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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/gcse/maths/aqa/grade-3-3-9-exchange-rates/flashcards","label":"Exchange Rates","subjectCode":"gcse_maths__aqa","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"13391b4c-e6b4-fe65-ce8c-2876b2546c5a","title":"Exchange Rates Flashcards","topicId":"3b7ac720-024f-4c6f-b34c-e2441871ff7c","topicSlug":"grade-3-3-9-exchange-rates","cards":[{"id":"5511b2c3-f485-be24-311b-09366828e308","cardType":"cloze","points":null,"front":"An exchange rate tells you how much one currency is worth in [ ].","back":"An exchange rate tells you how much one currency is worth in another currency.","mcqOptions":[{"text":"another currency","correct":true,"explanation":"An exchange rate compares the values of two currencies, expressing how much of another currency can be obtained for one unit of the first currency."},{"text":"the same currency","correct":false,"explanation":"An exchange rate compares two different currencies, not amounts within the same currency. It tells you how much one currency is worth in another currency."},{"text":"a percentage","correct":false,"explanation":"A percentage describes a proportion rather than a currency value. An exchange rate states how much one currency is worth in another currency."},{"text":"a bank account","correct":false,"explanation":"A bank account may hold currency, but it is not the comparison used by an exchange rate. The value is expressed in another currency."}]},{"id":"b54b6e66-485f-d3ee-3897-44ee8f2d248b","cardType":"basic","points":1,"front":"What does the exchange rate £1 = €1.16 mean?","back":"£1 is worth €1.16.","mcqOptions":[{"text":"£1 is worth €1.16.","correct":true,"explanation":"The rate places £1 on the left and its equivalent euro value on the right, so each pound can be exchanged for €1.16."},{"text":"€1 is worth £1.16.","correct":false,"explanation":"This swaps the currencies while keeping the same number, which does not preserve equivalent value. The given rate means £1 is worth €1.16."},{"text":"£1.16 is worth €1.","correct":false,"explanation":"This reverses the amounts and currencies shown in the rate. The original statement directly says that £1 has the same value as €1.16."},{"text":"£1 is worth €0.86.","correct":false,"explanation":"The value €0.86 is approximately the reciprocal rate for converting one euro into pounds. The stated rate means £1 is worth €1.16."}]},{"id":"07be9f3c-561b-3c42-9c0b-339b16e5149f","cardType":"cloze","points":null,"front":"When a rate starts with £1 and you change pounds into the other currency, [ ] by the rate.","back":"When a rate starts with £1 and you change pounds into the other currency, multiply by the rate.","mcqOptions":[{"text":"multiply","correct":true,"explanation":"Each pound is worth the stated number of units of the other currency, so multiplying the number of pounds by the rate gives the converted amount."},{"text":"divide","correct":false,"explanation":"Dividing would be appropriate when converting the other currency back into pounds. Starting with pounds at a £1-based rate requires multiplying by the rate."},{"text":"subtract","correct":false,"explanation":"An exchange rate is a scale factor, not an amount to remove. To change pounds into the other currency, multiply the pound amount by the rate."},{"text":"add","correct":false,"explanation":"Adding the rate treats it as a fixed currency amount rather than a value per pound. The correct operation is to multiply by the rate."}]},{"id":"ec7318b4-b6a2-fcf4-9f44-28c314c8a247","cardType":"cloze","points":null,"front":"If £1 = €1.18, changing euros into pounds means [ ] by 1.18.","back":"If £1 = €1.18, changing euros into pounds means dividing by 1.18.","mcqOptions":[{"text":"dividing","correct":true,"explanation":"The rate gives euros for each pound, so converting euros back into pounds requires the inverse operation: divide the euro amount by 1.18."},{"text":"multiplying","correct":false,"explanation":"Multiplying by 1.18 converts pounds into euros, not euros into pounds. For the reverse conversion, divide the euro amount by 1.18."},{"text":"adding","correct":false,"explanation":"Adding 1.18 ignores that an exchange rate is a multiplier relating two currencies. To find pounds from euros, divide by 1.18."},{"text":"subtracting","correct":false,"explanation":"Subtracting the rate treats 1.18 as a fixed amount rather than euros per pound. The correct reverse conversion is division by 1.18."}]},{"id":"83e450ef-004f-3f23-4d2b-85515d18a09d","cardType":"basic","points":1,"front":"How should £67.796... be rounded to the nearest penny?","back":"£67.80.","mcqOptions":[{"text":"£67.80.","correct":true,"explanation":"Rounding to the nearest penny means keeping two decimal places. The third decimal digit is 6, so the hundredths digit rounds up from 9, carrying to give £67.80."},{"text":"£67.79.","correct":false,"explanation":"This truncates the value instead of rounding it. Because the third decimal digit is 6, the second decimal place rounds up, giving £67.80."},{"text":"£67.796.","correct":false,"explanation":"This keeps three decimal places, but pounds and pence require two decimal places. Rounding using the third decimal digit gives £67.80."},{"text":"£68.00.","correct":false,"explanation":"This rounds to the nearest pound rather than the nearest penny. Keeping two decimal places and rounding correctly gives £67.80."}]},{"id":"0d677dd1-0d11-4e9b-0b60-de8980f32f35","cardType":"basic","points":2,"front":"Calculate £265 in euros if £1 = €1.18.","back":"265 × 1.18 = €312.70.","mcqOptions":[{"text":"265 × 1.18 = €312.70.","correct":true,"explanation":"The rate gives €1.18 for each pound, so £265 is multiplied by 1.18. This calculation gives €312.70."},{"text":"265 ÷ 1.18 = €224.58.","correct":false,"explanation":"Division reverses the conversion and would be used when changing euros into pounds. Converting £265 into euros requires multiplication, giving €312.70."},{"text":"265 × 1.18 = €312.07.","correct":false,"explanation":"The conversion operation is correct, but the decimal digits have been misplaced in the product. Calculating 265 × 1.18 accurately gives €312.70."},{"text":"265 + 1.18 = €266.18.","correct":false,"explanation":"Adding treats the exchange rate as a fixed amount rather than euros per pound. Multiply £265 by 1.18 to obtain €312.70."}]},{"id":"f9cb826f-190d-ef3a-52de-3dae574bff10","cardType":"basic","points":2,"front":"Calculate €80 in pounds if £1 = €1.18, to the nearest penny.","back":"80 ÷ 1.18 = £67.80.","mcqOptions":[{"text":"80 ÷ 1.18 = £67.80.","correct":true,"explanation":"The rate gives euros per pound, so euros are converted back into pounds by division. The result is £67.796..., which rounds to £67.80."},{"text":"80 × 1.18 = £94.40.","correct":false,"explanation":"Multiplication converts pounds into euros, so it uses the rate in the wrong direction here. Dividing €80 by 1.18 gives £67.80 to the nearest penny."},{"text":"80 ÷ 1.18 = £67.79.","correct":false,"explanation":"The division is correct, but the result has been truncated rather than rounded. Since £67.796... has a third decimal digit of 6, it rounds to £67.80."},{"text":"80 × 0.18 = £14.40.","correct":false,"explanation":"Using only the decimal part of the rate mistakes 1.18 for an 18% conversion. The full reverse calculation is 80 ÷ 1.18, giving £67.80."}]},{"id":"56433b98-a254-bb0d-64ea-370ad6d79645","cardType":"basic","points":1,"front":"If €1 = £0.87, what operation changes euros into pounds?","back":"Multiply by 0.87.","mcqOptions":[{"text":"Multiply by 0.87.","correct":true,"explanation":"The rate directly gives £0.87 for every euro, so multiplying the number of euros by 0.87 produces the equivalent amount in pounds."},{"text":"Divide by 0.87.","correct":false,"explanation":"Division would reverse the stated conversion and change pounds into euros. Since each euro equals £0.87, euros are converted into pounds by multiplying by 0.87."},{"text":"Add 0.87.","correct":false,"explanation":"Adding assumes the rate is a single fixed amount rather than an amount for every euro. The euro amount must be multiplied by 0.87."},{"text":"Multiply by 1.87.","correct":false,"explanation":"Adding 1 to the rate incorrectly treats £0.87 as an extra amount on top of every euro. The stated conversion factor is exactly 0.87."}]},{"id":"0904e20f-8b66-e4c5-b340-c1918604f65d","cardType":"basic","points":2,"front":"A meal costs €32. If €1 = £0.87, what is the cost in pounds?","back":"32 × 0.87 = £27.84.","mcqOptions":[{"text":"32 × 0.87 = £27.84.","correct":true,"explanation":"The rate gives £0.87 for each euro, so multiply the euro price by 0.87. This gives 32 × 0.87 = £27.84."},{"text":"32 ÷ 0.87 = £36.78.","correct":false,"explanation":"Dividing reverses the required conversion because the rate states the pound value of one euro. Multiply instead: 32 × 0.87 = £27.84."},{"text":"32 × 87 = £2784.","correct":false,"explanation":"This calculation treats 87 pence as £87 by omitting the decimal point. Using £0.87 per euro gives 32 × 0.87 = £27.84."},{"text":"32 × 0.87 = £27.13.","correct":false,"explanation":"The conversion operation is correct, but the multiplication has been evaluated inaccurately. Multiplying 32 by 0.87 gives £27.84, not £27.13."}]},{"id":"c2c1581c-2846-c45e-e7d5-f02c118d9c50","cardType":"cloze","points":null,"front":"In a cost such as £40 per night, per means [ ].","back":"In a cost such as £40 per night, per means for each.","mcqOptions":[{"text":"for each","correct":true,"explanation":"The word “per” associates a stated price or quantity with each single unit. Therefore, £40 per night means £40 for each night."},{"text":"for all","correct":false,"explanation":"“Per” describes the cost for one unit, not the combined cost for all units. The correct completion is “for each”, as in £40 for each night."},{"text":"in total","correct":false,"explanation":"“Per” gives a unit rate rather than an overall total. The correct term is “for each”, because the £40 charge applies to each separate night."},{"text":"less than","correct":false,"explanation":"“Per” does not express a comparison between two quantities. It means “for each”, so £40 per night is a charge of £40 for every individual night."}]},{"id":"2ea0a748-52e6-3a44-a4b4-350de5a2e1f5","cardType":"basic","points":1,"front":"In a multi-step exchange-rate question with a cost per night, what should you find before converting?","back":"Find the total starting-currency cost first.","mcqOptions":[{"text":"Find the total starting-currency cost first.","correct":true,"explanation":"Multiply the cost per night by the number of nights to obtain the complete cost in the original currency. Convert that total using the exchange rate."},{"text":"Find the average starting-currency cost first.","correct":false,"explanation":"An average is not needed when the cost per night and number of nights are known. Find the total starting-currency cost by multiplying them before converting."},{"text":"Find the total destination-currency cost first.","correct":false,"explanation":"The destination-currency total cannot be found before carrying out the conversion. First calculate the total starting-currency cost, then apply the exchange rate."},{"text":"Find the cheapest single-night cost first.","correct":false,"explanation":"Choosing a single-night cost ignores the full length of the stay. Multiply the nightly cost by the number of nights to find the total starting-currency cost first."}]},{"id":"d1274abe-ee31-a5af-86c3-baeb30eca0c4","cardType":"basic","points":1,"front":"A hotel costs ¥9000 per night for 5 nights. What is the total cost in yen?","back":"9000 × 5 = ¥45000.","mcqOptions":[{"text":"9000 × 5 = ¥45000.","correct":true,"explanation":"The ¥9000 charge applies to each of the 5 nights, so multiplication gives the total: 9000 × 5 = ¥45000."},{"text":"9000 + 5 = ¥9005.","correct":false,"explanation":"Adding 5 treats the number of nights as an extra yen amount. The hotel charges ¥9000 on each of 5 nights, so 9000 × 5 = ¥45000."},{"text":"9000 × 4 = ¥36000.","correct":false,"explanation":"This off-by-one error charges for only 4 nights rather than all 5. The correct calculation is 9000 × 5 = ¥45000."},{"text":"9000 ÷ 5 = ¥1800.","correct":false,"explanation":"Dividing finds one fifth of the nightly charge rather than the cost of 5 nights. Multiply instead: 9000 × 5 = ¥45000."}]},{"id":"52486574-ab18-4296-a34a-8734b789213e","cardType":"basic","points":2,"front":"Convert ¥45000 to pounds if £1 = ¥150.","back":"45000 ÷ 150 = £300.","mcqOptions":[{"text":"45000 ÷ 150 = £300.","correct":true,"explanation":"Since £1 corresponds to ¥150, divide the number of yen by 150 to find the number of pounds. Therefore, 45000 ÷ 150 = £300."},{"text":"45000 × 150 = £6750000.","correct":false,"explanation":"Multiplying uses the exchange rate in the wrong direction and makes the converted value far too large. Divide by 150 instead to obtain £300."},{"text":"45000 ÷ 15 = £3000.","correct":false,"explanation":"This drops a zero from the exchange rate and divides by 15 rather than 150. Using the stated rate gives 45000 ÷ 150 = £300."},{"text":"45000 ÷ 100 = £450.","correct":false,"explanation":"Dividing by 100 incorrectly treats ¥100 as equal to £1. The stated rate is ¥150 per pound, so 45000 ÷ 150 = £300."}]},{"id":"e82d37b3-d063-7491-0311-569f4c06d7ad","cardType":"cloze","points":null,"front":"To compare two prices, they must be in the [ ].","back":"To compare two prices, they must be in the same currency.","mcqOptions":[{"text":"same currency","correct":true,"explanation":"Currency amounts can be compared directly only when they use the same unit of money. Convert one or both prices so both are in the same currency."},{"text":"different currencies","correct":false,"explanation":"Prices in different currencies are not directly comparable because their numerical values use different monetary units. They must first be converted into the same currency."},{"text":"same country","correct":false,"explanation":"Being offered in the same country does not guarantee that prices use the same monetary unit. Direct comparison requires both prices to be in the same currency."},{"text":"same amount","correct":false,"explanation":"Prices do not need to have the same numerical amount to be compared. They need to be expressed in the same currency so their values are equivalent units."}]},{"id":"49680295-e78a-eae3-de7a-fbeddfce7c6a","cardType":"cloze","points":null,"front":"The difference between two prices is found by subtracting the [ ] price from the [ ] price.","back":"The difference between two prices is found by subtracting the smaller price from the larger price.","mcqOptions":[{"text":"The difference between two prices is found by subtracting the smaller price from the larger price.","correct":true,"explanation":"Subtracting the smaller value from the larger value gives a positive measure of the gap between them. This is the difference between the two prices."},{"text":"The difference between two prices is found by subtracting the larger price from the larger price.","correct":false,"explanation":"Subtracting the larger price from itself always gives zero, not the gap between two distinct prices. Subtract the smaller price from the larger price instead."},{"text":"The difference between two prices is found by subtracting the smaller price from the smaller price.","correct":false,"explanation":"Subtracting the smaller price from itself always produces zero. To find the actual difference, subtract the smaller of the two prices from the larger one."},{"text":"The difference between two prices is found by subtracting the larger price from the smaller price.","correct":false,"explanation":"This reverses the subtraction and produces a negative result rather than the usual positive difference. The smaller price should be subtracted from the larger price."}]},{"id":"b68aa5f1-6fd1-27b4-7922-4d48a5852872","cardType":"basic","points":2,"front":"Convert 3200 rupees to pounds if £1 = 80 rupees.","back":"3200 ÷ 80 = £40.","mcqOptions":[{"text":"3200 ÷ 80 = £40.","correct":true,"explanation":"Each pound is worth 80 rupees, so divide the rupee amount by 80 to find the pounds. Thus, 3200 ÷ 80 = £40."},{"text":"3200 × 80 = £256000.","correct":false,"explanation":"Multiplying applies the exchange rate in the wrong direction and makes the result much too large. Divide 3200 rupees by 80 to obtain £40."},{"text":"3200 ÷ 8 = £400.","correct":false,"explanation":"This drops a zero from the exchange rate and divides by 8 rather than 80, making the result ten times too large. The correct answer is £40."},{"text":"80 ÷ 3200 = £0.025.","correct":false,"explanation":"This reverses the division by dividing the rate by the amount being converted. Since there are 80 rupees per pound, calculate 3200 ÷ 80 = £40."}]},{"id":"51817888-e3ea-80ac-d3bf-706177b34d89","cardType":"basic","points":1,"front":"Trainers cost £40 in India and £45 in the UK. Which is cheaper?","back":"India is cheaper.","mcqOptions":[{"text":"India is cheaper.","correct":true,"explanation":"The trainers cost £40 in India and £45 in the UK. Since £40 is £5 less than £45, buying them in India is cheaper."},{"text":"The UK is cheaper.","correct":false,"explanation":"This reverses the comparison: the UK price is £45, whereas the Indian price is only £40. Therefore, India is cheaper by £5."},{"text":"Both countries cost the same.","correct":false,"explanation":"The prices are not equal because £40 and £45 differ by £5. The lower price is £40, so India is the cheaper country."},{"text":"India is more expensive.","correct":false,"explanation":"This confuses the lower price with the higher price. India’s price is £40 rather than £45, so India is cheaper, not more expensive."}]},{"id":"80bbe9f3-0b2a-c0c8-36cb-c11400e7fb12","cardType":"basic","points":1,"front":"What is the difference between £45 and £40?","back":"45 - 40 = £5.","mcqOptions":[{"text":"45 - 40 = £5.","correct":true,"explanation":"The difference is found by subtracting the smaller amount from the larger amount. Subtracting £40 from £45 gives a difference of £5."},{"text":"45 + 40 = £85.","correct":false,"explanation":"Adding finds the total of the two prices, not the difference between them. The difference is found using 45 - 40, which equals £5."},{"text":"45 - 40 = £15.","correct":false,"explanation":"This is a subtraction error, often caused by subtracting the tens and units incorrectly. Counting from £40 to £45 shows that the difference is £5."},{"text":"45 - 40 = £1.","correct":false,"explanation":"This incorrectly compares only part of the place value or treats the numbers as consecutive. Subtracting £40 from £45 gives £5."}]},{"id":"a721a46b-ff7c-b2ac-1fb2-b13712c308f8","cardType":"basic","points":1,"front":"When choosing the better rate for changing pounds into euros, what should you compare?","back":"Compare the euros received for £1.","mcqOptions":[{"text":"Compare the euros received for £1.","correct":true,"explanation":"Expressing every exchange rate as euros received for £1 creates a like-for-like comparison. The rate giving the most euros for £1 is better."},{"text":"Compare the pounds needed for €1.","correct":false,"explanation":"This uses the reverse direction of exchange. For pounds into euros, compare euros received for £1; the greatest number of euros gives the better rate."},{"text":"Compare the euros received for £100.","correct":false,"explanation":"Although equivalent rates can be scaled to £100, this is not the standard direct comparison requested. Convert both rates to euros received for £1."},{"text":"Compare the pounds received for €1.","correct":false,"explanation":"This describes changing euros into pounds, which is the opposite transaction. For pounds into euros, compare how many euros each exchange gives for £1."}]},{"id":"b0f3c241-370b-21cf-2ebe-117cb81b3ca2","cardType":"basic","points":3,"front":"City A: £1 = €1.12. City B: €1 = £0.88. For pounds to euros, which gives more?","back":"

City B gives €1.136... per £1.
City B gives more euros.

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

City B gives €1.136... per £1.
City B gives more euros.

","correct":true,"explanation":"City B’s rate must be inverted: £1 buys €1 ÷ 0.88 = €1.136.... This exceeds City A’s €1.12, so City B gives more."},{"text":"

City B gives €0.88 per £1.
City A gives more euros.

","correct":false,"explanation":"This treats €1 = £0.88 as though it also meant £1 = €0.88. Inverting gives €1.136... per £1, so City B gives more."},{"text":"

City B gives €1.10 per £1.
City A gives more euros.

","correct":false,"explanation":"This comes from calculating the reciprocal of 0.88 inaccurately. The correct value is €1.136... per £1, which is greater than City A’s €1.12."},{"text":"

City B gives €1.12 per £1.
Both cities give the same euros.

","correct":false,"explanation":"This assumes the reciprocal of 0.88 is exactly 1.12. It is actually 1.136..., so City B gives slightly more euros than City A."}]},{"id":"a1afbcf6-087e-b5c1-c7a8-79f2c91e1775","cardType":"cloze","points":null,"front":"For the greatest number of notes, round [ ], not to the nearest whole number.","back":"For the greatest number of notes, round down, not to the nearest whole number.","mcqOptions":[{"text":"down","correct":true,"explanation":"Only complete notes can be received, so any fractional result must be rounded down. Rounding up would require more dong than the traveller actually has."},{"text":"up","correct":false,"explanation":"Rounding up would count a note that cannot be fully paid for. To find the greatest possible number of complete notes, the result must be rounded down."},{"text":"upwards","correct":false,"explanation":"Rounding upwards overestimates the number of complete notes available and may exceed the traveller’s money. The quotient must instead be rounded down."},{"text":"away from zero","correct":false,"explanation":"For a positive quotient, rounding away from zero means rounding up, which could include an unaffordable extra note. The number of complete notes is rounded down."}]},{"id":"942e078e-edb0-8789-0dc2-b1f1ab4276f5","cardType":"basic","points":3,"front":"A traveller changes £600 at £1 = 25000 dong and wants 200000 dong notes. What is the greatest number of notes?","back":"

600 × 25000 = 15000000 dong.
15000000 ÷ 200000 = 75 notes.

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

600 × 25000 = 15000000 dong.
15000000 ÷ 200000 = 75 notes.

","correct":true,"explanation":"Multiplying £600 by 25000 gives 15000000 dong. Dividing this total by 200000 dong per note gives exactly 75 complete notes."},{"text":"

600 × 2500 = 1500000 dong.
1500000 ÷ 200000 = 7 notes.

","correct":false,"explanation":"The exchange rate has lost a zero, making the dong total ten times too small. Using 25000 dong per pound gives 15000000 dong and 75 notes."},{"text":"

600 × 25000 = 15000000 dong.
15000000 ÷ 20000 = 750 notes.

","correct":false,"explanation":"The note value has lost a zero, so the number of notes becomes ten times too large. Dividing by 200000 dong gives 75 notes."},{"text":"

600 ÷ 25000 = 0.024 dong.
0.024 ÷ 200000 = 0 notes.

","correct":false,"explanation":"This divides by the exchange rate instead of multiplying, reversing the conversion. £600 gives 15000000 dong, which can be exchanged for 75 notes."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Exchange Rates","title":"Exchange Rates Flashcards","topbar":{"backHref":"/gcse/maths/aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"3b7ac720-024f-4c6f-b34c-e2441871ff7c","walled":"$L39"}],"$L3a","$L3b"]