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For example, if one quantity doubles, the other quantity must also double."},{"text":"same amount","correct":false,"explanation":"Adding or subtracting the same amount describes a constant difference, not direct proportion. Directly proportional quantities increase or decrease by the same multiplier."},{"text":"same difference","correct":false,"explanation":"A constant difference does not guarantee direct proportion because the ratio may change. Direct proportion requires both quantities to be changed by the same multiplier."},{"text":"reciprocal multiplier","correct":false,"explanation":"Using reciprocal multipliers would make one quantity increase while the other decreases. In direct proportion, both quantities are changed by the same multiplier."}]},{"id":"ccb839da-afe7-01ab-2707-82a8997bf261","cardType":"basic","points":1,"front":"If a recipe is doubled from 10 cakes to 20 cakes, what happens to every ingredient?","back":"Every ingredient doubles.","mcqOptions":[{"text":"Every ingredient doubles.","correct":true,"explanation":"The number of cakes is multiplied by 2, so direct proportion requires every ingredient amount to be multiplied by 2 as well."},{"text":"Every ingredient halves.","correct":false,"explanation":"Halving confuses the direction of the scale change. The number of cakes rises from 10 to 20, so every ingredient doubles."},{"text":"Every ingredient stays unchanged.","correct":false,"explanation":"Keeping the ingredients unchanged would make the same mixture produce twice as many cakes. To preserve the recipe, every ingredient must double."},{"text":"Every ingredient increases by 10.","correct":false,"explanation":"The increase of 10 applies to the number of cakes, not each ingredient amount. Each ingredient must be multiplied by 2, so it doubles."}]},{"id":"945ba407-ab7f-2c21-6b33-710043d7e9bf","cardType":"basic","points":1,"front":"To scale a recipe from an old number made to a new number made, what multiplier do you use?","back":"$\\frac{\\text{new number made}}{\\text{old number made}}$","mcqOptions":[{"text":"$\\frac{\\text{new number made}}{\\text{old number made}}$","correct":true,"explanation":"The scale multiplier compares the required new output with the original output. Multiplying each old ingredient amount by this ratio gives the new amount."},{"text":"$\\frac{\\text{old number made}}{\\text{new number made}}$","correct":false,"explanation":"This reverses the required ratio and scales in the opposite direction. The correct multiplier is new number made divided by old number made."},{"text":"$\\frac{\\text{new number made}}{\\text{new number made}}$","correct":false,"explanation":"Dividing the new number by itself always gives 1, so no scaling would occur. The correct multiplier compares the new number with the old number."},{"text":"$\\frac{\\text{old number made}}{\\text{old number made}}$","correct":false,"explanation":"Dividing the old number by itself gives 1 and leaves every ingredient unchanged. Use new number made divided by old number made instead."}]},{"id":"821da2dc-070f-7e63-b9b1-ca9529a57153","cardType":"cloze","points":null,"front":"For recipe proportion, multiply the old amount by [ ] divided by [ ].","back":"For recipe proportion, multiply the old amount by new number made divided by old number made.","mcqOptions":[{"text":"For recipe proportion, multiply the old amount by new number made divided by old number made.","correct":true,"explanation":"The required scale factor is the new number made divided by the old number made. Multiplying the old ingredient amount by this factor gives the new amount."},{"text":"For recipe proportion, multiply the old amount by old number made divided by new number made.","correct":false,"explanation":"The ratio has been reversed, so it would scale the recipe in the opposite direction. Use new number made divided by old number made."},{"text":"For recipe proportion, multiply the old amount by old number made divided by old number made.","correct":false,"explanation":"This ratio equals 1, so the ingredient amount would remain unchanged. The numerator must be the new number made, with the old number made as denominator."},{"text":"For recipe proportion, multiply the old amount by new number made divided by new number made.","correct":false,"explanation":"Dividing the new number by itself gives a multiplier of 1. The denominator should be the old number made so the ratio measures the required scale change."}]},{"id":"4fac6801-e48e-9dc0-eb0c-94a89eddd4e0","cardType":"basic","points":1,"front":"What multiplier changes 12 cakes to 6 cakes?","back":"$\\frac{1}{2}$","mcqOptions":[{"text":"$\\frac{1}{2}$","correct":true,"explanation":"The multiplier is $\\frac{6}{12}=\\frac{1}{2}$. Multiplying 12 by $\\frac{1}{2}$ gives the required 6 cakes."},{"text":"$2$","correct":false,"explanation":"This reverses the scale factor and would change 12 cakes to 24. The correct multiplier is $\\frac{6}{12}=\\frac{1}{2}$."},{"text":"$\\frac{1}{3}$","correct":false,"explanation":"Dividing by 3 would reduce 12 cakes to 4, not 6. The required multiplier is $\\frac{6}{12}=\\frac{1}{2}$."},{"text":"$\\frac{3}{2}$","correct":false,"explanation":"This multiplier increases 12 cakes to 18 instead of reducing the quantity. The correct scale factor is $\\frac{6}{12}=\\frac{1}{2}$."}]},{"id":"6ab84824-ec5f-dfda-3956-45a482f7d63b","cardType":"basic","points":1,"front":"What multiplier changes 30 biscuits to 45 biscuits?","back":"$\\frac{3}{2}$ or 1.5.","mcqOptions":[{"text":"$\\frac{3}{2}$ or 1.5.","correct":true,"explanation":"The multiplier is $\\frac{45}{30}=\\frac{3}{2}=1.5$. Applying it to 30 gives $30\\times1.5=45$ biscuits."},{"text":"$\\frac{2}{3}$ or 0.67.","correct":false,"explanation":"This is the reciprocal ratio $\\frac{30}{45}$, so it scales in the wrong direction. The required multiplier is $\\frac{45}{30}=\\frac{3}{2}=1.5$."},{"text":"$\\frac{1}{2}$ or 0.5.","correct":false,"explanation":"Using only the increase of 15 as a fraction of 30 leads to this incorrect multiplier. The total scale factor is $\\frac{45}{30}=1.5$."},{"text":"$\\frac{5}{2}$ or 2.5.","correct":false,"explanation":"This incorrectly adds 1 to the required multiplier and would produce 75 biscuits. The correct multiplier is $\\frac{45}{30}=\\frac{3}{2}=1.5$."}]},{"id":"c261f37c-d6d5-36d4-90af-8522a079c043","cardType":"cloze","points":null,"front":"Multiplying by $\\frac{3}{2}$ means divide by [ ], then multiply by [ ].","back":"Multiplying by $\\frac{3}{2}$ means divide by 2, then multiply by 3.","mcqOptions":[{"text":"Multiplying by $\\frac{3}{2}$ means divide by 2, then multiply by 3.","correct":true,"explanation":"For a fractional multiplier, divide by the denominator and multiply by the numerator. Therefore $\\frac{3}{2}$ means divide by 2, then multiply by 3."},{"text":"Multiplying by $\\frac{3}{2}$ means divide by 3, then multiply by 2.","correct":false,"explanation":"This swaps the numerator and denominator, giving multiplication by $\\frac{2}{3}$ instead. For $\\frac{3}{2}$, divide by 2 and multiply by 3."},{"text":"Multiplying by $\\frac{3}{2}$ means divide by 2, then multiply by 2.","correct":false,"explanation":"Dividing and multiplying by 2 cancel, producing no overall change. To multiply by $\\frac{3}{2}$, divide by 2 and then multiply by 3."},{"text":"Multiplying by $\\frac{3}{2}$ means divide by 3, then multiply by 3.","correct":false,"explanation":"Dividing and multiplying by 3 gives an overall multiplier of 1. The denominator is 2, so divide by 2 before multiplying by 3."}]},{"id":"25add3fc-0d3b-a405-263b-a6e750821b9b","cardType":"basic","points":1,"front":"A recipe uses 240 g flour for 30 biscuits. How much flour for 45 biscuits?","back":"360 g","mcqOptions":[{"text":"360 g","correct":true,"explanation":"The biscuit quantity is multiplied by $\\frac{45}{30}=1.5$. Therefore the flour needed is $240\\times1.5=360$ g."},{"text":"160 g","correct":false,"explanation":"This uses the reciprocal multiplier $\\frac{30}{45}=\\frac{2}{3}$ and scales the flour down. For 45 biscuits, use $240\\times1.5=360$ g."},{"text":"300 g","correct":false,"explanation":"This adds 60 g after treating the 15 extra biscuits as one quarter of 240. Since 45 is 1.5 times 30, the answer is 360 g."},{"text":"480 g","correct":false,"explanation":"This doubles the flour as though the biscuit number rose from 30 to 60. The actual multiplier is $\\frac{45}{30}=1.5$, giving 360 g."}]},{"id":"a546d877-5bd9-a593-0662-23c914c48bb6","cardType":"basic","points":1,"front":"A recipe uses 2 eggs for 30 biscuits. How many eggs for 45 biscuits?","back":"3 eggs","mcqOptions":[{"text":"3 eggs","correct":true,"explanation":"The number of biscuits increases by a multiplier of $45 \\div 30 = 1.5$, so the eggs required are $2 \\times 1.5 = 3$."},{"text":"2 eggs","correct":false,"explanation":"This keeps the number of eggs unchanged even though more biscuits are being made. Scaling $30$ biscuits to $45$ requires $2 \\times 1.5 = 3$ eggs."},{"text":"4 eggs","correct":false,"explanation":"This treats the increase from $30$ to $45$ biscuits as doubling. The actual multiplier is $45 \\div 30 = 1.5$, giving $3$ eggs."},{"text":"5 eggs","correct":false,"explanation":"This incorrectly adds the biscuit multiplier to the original number of eggs. Direct proportion requires multiplication: $2 \\times (45 \\div 30) = 3$ eggs."}]},{"id":"4f20ba17-8546-50cf-a898-3b4f33dc4046","cardType":"cloze","points":null,"front":"When finding a multiplier from an ingredient amount, use [ ] divided by [ ].","back":"When finding a multiplier from an ingredient amount, use new amount divided by old amount.","mcqOptions":[{"text":"When finding a multiplier from an ingredient amount, use new amount divided by old amount.","correct":true,"explanation":"A scale multiplier compares the required new amount with the original amount, so it is calculated using new amount divided by old amount."},{"text":"When finding a multiplier from an ingredient amount, use old amount divided by new amount.","correct":false,"explanation":"This reverses the division and produces the reciprocal multiplier. The correct scale multiplier is new amount divided by old amount."},{"text":"When finding a multiplier from an ingredient amount, use new amount divided by difference.","correct":false,"explanation":"Dividing by the difference does not compare the new quantity with the original quantity. The correct multiplier is new amount divided by old amount."},{"text":"When finding a multiplier from an ingredient amount, use old amount divided by difference.","correct":false,"explanation":"This uses the change between the amounts rather than the original amount as the denominator. A proportional multiplier is new amount divided by old amount."}]},{"id":"c81b4269-7bf8-2101-0b0d-d6c20a5e3c3d","cardType":"basic","points":2,"front":"A recipe makes 12 shortcakes with 15 ml milk. If 40 ml milk is used, how many shortcakes are made?","back":"32 shortcakes","mcqOptions":[{"text":"32 shortcakes","correct":true,"explanation":"The milk multiplier is $40 \\div 15 = \\frac{8}{3}$. Multiplying $12$ shortcakes by $\\frac{8}{3}$ gives $32$ shortcakes."},{"text":"27 shortcakes","correct":false,"explanation":"This effectively adds the $15$ ml increase to the original number of shortcakes. Direct proportion requires $12 \\times (40 \\div 15) = 32$ shortcakes."},{"text":"30 shortcakes","correct":false,"explanation":"This uses an inaccurate scale factor of $2.5$. The correct milk multiplier is $40 \\div 15 = \\frac{8}{3}$, producing $32$ shortcakes."},{"text":"36 shortcakes","correct":false,"explanation":"This assumes the milk amount has tripled, but $40$ ml is only $\\frac{8}{3}$ times $15$ ml. The recipe therefore makes $32$ shortcakes."}]},{"id":"e94a9c3c-ba51-6848-94e9-35e558eeee41","cardType":"basic","points":1,"front":"A recipe needs 225 g flour for 9 cakes. How much flour is needed per cake?","back":"25 g per cake.","mcqOptions":[{"text":"25 g per cake.","correct":true,"explanation":"Dividing the total flour equally among $9$ cakes gives $225 \\div 9 = 25$, so each cake needs $25$ g."},{"text":"20 g per cake.","correct":false,"explanation":"This comes from an incorrect division of $225$ by $9$. Since $9 \\times 25 = 225$, the amount required is $25$ g per cake."},{"text":"24 g per cake.","correct":false,"explanation":"This is an off-by-one division error, as $9 \\times 24 = 216$, not $225$. Dividing correctly gives $25$ g per cake."},{"text":"27 g per cake.","correct":false,"explanation":"This confuses the number of cakes with a nearby factor of $225$. Sharing $225$ g equally between $9$ cakes gives $25$ g per cake."}]},{"id":"75bf3b17-5dc1-c4cb-6d2b-e97c4a6258b5","cardType":"basic","points":1,"front":"A student has 500 g flour and needs 25 g per cake. What is the maximum number of cakes?","back":"20 cakes","mcqOptions":[{"text":"20 cakes","correct":true,"explanation":"The number of complete cakes is the available flour divided by the flour per cake: $500 \\div 25 = 20$ cakes."},{"text":"15 cakes","correct":false,"explanation":"This results from an incorrect division of $500$ by $25$. Since $25 \\times 20 = 500$, there is enough flour for $20$ cakes."},{"text":"19 cakes","correct":false,"explanation":"This unnecessarily rounds the exact quotient down by one. The calculation $500 \\div 25$ equals exactly $20$, so $20$ complete cakes can be made."},{"text":"25 cakes","correct":false,"explanation":"This confuses the flour needed per cake with the number of cakes. Dividing $500$ g by $25$ g per cake gives $20$ cakes."}]},{"id":"eb5ec180-3b34-b0a6-129a-408be6f427ae","cardType":"basic","points":1,"front":"If a maximum-number answer is 18.6 biscuits, what whole number should you give?","back":"18 biscuits","mcqOptions":[{"text":"18 biscuits","correct":true,"explanation":"A maximum count must include only complete biscuits. Since $18.6$ means there is enough for $18$ whole biscuits but not $19$, the answer is $18$."},{"text":"19 biscuits","correct":false,"explanation":"Rounding normally to the nearest integer would give $19$, but a maximum-number problem requires rounding down because there is not enough material for the nineteenth biscuit."},{"text":"20 biscuits","correct":false,"explanation":"Rounding $18.6$ up to the next multiple of ten overstates the available quantity. Only $18$ complete biscuits can be made, so the maximum is $18$."},{"text":"17 biscuits","correct":false,"explanation":"This rounds down one whole biscuit too far. The decimal result shows that $18$ complete biscuits can be made, although there is not enough for $19$."}]},{"id":"2f715a94-3f12-50b5-6497-60a86060cdca","cardType":"basic","points":2,"front":"A recipe needs 180 g flour for 8 cakes. How much flour is needed for 20 cakes?","back":"450 g","mcqOptions":[{"text":"450 g","correct":true,"explanation":"The number of cakes increases by $20 \\div 8 = 2.5$, so the flour must also increase by this factor: $180 \\times 2.5 = 450$ g."},{"text":"360 g","correct":false,"explanation":"This doubles the flour, but the number of cakes rises from $8$ to $20$, a multiplier of $2.5$. The correct amount is $450$ g."},{"text":"400 g","correct":false,"explanation":"This assumes each cake needs $20$ g of flour. In fact, $180 \\div 8 = 22.5$ g per cake, giving $450$ g."},{"text":"480 g","correct":false,"explanation":"This uses an incorrect multiplier based on the increase of $12$ cakes. Direct proportion uses $20 \\div 8 = 2.5$, so $450$ g is needed."}]},{"id":"7e894a18-0244-cab0-d529-75d9a7fe76b9","cardType":"basic","points":1,"front":"Aisha needs 450 g flour and has 430 g. How many grams short is she?","back":"20 g","mcqOptions":[{"text":"20 g","correct":true,"explanation":"The shortage is the required amount minus the available amount: $450 - 430 = 20$, so Aisha is $20$ g short."},{"text":"10 g","correct":false,"explanation":"This understates the difference between the required and available amounts. Subtracting accurately gives $450 - 430 = 20$, so the shortage is $20$ g."},{"text":"30 g","correct":false,"explanation":"This is a subtraction error caused by miscalculating the difference between $450$ and $430$. The correct shortage is $450 - 430 = 20$ g."},{"text":"880 g","correct":false,"explanation":"This adds the required and available amounts instead of finding their difference. A shortage is calculated by subtraction, giving $450 - 430 = 20$ g."}]},{"id":"e20e155a-2430-1e71-9605-613663ae9427","cardType":"cloze","points":null,"front":"The limiting ingredient is the ingredient that allows the [ ].","back":"The limiting ingredient is the ingredient that allows the fewest complete items.","mcqOptions":[{"text":"fewest complete items","correct":true,"explanation":"The ingredient producing the fewest complete items runs out first. It therefore limits the total number of complete items that can be made."},{"text":"most complete items","correct":false,"explanation":"Choosing the most complete items ignores the ingredient that runs out first. The limiting ingredient is the one allowing the fewest complete items."},{"text":"fewest leftover items","correct":false,"explanation":"The calculation compares complete items that each ingredient can produce, not leftovers. The limiting ingredient allows the fewest complete items."},{"text":"most leftover items","correct":false,"explanation":"A large amount left over does not determine the production limit. The limiting ingredient is whichever one allows the fewest complete items."}]},{"id":"4eca3667-a7d8-0ce9-c14e-0698e8bedf50","cardType":"basic","points":1,"front":"For several available ingredients, which result decides the greatest number of complete items?","back":"The smallest number any ingredient allows.","mcqOptions":[{"text":"The smallest number any ingredient allows.","correct":true,"explanation":"Every complete item needs all the required ingredients, so production stops when the first ingredient runs out. This corresponds to the smallest number allowed."},{"text":"The largest number any ingredient allows.","correct":false,"explanation":"The largest value assumes the most plentiful ingredient sets the limit, but another ingredient would run out earlier. The smallest number allowed is decisive."},{"text":"The total number all ingredients allow.","correct":false,"explanation":"Adding the separate results wrongly treats ingredients as substitutes. Because every item needs each ingredient, the smallest number any ingredient allows sets the maximum."},{"text":"The average number the ingredients allow.","correct":false,"explanation":"Averaging can give a quantity that some ingredients cannot support. The greatest feasible number of complete items is the smallest number allowed by any ingredient."}]},{"id":"aa81179c-640a-1f91-c10c-5595c689bf5b","cardType":"basic","points":1,"front":"Sam's ingredients allow 36, 45, 40 and 48 shortcakes. What is the greatest number he can make?","back":"36 shortcakes","mcqOptions":[{"text":"36 shortcakes","correct":true,"explanation":"All four ingredients are needed, so the ingredient allowing only 36 shortcakes runs out first. Therefore, Sam can make at most 36 complete shortcakes."},{"text":"48 shortcakes","correct":false,"explanation":"Selecting 48 uses the largest allowance rather than the limiting one. An ingredient runs out after 36 shortcakes, so Sam can make only 36 complete shortcakes."},{"text":"40 shortcakes","correct":false,"explanation":"Selecting 40 overlooks the ingredient that supports only 36 shortcakes. Because every shortcake needs all ingredients, the maximum is 36 shortcakes."},{"text":"42 shortcakes","correct":false,"explanation":"Averaging 36, 45, 40 and 48 gives about 42, but averages do not determine the limit. The smallest allowance makes 36 shortcakes the maximum."}]},{"id":"63c8ac78-2eb3-3f8f-a6c6-c883ffdec6c2","cardType":"cloze","points":null,"front":"Before comparing units, convert 1 kg to [ ].","back":"Before comparing units, convert 1 kg to 1000 g.","mcqOptions":[{"text":"1000 g","correct":true,"explanation":"There are 1000 grams in one kilogram, so multiplying kilograms by 1000 converts the mass into grams for a valid comparison."},{"text":"100 g","correct":false,"explanation":"This uses a factor of 100 instead of 1000. Since one kilogram contains 1000 grams, the correct converted mass is 1000 g."},{"text":"10 g","correct":false,"explanation":"This confuses the kilogram-to-gram conversion with a much smaller factor. One kilogram equals 1000 grams, so the required value is 1000 g."},{"text":"0.001 g","correct":false,"explanation":"Dividing by 1000 reverses the conversion and gives the kilograms in one gram. Converting 1 kg to grams requires multiplying by 1000, giving 1000 g."}]},{"id":"5aff7394-f549-dc20-c1b2-ef957d55cc6d","cardType":"basic","points":1,"front":"How many millilitres are in 1 litre?","back":"1000 ml","mcqOptions":[{"text":"1000 ml","correct":true,"explanation":"The prefix milli means one-thousandth, so one litre is divided into 1000 millilitres. Therefore, 1 litre equals 1000 ml."},{"text":"100 ml","correct":false,"explanation":"This uses a conversion factor of 100, confusing litres and millilitres with a centi-based conversion. One litre actually contains 1000 ml."},{"text":"10 ml","correct":false,"explanation":"This uses a factor of 10, which is too small for the milli prefix. One litre is equal to 1000 ml."},{"text":"0.001 ml","correct":false,"explanation":"This reverses the conversion: one millilitre is 0.001 litres, not the other way around. One litre contains 1000 ml."}]},{"id":"3dfb6e40-b577-7edc-faf6-c08793fb6c74","cardType":"basic","points":2,"front":"A recipe uses 250 g flour for 20 biscuits. Ben has 1 kg flour. What is the maximum number of biscuits?","back":"80 biscuits","mcqOptions":[{"text":"80 biscuits","correct":true,"explanation":"One kilogram is 1000 g, which is four lots of 250 g. Multiplying 20 biscuits by four gives a maximum of 80 biscuits."},{"text":"40 biscuits","correct":false,"explanation":"This only doubles the recipe, but 1000 g is four times 250 g. The biscuit quantity must also be multiplied by four, giving 80 biscuits."},{"text":"60 biscuits","correct":false,"explanation":"This treats 1 kg as three lots of 250 g, but 1000 divided by 250 is four. Four batches make 80 biscuits."},{"text":"100 biscuits","correct":false,"explanation":"This incorrectly treats 1 kg as five lots of 250 g. Since 1000 g contains four such lots, Ben can make 80 biscuits."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Proportion","title":"Proportion Flashcards","topbar":{"backHref":"/gcse/maths/ocr/flashcards"},"topicSidebar":"$L36"}]}],"topicId":"63c5d9be-9583-471c-a64f-59d121c7b447","walled":"$L37"}],"$L38","$L39"]