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24:[["$","$L32",null,{"feature":"flashcards"}],"$L33",["$","$L34",null,{"href":"/igcse/maths/cie/grade-3-3-8-exchange-rates/flashcards","label":"Exchange Rates","subjectCode":"igcse_maths__cie","surface":"flashcards"}],["$","$L35",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L36",null,{"decks":[{"id":"af8daa68-bf1b-44c3-b46d-a31793ca5133","title":"Exchange Rates Flashcards","topicId":"5f4deb8d-3b62-45da-a624-186e729ddd44","topicSlug":"grade-3-3-8-exchange-rates","cards":[{"id":"a5ba80f2-b365-4f84-a038-4975fa75dcd9","cardType":"cloze","points":null,"front":"A [ ] is the type of money used in a country.","back":"A currency is the type of money used in a country.","mcqOptions":[{"text":"currency","correct":true,"explanation":"Currency is the general term for the money officially used within a particular country, such as pounds in the UK or euros in many European countries."},{"text":"exchange rate","correct":false,"explanation":"An exchange rate compares the value of two currencies, rather than naming the money used in a country. The correct term is currency, meaning a country’s type of money."},{"text":"denomination","correct":false,"explanation":"A denomination is a specific value of a note or coin, such as £5 or £10. The general type of money used in a country is called currency."},{"text":"interest rate","correct":false,"explanation":"An interest rate describes the cost of borrowing or the return on savings. It does not name a country’s money; the correct term is currency."}]},{"id":"46f7dacc-993a-4d70-88c0-97706e05d599","cardType":"cloze","points":null,"front":"An exchange rate tells you how much [ ].","back":"An exchange rate tells you how much one currency is worth in another currency.","mcqOptions":[{"text":"one currency is worth in another currency","correct":true,"explanation":"An exchange rate compares the value of one currency with another, showing how much of one currency is equivalent to a given amount of the other."},{"text":"one country spends in another country","correct":false,"explanation":"This describes spending across borders, not the value comparison between currencies. An exchange rate tells you how much one currency is worth in another currency."},{"text":"one currency weighs compared with another currency","correct":false,"explanation":"Currencies are compared by value rather than physical weight. The correct meaning is how much one currency is worth in another currency."},{"text":"one currency earns as interest in another currency","correct":false,"explanation":"Interest is an amount gained from savings or charged on borrowing, not the definition of an exchange rate. The rate compares the value of currencies."}]},{"id":"de0effcc-a4a2-443f-9740-dff3e7b00420","cardType":"basic","points":1,"front":"In an exchange rate, what tells you whether to multiply or divide?","back":"The currency with the 1.","mcqOptions":[{"text":"The currency with the 1.","correct":true,"explanation":"The currency written beside 1 is the reference currency. Converting away from it usually involves multiplying, while converting back to it involves dividing."},{"text":"The currency with the larger number.","correct":false,"explanation":"The larger number is not what determines the operation, because exchange rates can be greater or less than 1. Use the currency with the 1 as the reference."},{"text":"The currency being converted into.","correct":false,"explanation":"The destination currency does not by itself decide whether to multiply or divide. The key is identifying which currency has the value 1 in the exchange rate."},{"text":"The currency with the smaller value.","correct":false,"explanation":"The smaller numerical value may not be the reference currency and cannot reliably determine the operation. The currency with the 1 gives the correct direction."}]},{"id":"ad63e093-fab6-4e13-ab40-c799e78dc4d5","cardType":"basic","points":1,"front":"If £1 = €1.18, how do you convert pounds to euros?","back":"Multiply the pounds by 1.18.","mcqOptions":[{"text":"Multiply the pounds by 1.18.","correct":true,"explanation":"Since £1 is equal to €1.18, each pound produces 1.18 euros. Multiplying the number of pounds by 1.18 gives the equivalent amount in euros."},{"text":"Divide the pounds by 1.18.","correct":false,"explanation":"Dividing would convert euros back into pounds when £1 = €1.18. To convert pounds into euros, multiply the pounds by 1.18."},{"text":"Add the pounds to 1.18.","correct":false,"explanation":"Exchange rates scale an amount rather than adding a fixed number. For pounds to euros, multiply the pounds by 1.18 to account for the value of each pound."},{"text":"Multiply the pounds by 0.18.","correct":false,"explanation":"The factor 0.18 is only the extra amount above one euro equivalent, not the full conversion factor. The pounds must be multiplied by 1.18."}]},{"id":"1fde3cbd-ac8b-4f2c-953f-5ded5d3315c7","cardType":"basic","points":2,"front":"At £1 = €1.18, convert £280 to euros.","back":"€330.40","mcqOptions":[{"text":"€330.40","correct":true,"explanation":"Using £1 = €1.18, calculate $280 \\times 1.18 = 330.40$. Therefore, £280 is worth €330.40."},{"text":"€237.29","correct":false,"explanation":"This comes from dividing 280 by 1.18, which reverses the required direction. Since pounds are being converted into euros, calculate $280 \\times 1.18 = 330.40$."},{"text":"€329.20","correct":false,"explanation":"This is a near miss caused by using an inaccurate multiplication result. The correct calculation is $280 \\times 1.18 = 330.40$, so the answer is €330.40."},{"text":"€281.18","correct":false,"explanation":"Adding the exchange rate instead of multiplying treats the rate as a fixed extra amount. Each pound becomes €1.18, so $280 \\times 1.18 = 330.40$."}]},{"id":"85d7f7fd-4ee5-4a45-8ee4-c3d1347f14f1","cardType":"cloze","points":null,"front":"When £1 equals a foreign amount, converting foreign currency back to pounds means [ ] by the exchange rate.","back":"When £1 equals a foreign amount, converting foreign currency back to pounds means dividing by the exchange rate.","mcqOptions":[{"text":"dividing","correct":true,"explanation":"When £1 equals a foreign amount, the foreign currency is the multiplied side of the rate. To return to pounds, divide the foreign amount by the exchange rate."},{"text":"multiplying","correct":false,"explanation":"Multiplication converts pounds into the foreign currency when the rate is written as £1 equal to a foreign amount. Converting back to pounds requires dividing by the rate."},{"text":"adding","correct":false,"explanation":"Adding the exchange rate does not scale the foreign amount according to the currency relationship. To convert foreign currency back to pounds, divide by the exchange rate."},{"text":"subtracting","correct":false,"explanation":"Subtracting the exchange rate does not reverse a currency conversion because the rate represents a multiplier. The correct operation for returning to pounds is division."}]},{"id":"e2d954c5-f958-4783-b2e3-e6654c1202f1","cardType":"basic","points":1,"front":"If £1 = €1.17, how do you convert euros to pounds?","back":"Divide the euros by 1.17.","mcqOptions":[{"text":"Divide the euros by 1.17.","correct":true,"explanation":"Because £1 equals €1.17, euros are the foreign amount relative to pounds. Dividing the euros by 1.17 converts them back into pounds."},{"text":"Multiply the euros by 1.17.","correct":false,"explanation":"Multiplication by 1.17 converts pounds into euros, not euros into pounds. To change euros back to pounds, divide the euros by 1.17."},{"text":"Divide the euros by 0.17.","correct":false,"explanation":"The value 0.17 is only the difference between 1.17 and 1, not the exchange rate. The euros must be divided by the full rate, 1.17."},{"text":"Subtract 1.17 from the euros.","correct":false,"explanation":"Subtracting a fixed amount does not account for the proportional relationship between euros and pounds. Divide the euros by 1.17 to convert them correctly."}]},{"id":"88e0f64f-6412-49d3-9944-fcf095cceb09","cardType":"basic","points":2,"front":"At £1 = €1.17, convert €95 to pounds to the nearest penny.","back":"£81.20","mcqOptions":[{"text":"£81.20","correct":true,"explanation":"Convert euros to pounds by dividing: $95 \\div 1.17 = 81.1965\\ldots$. Rounding to the nearest penny gives £81.20."},{"text":"£111.15","correct":false,"explanation":"This results from multiplying 95 by 1.17, which converts in the wrong direction. Since euros must become pounds, calculate $95 \\div 1.17 = 81.1965\\ldots$, giving £81.20."},{"text":"£80.95","correct":false,"explanation":"Subtracting the difference between 1.17 and 1 from 95 is not a valid exchange-rate conversion. Dividing by 1.17 and rounding to the nearest penny gives £81.20."},{"text":"£81.19","correct":false,"explanation":"The unrounded result is £81.1965..., which rounds up because the third decimal digit is 6. Therefore, the nearest-penny answer is £81.20, not £81.19."}]},{"id":"05ff5389-066c-4e3b-95e5-78afea8555db","cardType":"basic","points":1,"front":"What does giving money to the nearest penny require?","back":"Write it to two decimal places.","mcqOptions":[{"text":"Write it to two decimal places.","correct":true,"explanation":"A penny is one hundredth of a pound, so an amount given to the nearest penny must have exactly two digits after the decimal point."},{"text":"Write it to one decimal place.","correct":false,"explanation":"One decimal place gives the amount to the nearest ten pence, not the nearest penny. The amount must be written to two decimal places."},{"text":"Write it to three decimal places.","correct":false,"explanation":"Three decimal places gives thousandths of a pound, equivalent to tenths of a penny. The nearest penny requires two decimal places."},{"text":"Write it to the nearest whole number.","correct":false,"explanation":"Rounding to a whole number gives the nearest pound and discards the pence. The nearest penny requires the amount to be written to two decimal places."}]},{"id":"b10ac23f-0b8b-48e1-b199-678c028d5cc3","cardType":"basic","points":1,"front":"If €1 = £0.86, how do you convert euros to pounds?","back":"Multiply the euros by 0.86.","mcqOptions":[{"text":"Multiply the euros by 0.86.","correct":true,"explanation":"Each euro is worth £0.86, so multiplying the number of euros by 0.86 gives the equivalent amount in pounds."},{"text":"Divide the euros by 0.86.","correct":false,"explanation":"Dividing reverses the stated conversion and would be appropriate when converting pounds to euros. To convert euros to pounds, multiply the euros by 0.86."},{"text":"Add 0.86 to the euros.","correct":false,"explanation":"The exchange rate is a value per euro, not a fixed amount to add. Multiply the number of euros by 0.86 to obtain pounds."},{"text":"Subtract 0.86 from the euros.","correct":false,"explanation":"Subtracting treats the exchange rate as a fixed reduction rather than a multiplier. Each euro contributes £0.86, so the euros must be multiplied by 0.86."}]},{"id":"b892499b-be61-457a-996e-231992604776","cardType":"cloze","points":null,"front":"Do not memorise “foreign to pounds means divide”; always check which currency has [ ].","back":"Do not memorise “foreign to pounds means divide”; always check which currency has the 1.","mcqOptions":[{"text":"the 1","correct":true,"explanation":"The currency beside 1 determines the direction of the exchange rate. Use the rate according to which currency represents one complete unit."},{"text":"the 0","correct":false,"explanation":"Exchange rates are normally expressed using 1 unit of one currency, not 0 units. Check which currency has the 1 before choosing multiplication or division."},{"text":"the larger number","correct":false,"explanation":"Choosing an operation from the larger number is unreliable because exchange-rate values vary. The correct method is to identify which currency has the 1."},{"text":"the smaller number","correct":false,"explanation":"The smaller number does not determine whether to multiply or divide. Instead, inspect the exchange-rate statement and identify which currency has the 1."}]},{"id":"b3462bab-1720-4249-bcd8-e90c778224d5","cardType":"basic","points":1,"front":"Before comparing prices in different currencies, what must you do?","back":"Convert so both prices are in the same currency.","mcqOptions":[{"text":"Convert so both prices are in the same currency.","correct":true,"explanation":"Prices can only be compared fairly when they use the same unit. Convert one price so that both amounts are expressed in the same currency."},{"text":"Convert so both prices have the same number.","correct":false,"explanation":"A conversion should preserve value, not force the numerical amounts to match. Both prices must instead be expressed in the same currency before comparison."},{"text":"Round so both prices are to the nearest pound.","correct":false,"explanation":"Rounding does not resolve the fact that the prices use different currencies and may also reduce accuracy. Convert both prices into the same currency first."},{"text":"Calculate so both prices use a different exchange rate.","correct":false,"explanation":"Using different exchange rates would make the comparison inconsistent. Apply the given exchange rate so both prices are expressed in the same currency."}]},{"id":"467fb9ae-f551-40aa-8c5b-ee738b144262","cardType":"basic","points":2,"front":"Why is comparing €54 with £49.99 directly unfair?","back":"They are different currencies with different values.","mcqOptions":[{"text":"They are different currencies with different values.","correct":true,"explanation":"Euros and pounds are different units of money, and one euro does not equal one pound. One price must be converted before their values are compared."},{"text":"They have different decimal places with different accuracy.","correct":false,"explanation":"The number of decimal places does not prevent comparison once units match. The real problem is that euros and pounds are different currencies with different values."},{"text":"They are different prices for identical values.","correct":false,"explanation":"Different displayed numbers do not establish which price represents better value when the currencies differ. Convert one amount so both prices use the same currency."},{"text":"They use different symbols for equal values.","correct":false,"explanation":"The symbols identify genuinely different currencies, not alternative notation for equal amounts. Euros and pounds have different values, so a currency conversion is necessary."}]},{"id":"77bbf8da-f47e-458a-a0bf-a07776b738a6","cardType":"basic","points":2,"front":"A jacket costs €54 abroad and £49.99 in the UK. If £1 = €1.20, where is it cheaper?","back":"Abroad, because €54 = £45.","mcqOptions":[{"text":"Abroad, because €54 = £45.","correct":true,"explanation":"Since £1 equals €1.20, convert euros to pounds by dividing: €54 ÷ 1.20 = £45. This is less than the UK price of £49.99."},{"text":"The UK, because €54 = £64.80.","correct":false,"explanation":"Multiplying €54 by 1.20 applies the exchange rate in the wrong direction. Dividing by 1.20 gives £45, so the jacket is cheaper abroad."},{"text":"The UK, because 54 is greater than 49.99.","correct":false,"explanation":"Comparing 54 and 49.99 directly ignores that they represent different currencies. Converting €54 gives £45, which means the jacket is cheaper abroad."},{"text":"Neither, because the prices cannot be compared.","correct":false,"explanation":"The prices can be compared after converting them into the same currency. €54 is £45 at this rate, so the jacket is cheaper abroad."}]},{"id":"906b64b5-269e-4845-9908-accdfec8a622","cardType":"basic","points":1,"front":"After two prices are in the same currency, how do you find the difference?","back":"Subtract the smaller price from the larger price.","mcqOptions":[{"text":"Subtract the smaller price from the larger price.","correct":true,"explanation":"The positive difference between two prices is found by taking the smaller amount away from the larger amount after both have been converted to the same currency."},{"text":"Subtract the larger price from the smaller price.","correct":false,"explanation":"Reversing the subtraction produces a negative result rather than the usual positive price difference. Subtract the smaller price from the larger price."},{"text":"Add the smaller price to the larger price.","correct":false,"explanation":"Adding finds the total cost of the two items, not the difference between their prices. The smaller price must be subtracted from the larger price."},{"text":"Divide the larger price by the smaller price.","correct":false,"explanation":"Division finds a ratio showing how many times one price is another. To find the monetary difference, subtract the smaller price from the larger price."}]},{"id":"555192fc-07c5-439f-8f5f-3cffbbdf98c3","cardType":"basic","points":2,"front":"Trainers cost 5175 rupees abroad and £62 in the UK. If £1 = 75 rupees, what is the difference in pounds?","back":"£7","mcqOptions":[{"text":"£7","correct":true,"explanation":"Convert the foreign price by dividing 5175 by 75, giving £69. The difference from the £62 UK price is £69 - £62 = £7."},{"text":"£69","correct":false,"explanation":"£69 is the converted price of the trainers abroad, not the difference. Subtracting the UK price gives £69 - £62 = £7."},{"text":"£13","correct":false,"explanation":"Subtracting £62 from the exchange-rate number 75 mixes incompatible quantities. First calculate 5175 ÷ 75 = £69, then subtract £62 to get £7."},{"text":"£8","correct":false,"explanation":"Rounding the converted price from £69 to £70 before subtracting creates an unnecessary £1 error. Using the exact value gives £69 - £62 = £7."}]},{"id":"0a6e34d0-0371-4012-9ae3-2e88c8939d64","cardType":"cloze","points":null,"front":"When changing pounds into euros, the better rate gives the [ ] number of euros for £1.","back":"When changing pounds into euros, the better rate gives the larger number of euros for £1.","mcqOptions":[{"text":"larger","correct":true,"explanation":"A larger number of euros for each pound means the traveller receives more foreign currency for the same amount of sterling, so it is the better rate."},{"text":"smaller","correct":false,"explanation":"Choosing the smaller amount reverses the value comparison. The better rate gives the larger number of euros for £1 because each pound purchases more euros."},{"text":"same","correct":false,"explanation":"Different exchange rates do not necessarily produce the same return. The better rate is the one giving the larger number of euros for each £1."},{"text":"fixed","correct":false,"explanation":"The number of euros received is determined by the exchange rate, so it is not fixed. The better rate gives the larger number of euros for £1."}]},{"id":"2c5dcaf2-3a15-44c8-8e04-640d9e68b780","cardType":"basic","points":2,"front":"City B gives €1 = £0.86. How many euros does £1 give?","back":"€1.16 approximately.","mcqOptions":[{"text":"€1.16 approximately.","correct":true,"explanation":"Since €1 costs £0.86, divide £1 by 0.86: $1 \\div 0.86 \\approx 1.1628$. This rounds to approximately €1.16."},{"text":"€0.86 approximately.","correct":false,"explanation":"Using 0.86 directly confuses pounds per euro with euros per pound. The rate must be inverted, giving $1 \\div 0.86 \\approx €1.16$."},{"text":"€1.14 approximately.","correct":false,"explanation":"This value may be confused with a competing quoted rate, but it is not the reciprocal of 0.86. Dividing 1 by 0.86 gives approximately €1.16."},{"text":"€1.20 approximately.","correct":false,"explanation":"This rounds the result too generously. The calculation gives $1 \\div 0.86 \\approx 1.1628$, which rounds to €1.16 to the nearest cent."}]},{"id":"76a35584-8c1e-4c2c-b98c-22a7c4f7e7c2","cardType":"basic","points":2,"front":"Which gives more euros per £1: £1 = €1.14 or €1 = £0.86?","back":"€1 = £0.86 gives more euros per £1.","mcqOptions":[{"text":"€1 = £0.86 gives more euros per £1.","correct":true,"explanation":"Invert €1 = £0.86 to obtain $£1 = €(1 \\div 0.86) \\approx €1.16$. Since €1.16 exceeds €1.14, this rate gives more euros."},{"text":"£1 = €1.14 gives more euros per £1.","correct":false,"explanation":"Comparing 1.14 directly with 0.86 ignores that the second quote is pounds per euro. Its reciprocal is about €1.16 per £1, which is greater than €1.14."},{"text":"Both rates give the same euros per £1.","correct":false,"explanation":"The rates look close but are not equal. Converting €1 = £0.86 gives approximately €1.16 per £1, which exceeds €1.14 per £1."},{"text":"€1 = £0.86 gives fewer euros per £1.","correct":false,"explanation":"This reverses the comparison after conversion. The quote €1 = £0.86 is approximately €1.16 per £1, so it gives more, not fewer, euros."}]},{"id":"f4b450e6-ca1a-4c06-aca8-51884915fd28","cardType":"cloze","points":null,"front":"For a greatest number of whole notes, if the number of notes is a decimal, [ ].","back":"For a greatest number of whole notes, if the number of notes is a decimal, round down.","mcqOptions":[{"text":"round down","correct":true,"explanation":"Only complete notes can be received. Rounding down discards the unusable fractional part and gives the greatest whole number that does not exceed the available money."},{"text":"round up","correct":false,"explanation":"Rounding up would require enough money for an additional complete note. To find the greatest affordable number of whole notes, the decimal result must be rounded down."},{"text":"round to the nearest whole number","correct":false,"explanation":"Ordinary rounding can increase the answer when the decimal part is at least 0.5, producing more notes than can be afforded. The result must always be rounded down."},{"text":"keep the decimal","correct":false,"explanation":"A decimal number of notes would imply receiving part of a note, which is not allowed. Keep only the greatest whole number by rounding down."}]},{"id":"e79cdbf8-060d-460f-affa-8623ea50c5c8","cardType":"basic","points":2,"front":"£730 is changed into dong at £1 = 28 000 dong. How many 200 000 dong notes can be received at most?","back":"102 notes.","mcqOptions":[{"text":"102 notes.","correct":true,"explanation":"The exchange produces $730 \\times 28\\,000 = 20\\,440\\,000$ dong. Dividing by 200 000 gives 102.2, so at most 102 complete notes can be received."},{"text":"103 notes.","correct":false,"explanation":"Rounding 102.2 up would require more dong than are available. Because only whole notes can be received, the result must be rounded down to 102 notes."},{"text":"102.2 notes.","correct":false,"explanation":"The division gives 102.2, but 0.2 of a banknote cannot be received as a whole note. Rounding down gives a maximum of 102 notes."},{"text":"10 notes.","correct":false,"explanation":"This loses a factor of ten when handling the zeros in 20 440 000 divided by 200 000. The quotient is 102.2, allowing 102 whole notes."}]},{"id":"85988d54-d685-449b-807d-62a2a73880c4","cardType":"cloze","points":null,"front":"A [ ] is the maximum amount someone is allowed to spend.","back":"A budget is the maximum amount someone is allowed to spend.","mcqOptions":[{"text":"budget","correct":true,"explanation":"A budget sets the spending limit for a person, project or activity. Actual costs must not exceed this maximum if the spending is to remain affordable."},{"text":"income","correct":false,"explanation":"Income is money received, not the maximum amount permitted for spending. The planned upper spending limit is called a budget."},{"text":"balance","correct":false,"explanation":"A balance is the amount currently remaining or held in an account, rather than a planned maximum spending amount. That limit is the budget."},{"text":"cost","correct":false,"explanation":"A cost is an amount charged or paid for something, not the maximum someone is permitted to spend. The maximum allowed amount is the budget."}]},{"id":"f672c3c9-f874-4fa9-b3a2-c1bbf1668938","cardType":"basic","points":2,"front":"A trip costs £1003.07 and the budget is £1000. Can the traveller afford it?","back":"No, because £1003.07 is over budget.","mcqOptions":[{"text":"No, because £1003.07 is over budget.","correct":true,"explanation":"The trip exceeds the spending limit by $£1003.07 - £1000 = £3.07$. Any amount above the budget means it cannot be afforded within that budget."},{"text":"Yes, because £1003.07 is within budget.","correct":false,"explanation":"The cost is not within the £1000 limit: it exceeds it by £3.07. Therefore, the traveller cannot afford the trip while staying within budget."},{"text":"Yes, because it is only £3.07 over budget.","correct":false,"explanation":"Being only slightly above the limit does not make the trip affordable within the stated budget. It costs £3.07 too much, so the answer is no."},{"text":"Yes, because it rounds to £1000.","correct":false,"explanation":"Rounding the cost before checking affordability hides the £3.07 overspend. The exact figures must be compared, and £1003.07 exceeds the £1000 budget."}]},{"id":"50891be2-7966-4fd0-b8a9-95897680fa37","cardType":"basic","points":2,"front":"For value-for-money comparisons with different currencies and units, what must match before comparing?","back":"

Currency
Unit

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

Currency
Unit

","correct":true,"explanation":"Prices must be converted into the same currency and expressed for the same unit, such as per kilogram. Only then does a direct value-for-money comparison use equivalent quantities."},{"text":"

Currency
Shop

","correct":false,"explanation":"The shop does not need to be the same, since comparing different sellers is often the purpose. The currency and unit must match before prices are compared."},{"text":"

Exchange rate
Unit

","correct":false,"explanation":"Different exchange rates are used to convert prices rather than made identical. For a fair final comparison, both prices must have the same currency and unit."},{"text":"

Price
Quantity

","correct":false,"explanation":"Price and quantity are the values being compared, not the common forms required. Convert both offers to the same currency and the same unit first."}]}]}],"examCountdown":null,"heading":"Exchange Rates","title":"Exchange Rates Flashcards","topbar":{"backHref":"/igcse/maths/cie/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"5f4deb8d-3b62-45da-a624-186e729ddd44","walled":"$L38"}],"$L39","$L3a"]