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Converting first prevents errors such as directly mixing pounds with pence."},{"text":"digits","correct":false,"explanation":"Matching digits may help with written arithmetic, but it does not make differently measured quantities compatible. The units must match before calculating."},{"text":"operations","correct":false,"explanation":"Choosing an operation is important, but operations do not need to “match”. Convert the units to the same form first, then perform the required calculation."},{"text":"answers","correct":false,"explanation":"Answers are found after the calculation rather than matched beforehand. The units must be made consistent first so the arithmetic compares equivalent quantities."}]},{"id":"499fa323-3c26-9e81-fb99-76db4f06e53f","cardType":"cloze","points":null,"front":"In money questions, [ ] makes £1.","back":"In money questions, 100p makes £1.","mcqOptions":[{"text":"100p","correct":true,"explanation":"There are 100 pence in one pound, so amounts can be converted from pounds to pence by multiplying the number of pounds by 100."},{"text":"10p","correct":false,"explanation":"This confuses pounds with a smaller decimal subdivision. One pound contains 100p, not 10p, because one penny is one hundredth of a pound."},{"text":"50p","correct":false,"explanation":"This treats half a pound as a whole pound. Since 50p equals £0.50, the amount required to make £1 is 100p."},{"text":"1000p","correct":false,"explanation":"This adds an extra factor of ten when converting currency. Since £1 equals 100p, 1000p is actually equal to £10."}]},{"id":"2cac2148-3143-a10c-d89d-3d3617909a60","cardType":"basic","points":2,"front":"Why should you not subtract 434p directly from £10?","back":"Because the units differ; convert to pence or pounds first.","mcqOptions":[{"text":"Because the units differ; convert to pence or pounds first.","correct":true,"explanation":"Pounds and pence are different units, so direct subtraction would compare unlike quantities. Convert £10 to 1000p, or 434p to £4.34, first."},{"text":"Because the decimal places differ; round both amounts first.","correct":false,"explanation":"The issue is not differing decimal places or a need to round. The units differ, so both amounts must first be expressed in pounds or pence."},{"text":"Because the amounts differ; add them together before subtracting.","correct":false,"explanation":"Different monetary amounts can be subtracted, so their unequal values are not the problem. Their units differ and must be converted to pounds or pence first."},{"text":"Because the currency differs; convert both amounts into euros first.","correct":false,"explanation":"Both amounts use the same currency, sterling, so converting to euros is unnecessary. The mismatch is between pounds and pence, which must be made consistent."}]},{"id":"f437d060-f42e-c593-b6b3-43dacf9b939f","cardType":"basic","points":1,"front":"7 cakes cost 62p each. What is the total cost?","back":"The total cost is 434p.","mcqOptions":[{"text":"The total cost is 434p.","correct":true,"explanation":"Multiplying the number of cakes by the price of each gives $7 \\times 62 = 434$, so the seven cakes cost 434p altogether."},{"text":"The total cost is 424p.","correct":false,"explanation":"This results from an arithmetic error in multiplying 62 by 7. The correct calculation is $7 \\times 62 = 434$, giving a total of 434p."},{"text":"The total cost is 372p.","correct":false,"explanation":"This calculates the cost of only six cakes because $6 \\times 62 = 372$. Seven cakes cost $7 \\times 62 = 434$p."},{"text":"The total cost is 496p.","correct":false,"explanation":"This calculates the cost of eight cakes because $8 \\times 62 = 496$. The question asks for seven, so the total is 434p."}]},{"id":"44f4a7bf-a65f-f4f4-c02e-74a07e9ee87f","cardType":"basic","points":2,"front":"Pay £10 for goods costing 434p. What change is given?","back":"The change is £5.66.","mcqOptions":[{"text":"The change is £5.66.","correct":true,"explanation":"Convert £10 to 1000p, then subtract: $1000 - 434 = 566$p. Converting 566p back to pounds gives £5.66."},{"text":"The change is £6.34.","correct":false,"explanation":"This commonly comes from mishandling the subtraction across place values. Correctly calculating $£10.00 - £4.34$ gives £5.66 change."},{"text":"The change is £5.76.","correct":false,"explanation":"This is a ten-pence subtraction error. Writing both amounts with two decimal places gives $£10.00 - £4.34 = £5.66$, not £5.76."},{"text":"The change is £56.60.","correct":false,"explanation":"This misplaces the decimal point by one place when converting pence back to pounds. The 566p change equals £5.66, not £56.60."}]},{"id":"25ce3f35-1f9d-0b36-c66a-3859eebb42f1","cardType":"cloze","points":null,"front":"When dividing but another full group cannot be made, the leftover amount is the [ ].","back":"When dividing but another full group cannot be made, the leftover amount is the remainder.","mcqOptions":[{"text":"remainder","correct":true,"explanation":"The remainder is the amount left after forming as many complete equal groups as possible. It is smaller than the size of one full group."},{"text":"quotient","correct":false,"explanation":"The quotient is the result of division, representing the number of groups rather than the leftover amount. Any amount left over is the remainder."},{"text":"divisor","correct":false,"explanation":"The divisor is the number by which another number is divided, often representing group size. The leftover amount after making full groups is the remainder."},{"text":"multiple","correct":false,"explanation":"A multiple is produced by multiplying a number by an integer; it is not the leftover from division. The leftover amount is called the remainder."}]},{"id":"8b3ebbef-c6c3-6721-767a-72b121b4f6cf","cardType":"basic","points":1,"front":"In as many as possible questions, which operation finds the number of full items?","back":"Use division.","mcqOptions":[{"text":"Use division.","correct":true,"explanation":"Division determines how many times the cost or size of one item fits into the total available amount, giving the number of complete items."},{"text":"Use multiplication.","correct":false,"explanation":"Multiplication finds the total for a known number of items, rather than how many items can be made. Finding the number of full items requires division."},{"text":"Use addition.","correct":false,"explanation":"Addition could repeatedly combine item costs, but it is not the direct operation for finding how many equal groups fit. Division gives the number of full items."},{"text":"Use subtraction.","correct":false,"explanation":"Subtraction may be repeated until insufficient money remains, but the direct operation for finding the number of complete equal groups is division."}]},{"id":"7a3cf6c6-555a-a44b-474a-b7e0d335bde3","cardType":"basic","points":2,"front":"£4 is spent on 35p bars. How many full bars can be bought?","back":"11 bars.","mcqOptions":[{"text":"11 bars.","correct":true,"explanation":"Convert £4 to 400p and divide: $400 \\div 35 = 11$ remainder 15. Therefore, 11 complete bars can be bought."},{"text":"10 bars.","correct":false,"explanation":"This stops one group too soon. Ten bars cost 350p, leaving 50p, which is enough for one more bar, so 11 can be bought."},{"text":"12 bars.","correct":false,"explanation":"This rounds $400 \\div 35 \\approx 11.43$ up, but only complete affordable bars count. Twelve bars cost 420p, so only 11 can be bought."},{"text":"15 bars.","correct":false,"explanation":"This confuses the 15p remainder with the number of bars. Dividing 400p by 35p gives 11 complete bars with 15p left."}]},{"id":"ad2e7827-c89f-d371-cd1d-6e7f7fcd29ec","cardType":"basic","points":2,"front":"£4 is spent on 35p bars as many as possible. What change is left?","back":"The change is 15p.","mcqOptions":[{"text":"The change is 15p.","correct":true,"explanation":"£4 is 400p, and 11 bars cost 385p. A twelfth bar would exceed the budget, so the change is 400p - 385p = 15p."},{"text":"The change is 50p.","correct":false,"explanation":"This stops after buying only 10 bars for 350p. Another 35p bar can still be afforded, so 11 bars are bought and 15p remains."},{"text":"The change is 5p.","correct":false,"explanation":"This incorrectly treats 395p as a possible total cost, but 395 is not a multiple of 35. Eleven bars cost 385p, leaving 15p."},{"text":"The change is 0p.","correct":false,"explanation":"This assumes the whole £4 can be spent exactly. Since 400p is not divisible by 35p, 11 bars cost 385p and leave 15p."}]},{"id":"f64e3719-48c8-1d2f-6970-7fce55fbcafa","cardType":"basic","points":1,"front":"For full cups or cut lengths, should you round a remainder up or down?","back":"Round down.","mcqOptions":[{"text":"Round down.","correct":true,"explanation":"Only complete cups or lengths can be counted. Any remainder represents an incomplete item, so the quotient must be rounded down to the number of full items."},{"text":"Round up.","correct":false,"explanation":"Rounding up would count an incomplete cup or cut length as a complete one. Only full items count, so a remainder must be rounded down."},{"text":"Round to the nearest whole number.","correct":false,"explanation":"Ordinary rounding could count an incomplete item when the remainder is large. The requirement for full cups or lengths means always rounding down."},{"text":"Do not round.","correct":false,"explanation":"A decimal answer would include part of a cup or length, rather than counting complete items. The result must be a whole number rounded down."}]},{"id":"74af90dd-db50-44a7-fd42-0716cd9878d2","cardType":"basic","points":1,"front":"For buying enough packs, should you round a remainder up or down?","back":"Round up.","mcqOptions":[{"text":"Round up.","correct":true,"explanation":"A partly needed pack still requires buying one complete additional pack. Therefore, any non-zero remainder means the number of packs must be rounded up."},{"text":"Round down.","correct":false,"explanation":"Rounding down would leave some items uncovered because too few packs would be bought. Any remainder requires an additional pack, so round up."},{"text":"Round to the nearest whole number.","correct":false,"explanation":"Rounding to the nearest integer can round down when the remainder is small, leaving too few items. Buying enough packs always requires rounding up."},{"text":"Do not round.","correct":false,"explanation":"Shops sell complete packs, so a decimal number of packs cannot be purchased. Any remainder requires one more whole pack, meaning round up."}]},{"id":"c60f7fac-0530-3a21-64b2-9d05b44569d2","cardType":"cloze","points":null,"front":"For a group price, work out how many [ ] are needed, then multiply by the group price.","back":"For a group price, work out how many groups are needed, then multiply by the group price.","mcqOptions":[{"text":"groups","correct":true,"explanation":"A group price applies once to each complete group. Find the number of groups required, then multiply that number by the stated price per group."},{"text":"items","correct":false,"explanation":"Counting individual items and multiplying by a group price charges the group rate once per item. The items must first be organised into groups."},{"text":"prices","correct":false,"explanation":"The price is the amount multiplied, not the quantity being counted. Work out how many groups are needed, then multiply by the group price."},{"text":"remainders","correct":false,"explanation":"A remainder only shows whether an additional group may be needed; it is not the quantity multiplied by the price. The required quantity is groups."}]},{"id":"c7c13c47-6460-e9e6-7fdb-df89f6177186","cardType":"basic","points":1,"front":"20 pens are sold at 5 for 80p. How many groups of 5 are needed?","back":"4 groups.","mcqOptions":[{"text":"4 groups.","correct":true,"explanation":"Each group contains 5 pens, so the number of groups is 20 ÷ 5 = 4. Four groups contain all 20 pens."},{"text":"5 groups.","correct":false,"explanation":"This confuses the number of pens in each group with the number of groups. Dividing 20 pens by 5 pens per group gives 4 groups."},{"text":"20 groups.","correct":false,"explanation":"This counts each pen as a separate group, ignoring that every group contains 5 pens. The correct calculation is 20 ÷ 5 = 4 groups."},{"text":"100 groups.","correct":false,"explanation":"This multiplies 20 by 5 instead of dividing by the group size. Splitting 20 pens into groups of 5 produces 4 groups."}]},{"id":"9c10ff12-d9ae-3680-a501-f7ebbee7be19","cardType":"basic","points":2,"front":"Costs are 320p, 720p and 2250p. What is the total in pounds?","back":"The total is £32.90.","mcqOptions":[{"text":"The total is £32.90.","correct":true,"explanation":"The costs total 320p + 720p + 2250p = 3290p. Dividing by 100 converts pence to pounds, giving £32.90."},{"text":"The total is £3290.00.","correct":false,"explanation":"This labels the total number of pence as pounds without converting it. The sum is 3290p, which equals £32.90 after dividing by 100."},{"text":"The total is £329.00.","correct":false,"explanation":"This moves the decimal point only one place, effectively dividing pence by 10. Converting 3290p to pounds requires division by 100, giving £32.90."},{"text":"The total is £3.29.","correct":false,"explanation":"This moves the decimal point three places and makes the total ten times too small. Since 100p equals £1, 3290p is £32.90."}]},{"id":"fe780820-350a-1e5c-88d8-99b041da916f","cardType":"cloze","points":null,"front":"To find equal instalments, subtract the [ ] first, then divide what is left.","back":"To find equal instalments, subtract the deposit first, then divide what is left.","mcqOptions":[{"text":"deposit","correct":true,"explanation":"The deposit is paid immediately, so it is removed from the full price first. The remaining balance is then divided equally among the instalments."},{"text":"instalment","correct":false,"explanation":"An instalment is one of the later equal payments, not the initial amount removed from the price. Subtract the deposit before dividing the balance."},{"text":"interest","correct":false,"explanation":"Interest may be added in some finance arrangements, but it is not the initial payment described here. The deposit is subtracted before calculating equal instalments."},{"text":"price","correct":false,"explanation":"Subtracting the full price from itself would leave nothing to divide. The correct method subtracts the deposit from the price, then divides the balance."}]},{"id":"a33b4cc7-db4f-ead5-884d-b011da8dc4d3","cardType":"basic","points":2,"front":"A bike costs £540 with a £120 deposit and 12 equal payments. What is each payment?","back":"Each payment is £35.","mcqOptions":[{"text":"Each payment is £35.","correct":true,"explanation":"After the £120 deposit, the unpaid balance is £540 - £120 = £420. Dividing £420 equally across 12 payments gives £35 each."},{"text":"Each payment is £45.","correct":false,"explanation":"This divides the full £540 price by 12 and ignores the deposit already paid. The remaining £420 divided by 12 gives £35 per payment."},{"text":"Each payment is £55.","correct":false,"explanation":"This adds the £120 deposit to the price before dividing: £660 ÷ 12 = £55. The deposit must instead be subtracted, giving £35."},{"text":"Each payment is £420.","correct":false,"explanation":"This is the full balance remaining after the deposit, not one instalment. The £420 balance must be divided by 12, producing payments of £35."}]},{"id":"747a2310-a68f-d96e-7618-a495ef351a7f","cardType":"cloze","points":null,"front":"If several identical items have a known total cost, [ ] to find the unit cost.","back":"If several identical items have a known total cost, divide to find the unit cost.","mcqOptions":[{"text":"divide","correct":true,"explanation":"Dividing the total cost by the number of identical items gives the cost of one item, which is the unit cost."},{"text":"multiply","correct":false,"explanation":"Multiplying would increase the total rather than find the cost of one item. Divide the total cost by the number of identical items."},{"text":"add","correct":false,"explanation":"Adding is used to combine separate costs, not to calculate a unit cost. Divide the known total by the number of identical items."},{"text":"subtract","correct":false,"explanation":"Subtracting finds a difference or removes an amount; it does not share the total equally. Divide by the number of items to find the unit cost."}]},{"id":"45f2d3d3-dcf4-5449-b903-831ee39600a0","cardType":"basic","points":1,"front":"4 pens cost £1.20. What is the cost of 1 pen?","back":"1 pen costs 30p.","mcqOptions":[{"text":"1 pen costs 30p.","correct":true,"explanation":"Convert £1.20 to 120p, then divide by 4. Since 120 ÷ 4 = 30, each pen costs 30p."},{"text":"1 pen costs 20p.","correct":false,"explanation":"This results from dividing 120p by 6 rather than by the 4 pens. The correct calculation is 120 ÷ 4 = 30p."},{"text":"1 pen costs 24p.","correct":false,"explanation":"This results from dividing 120p by 5, an off-by-one error in the number of pens. Dividing by 4 gives 30p per pen."},{"text":"1 pen costs 40p.","correct":false,"explanation":"This results from dividing the total by 3 instead of 4. There are four pens, so 120p ÷ 4 = 30p."}]},{"id":"7d2b963b-b3a1-7ba4-5e03-1d66738bb5ff","cardType":"basic","points":2,"front":"If 1 pen costs 30p and 1 pencil costs 15p, what do 1 pen and 2 pencils cost?","back":"They cost 60p.","mcqOptions":[{"text":"They cost 60p.","correct":true,"explanation":"Two pencils cost 2 × 15p = 30p. Adding the pen’s 30p gives a total cost of 60p."},{"text":"They cost 45p.","correct":false,"explanation":"This includes only one pencil with the pen. Two pencils cost 30p altogether, so adding the 30p pen gives 60p."},{"text":"They cost 75p.","correct":false,"explanation":"This effectively counts three pencils instead of two. One pen and two pencils cost 30p + 30p = 60p."},{"text":"They cost 90p.","correct":false,"explanation":"This double-counts part of the purchase after finding 30p for the pencils. Adding that once to the 30p pen gives 60p."}]},{"id":"8533e28e-2872-6d6d-04d0-a82c7c721d93","cardType":"basic","points":1,"front":"To decide if someone has enough money, what must you calculate first?","back":"Find the total cost first.","mcqOptions":[{"text":"Find the total cost first.","correct":true,"explanation":"The total cost must be calculated before it can be compared with the available money. This comparison shows whether there is enough money."},{"text":"Find the average cost first.","correct":false,"explanation":"An average does not show how much must be paid altogether. Find the total cost first, then compare it with the amount available."},{"text":"Find the most expensive item first.","correct":false,"explanation":"The most expensive item alone does not determine whether the whole purchase is affordable. Add all item costs to find the total cost first."},{"text":"Find the amount of change first.","correct":false,"explanation":"Change can only be calculated after establishing that the available money exceeds the total. Find the total cost first and compare the two amounts."}]},{"id":"dd0698fb-482c-4e3b-d449-62fd5fbfe269","cardType":"basic","points":1,"front":"Owen’s total cost is £114 and his budget is £110. How short is he?","back":"He is short by £4.","mcqOptions":[{"text":"He is short by £4.","correct":true,"explanation":"Subtract the £110 budget from the £114 total cost. The difference is £114 - £110 = £4, so Owen needs £4 more."},{"text":"He is short by £14.","correct":false,"explanation":"This subtracts £100 rather than the full £110 budget. Using the complete budget gives £114 - £110 = £4."},{"text":"He is short by £24.","correct":false,"explanation":"This adds the final amounts instead of finding their difference. The shortfall is calculated by £114 - £110, which equals £4."},{"text":"He is short by £224.","correct":false,"explanation":"This is the sum of £114 and £110, not the amount missing from the budget. Their difference is £4, so Owen is £4 short."}]},{"id":"8490f6cc-dbbc-9293-a5bc-67c1614d50f2","cardType":"cloze","points":null,"front":"1 litre = [ ].","back":"1 litre = 1000 ml.","mcqOptions":[{"text":"1000 ml","correct":true,"explanation":"The metric conversion is 1 litre = 1000 millilitres, so litres are converted to millilitres by multiplying by 1000."},{"text":"100 ml","correct":false,"explanation":"This confuses a litre with one tenth of a litre. There are 1000 millilitres in 1 litre, not 100 millilitres."},{"text":"10 ml","correct":false,"explanation":"This uses a conversion factor of 10 instead of 1000. One litre contains 1000 millilitres because milli means one thousandth."},{"text":"10,000 ml","correct":false,"explanation":"This adds an extra factor of 10 to the conversion. One litre is exactly 1000 millilitres, while 10,000 millilitres equals 10 litres."}]},{"id":"dfe2da32-f380-3cff-029a-43e24ba9b818","cardType":"basic","points":1,"front":"100 cm equals how many metres?","back":"100 cm = 1 m.","mcqOptions":[{"text":"100 cm = 1 m.","correct":true,"explanation":"There are 100 centimetres in one metre, so dividing 100 cm by 100 gives exactly 1 m."},{"text":"100 cm = 10 m.","correct":false,"explanation":"This divides by 10 instead of 100 when converting centimetres to metres. Since 100 cm make 1 m, the answer is 1 m."},{"text":"100 cm = 100 m.","correct":false,"explanation":"This incorrectly keeps the numerical value unchanged despite changing units. Metres are larger than centimetres, so 100 cm equals 1 m."},{"text":"100 cm = 0.1 m.","correct":false,"explanation":"This moves the decimal point one place too far. Dividing 100 cm by 100 gives 1 m, whereas 0.1 m is only 10 cm."}]},{"id":"57121b4b-ee03-66fe-21ff-1e63c723e8f0","cardType":"basic","points":1,"front":"1000 g equals how many kilograms?","back":"1000 g = 1 kg.","mcqOptions":[{"text":"1000 g = 1 kg.","correct":true,"explanation":"There are 1000 grams in one kilogram, so dividing 1000 g by 1000 gives exactly 1 kg."},{"text":"1000 g = 10 kg.","correct":false,"explanation":"This divides by 100 instead of 1000 when converting grams to kilograms. Since 1000 g make 1 kg, the answer is 1 kg."},{"text":"1000 g = 100 kg.","correct":false,"explanation":"This uses an incorrect conversion factor of 10. A kilogram contains 1000 grams, so 1000 g equals 1 kg, not 100 kg."},{"text":"1000 g = 0.1 kg.","correct":false,"explanation":"This moves the decimal point one place too far. Dividing 1000 g by 1000 gives 1 kg, while 0.1 kg is only 100 g."}]},{"id":"fedc0630-dfa3-3557-38e4-33ad7df1fe35","cardType":"basic","points":3,"front":"A jug has 1.6 litres and each cup needs 180 ml. How many full cups?","back":"8 full cups.","mcqOptions":[{"text":"8 full cups.","correct":true,"explanation":"Convert 1.6 litres to 1600 ml, then calculate $1600 \\div 180 = 8.88\\ldots$. Only eight complete 180 ml cups can be filled."},{"text":"9 full cups.","correct":false,"explanation":"Rounding $1600 \\div 180 = 8.88\\ldots$ up gives nine, but the ninth cup would not be full. Therefore, only eight full cups can be filled."},{"text":"7 full cups.","correct":false,"explanation":"This results from underestimating the quotient after converting 1.6 litres to 1600 ml. Since $1600 \\div 180 = 8.88\\ldots$, eight full cups can be filled."},{"text":"6 full cups.","correct":false,"explanation":"This may come from treating 1.6 litres as a smaller volume than 1600 ml. Dividing 1600 ml by 180 ml gives eight full cups, with some liquid remaining."}]},{"id":"8ddca268-dee2-4c9c-2f14-490035cc774a","cardType":"basic","points":2,"front":"Sam needs 900g of powder. Each pack has 600g. How many packs are needed?","back":"2 packs.","mcqOptions":[{"text":"2 packs.","correct":true,"explanation":"Calculate $900 \\div 600 = 1.5$ packs. Since packs must be bought whole, Sam must round up to two packs to obtain at least 900g."},{"text":"1 pack.","correct":false,"explanation":"One pack contains only 600g, leaving Sam 300g short of the required 900g. He therefore needs to buy two complete packs."},{"text":"1.5 packs.","correct":false,"explanation":"Dividing $900 \\div 600$ gives 1.5, but packs are bought as whole items rather than fractions. Sam must round up and buy two packs."},{"text":"3 packs.","correct":false,"explanation":"Three packs would provide 1800g, which is twice the required amount. As 1.5 packs are mathematically required, rounding up means buying two packs."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Unit 1"},"heading":"Calculation Problems","title":"Calculation Problems Flashcards","topbar":{"backHref":"/gcse/maths/wjec/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"b308ba2e-514b-b2d7-df29-6754e2cbd197","walled":"$L39"}],"$L3a","$L3b"]