s price label.
Selling price: amount spent advertising the item.

","correct":false,"explanation":"A price label usually shows the intended selling price, while advertising is a separate expense. Cost price is paid to obtain the item, and selling price is received from selling it."}]},{"id":"2c206b0e-f568-7530-d53d-14a249e6788e","cardType":"basic","points":2,"front":"What determines if a transaction has resulted in a profit or a loss?","back":"

Profit: Selling price is bigger than cost price.
Loss: Selling price is smaller than cost price.

","mcqOptions":[{"text":"

Profit: Selling price is bigger than cost price.
Loss: Selling price is smaller than cost price.

","correct":true,"explanation":"A business gains money when it sells for more than the item cost, creating a profit. Selling for less than the cost creates a loss."},{"text":"

Profit: Selling price is smaller than cost price.
Loss: Selling price is bigger than cost price.

","correct":false,"explanation":"The relationships have been reversed. Profit occurs when selling price is bigger than cost price, while a smaller selling price means the business has made a loss."},{"text":"

Profit: Selling price is equal to cost price.
Loss: Selling price is bigger than cost price.

","correct":false,"explanation":"Equal prices produce neither profit nor loss, and selling above cost produces profit. A loss occurs only when selling price is smaller than cost price."},{"text":"

Profit: Selling price is smaller than cost price.
Loss: Selling price is equal to cost price.

","correct":false,"explanation":"Selling below cost creates a loss, not a profit, while equal prices break even. Profit requires the selling price to be bigger than the cost price."}]},{"id":"430c0c51-7113-d4b7-bc50-50c98ec32f4e","cardType":"cloze","points":null,"front":"To convert kilograms (kg) to grams (g), you must multiply by [ ].","back":"To convert kilograms (kg) to grams (g), you must multiply by 1000.","mcqOptions":[{"text":"1000","correct":true,"explanation":"One kilogram contains 1000 grams, so multiplying the number of kilograms by 1000 gives the equivalent mass in grams."},{"text":"100","correct":false,"explanation":"This underestimates the conversion by a factor of 10, often from confusing kilograms with another metric step. One kilogram equals 1000 grams, so multiply by 1000."},{"text":"10","correct":false,"explanation":"This moves only one place in the metric scale and gives a result 100 times too small. One kilogram equals 1000 grams, so the multiplier is 1000."},{"text":"0.001","correct":false,"explanation":"This uses the conversion for grams to kilograms in the wrong direction. Converting kilograms to the smaller unit of grams requires multiplying by 1000."}]},{"id":"e4a731d5-4f48-44dd-ad1d-6248df21f6b7","cardType":"cloze","points":null,"front":"To convert pence (p) to pounds (£), you must divide by [ ].","back":"To convert pence (p) to pounds (£), you must divide by 100.","mcqOptions":[{"text":"100","correct":true,"explanation":"There are 100 pence in one pound, so dividing an amount in pence by 100 converts it to the equivalent amount in pounds."},{"text":"10","correct":false,"explanation":"Dividing by 10 moves the decimal point only one place and makes the pound value ten times too large. Since £1 equals 100p, divide by 100."},{"text":"1000","correct":false,"explanation":"This confuses the currency conversion with conversions such as kilograms to grams. There are 100 pence in a pound, so pence must be divided by 100."},{"text":"0.01","correct":false,"explanation":"Dividing by 0.01 is equivalent to multiplying by 100, so it converts in the wrong direction. To change pence into pounds, divide by 100."}]},{"id":"f5fbaa49-897c-1e9b-108c-f66c164ed11d","cardType":"basic","points":1,"front":"If a question involves costs in pounds and sales in pence, what must you do first?","back":"Convert the units to be the same (e.g., all into pounds).","mcqOptions":[{"text":"Convert the units to be the same (e.g., all into pounds).","correct":true,"explanation":"Amounts must use a common unit before they can be compared or used together reliably. For example, convert all pence amounts into pounds before calculating profit or loss."},{"text":"Round both amounts to the nearest whole unit first.","correct":false,"explanation":"Rounding does not resolve the mismatch between pounds and pence and may reduce accuracy. First convert both amounts into the same unit, such as pounds."},{"text":"Add the pounds and pence values together immediately.","correct":false,"explanation":"Adding the numerical values directly treats pounds and pence as equivalent units, producing an invalid result. Convert both amounts into the same unit before calculating."},{"text":"Compare the numbers without changing either unit first.","correct":false,"explanation":"The numerical sizes are not directly comparable because one pound equals 100 pence. Convert both amounts into the same unit before making the comparison."}]},{"id":"ea089c25-b563-c219-80e0-356439d842c2","cardType":"basic","points":2,"front":"A coat reduced from £80 to £60 has a £20 reduction. What is the calculation for the percentage reduction?","back":"$$$\\frac{20}{80} \\times 100$$","mcqOptions":[{"text":"$$$\\frac{20}{80} \\times 100$$","correct":true,"explanation":"Percentage reduction compares the £20 decrease with the original £80 price. Dividing the reduction by the original amount and multiplying by 100 gives 25%."},{"text":"$$$\\frac{20}{60} \\times 100$$","correct":false,"explanation":"This uses the reduced price as the denominator, a common percentage-change error. The reduction must be compared with the original £80 price, giving $\\frac{20}{80}\\times 100$."},{"text":"$$$\\frac{60}{80} \\times 100$$","correct":false,"explanation":"This calculates the reduced price as a percentage of the original price, giving 75%, rather than the percentage reduction. Use $\\frac{20}{80}\\times 100$ for the 25% decrease."},{"text":"$$$\\frac{80}{20} \\times 100$$","correct":false,"explanation":"This reverses the fraction by dividing the original price by the reduction. Percentage reduction requires reduction divided by original price, so use $\\frac{20}{80}\\times 100$."}]},{"id":"2c7fb448-2037-d888-aae5-2929cd64abb9","cardType":"basic","points":1,"front":"Why should you avoid rounding values halfway through a multi-step calculation?","back":"It can make the final answer inaccurate.","mcqOptions":[{"text":"It can make the final answer inaccurate.","correct":true,"explanation":"Rounding removes precision, and the resulting small error can be carried through later steps and enlarged. Keep full calculator values until the final answer, then round as required."},{"text":"It can make the final answer more accurate.","correct":false,"explanation":"Rounding early removes useful digits rather than improving accuracy, so errors can accumulate through later steps. Keep the unrounded values until the final stage of the calculation."},{"text":"It can make the final answer exact.","correct":false,"explanation":"A rounded value is an approximation, not an exact value. Using that approximation in further calculations can make the final answer inaccurate, so round only at the end."},{"text":"It cannot affect the final answer at all.","correct":false,"explanation":"Intermediate rounding errors can carry through and alter the final result, especially over several steps. Retaining full calculator values until the end keeps the answer more accurate."}]},{"id":"89182e8b-3ff6-423d-dfdc-078ce39ae570","cardType":"cloze","points":null,"front":"A decimal place refers to the number of digits [ ] the decimal point.","back":"A decimal place refers to the number of digits after the decimal point.","mcqOptions":[{"text":"after","correct":true,"explanation":"Decimal places count digits to the right of the decimal point. For example, $3.142$ has three decimal places because three digits appear after the point."},{"text":"before","correct":false,"explanation":"Digits before the decimal point form the whole-number part and are not decimal places. Decimal places are counted using the digits after the decimal point."},{"text":"around","correct":false,"explanation":"Decimal places are not counted on both sides or generally around the point. Only digits after the decimal point determine the number of decimal places."},{"text":"including","correct":false,"explanation":"The decimal point is a separator rather than a digit, so it is not included in the count. Decimal places count only the digits after the point."}]},{"id":"061753bf-c4c6-46f5-14b0-5a0b30e9b9d1","cardType":"cloze","points":null,"front":"Significant figures start counting from the [ ] digit.","back":"Significant figures start counting from the first non-zero digit.","mcqOptions":[{"text":"first non-zero","correct":true,"explanation":"Leading zeros only show place value and are not significant, so counting begins at the first digit that is not zero."},{"text":"first zero","correct":false,"explanation":"Starting at the first zero would count placeholder zeros, which are not significant. The correct rule is to begin with the first non-zero digit."},{"text":"last non-zero","correct":false,"explanation":"Starting from the end can omit earlier significant digits. Significant figures are counted from the first non-zero digit, moving from left to right."},{"text":"first decimal","correct":false,"explanation":"The decimal point does not determine where significant figures begin. Counting starts at the first non-zero digit, whether it appears before or after the decimal point."}]},{"id":"cea60c4f-d63f-0f18-3a02-4277cf6a15d4","cardType":"basic","points":1,"front":"Which value is the original if a price changes from £60 last year to £75 this year?","back":"£60.","mcqOptions":[{"text":"£60.","correct":true,"explanation":"The original value is the starting amount before the change. Since the price was £60 last year and later became £75, £60 is the original."},{"text":"£75.","correct":false,"explanation":"£75 is the new value after the price changed, not the original value. The original price is the earlier amount, £60."},{"text":"£15.","correct":false,"explanation":"£15 is the amount of the increase, found by subtracting £60 from £75. The original value is the starting price of £60."},{"text":"£135.","correct":false,"explanation":"£135 comes from adding the old and new prices, which does not identify the original value. The original is the earlier price of £60."}]},{"id":"fff2597b-9157-daaf-3b2a-ac70e1433928","cardType":"basic","points":1,"front":"Aisha buys a flat for £185,000 and sells for £199,800. What is the first step to find the percentage profit?","back":"Subtract £185,000 from £199,800 to find the actual profit (£14,800).","mcqOptions":[{"text":"Subtract £185,000 from £199,800 to find the actual profit (£14,800).","correct":true,"explanation":"Actual profit is the selling price minus the buying price. Subtracting £185,000 from £199,800 gives £14,800 before it is expressed as a percentage of the original price."},{"text":"Subtract £199,800 from £185,000 to find the actual loss (-£14,800).","correct":false,"explanation":"Reversing the subtraction produces a negative value and wrongly describes the sale as a loss. The selling price exceeds the buying price, so the actual profit is £14,800."},{"text":"Add £185,000 to £199,800 to find the total value (£384,800).","correct":false,"explanation":"Adding the buying and selling prices does not measure the change. The first step is to subtract £185,000 from £199,800, giving an actual profit of £14,800."},{"text":"Subtract £14,800 from £185,000 to find the sale price (£170,200).","correct":false,"explanation":"This subtracts the profit from the buying price and therefore moves in the wrong direction. First find the profit by calculating £199,800 - £185,000 = £14,800."}]},{"id":"5b18fadc-a898-9706-7571-d6a4467dba91","cardType":"basic","points":2,"front":"List the four labels that should be used to finish a percentage change answer.","back":"

Increase
Decrease
Profit
Loss

","mcqOptions":[{"text":"

Increase
Decrease
Profit
Loss

","correct":true,"explanation":"A percentage change answer needs a label showing its direction and context. The appropriate concluding labels are increase, decrease, profit and loss."},{"text":"

Original
Final
Change
Multiplier

","correct":false,"explanation":"These terms identify quantities or methods used during percentage calculations, not labels for the final result. The required labels are increase, decrease, profit and loss."},{"text":"

Add
Subtract
Multiply
Divide

","correct":false,"explanation":"These are mathematical operations rather than labels describing a percentage change. A finished answer should be labelled as an increase, decrease, profit or loss."},{"text":"

Fraction
Decimal
Percentage
Ratio

","correct":false,"explanation":"These are ways of representing or comparing values, but they do not describe the outcome of a change. The four concluding labels are increase, decrease, profit and loss."}]},{"id":"7af2f711-53ca-95e6-6ebf-0dbd3566abe3","cardType":"basic","points":2,"front":"A car was £12,500 and sold for £9,800. What is the calculation for the percentage loss?","back":"$$$\\frac{12500 - 9800}{12500} \\times 100$$","mcqOptions":[{"text":"$$$\\frac{12500 - 9800}{12500} \\times 100$$","correct":true,"explanation":"The loss is the original price minus the selling price, and percentage loss is measured against the original price. Therefore the £2,700 loss is divided by £12,500."},{"text":"$$$\\frac{12500 - 9800}{9800} \\times 100$$","correct":false,"explanation":"This uses the selling price as the denominator, a common percentage-change error. Percentage loss must be based on the original price, so the denominator should be 12,500."},{"text":"$$$\\frac{12500 + 9800}{12500} \\times 100$$","correct":false,"explanation":"Adding the two prices finds their combined value rather than the loss. The loss is found by subtraction, so the numerator should be $12500 - 9800$."},{"text":"$$$\\frac{9800 - 12500}{12500} \\times 100$$","correct":false,"explanation":"Reversing the subtraction makes the result negative. For percentage loss, calculate the positive amount lost using $12500 - 9800$, then divide by the original price."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Percentage Change","title":"Percentage Change Flashcards","topbar":{"backHref":"/gcse/maths/aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"e52e88e1-2e3e-4067-a30a-f6ab93d24a52","walled":"$L39"}],"$L3a","$L3b"]