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items.","mcqOptions":[{"text":"total number of items","correct":true,"explanation":"The denominator represents the whole group being considered, so it is the total number of items. The numerator represents the items belonging to the specified part."},{"text":"number of selected items","correct":false,"explanation":"This confuses the denominator with the numerator. The selected items form the part, while the denominator must be the total number of items in the whole group."},{"text":"number of unselected items","correct":false,"explanation":"Counting the unselected items gives the complementary part, not the denominator. The denominator is the total number of items, including both selected and unselected items."},{"text":"difference between the parts","correct":false,"explanation":"Subtracting the sizes of the parts does not give a fraction’s denominator. The denominator records the total number of items in the complete group."}]},{"id":"a556199a-b679-b9b3-b3f7-4cd72785840c","cardType":"basic","points":1,"front":"20 counters, 6 yellow: what fraction are yellow before simplifying?","back":"$\\frac{6}{20}$","mcqOptions":[{"text":"$\\frac{6}{20}$","correct":true,"explanation":"There are 6 yellow counters out of 20 counters altogether, so the part-over-total fraction is $\\frac{6}{20}$. No simplification is required by the question."},{"text":"$\\frac{14}{20}$","correct":false,"explanation":"This counts the 14 counters that are not yellow. The yellow counters are the required part, so the fraction before simplifying is $\\frac{6}{20}$."},{"text":"$\\frac{6}{14}$","correct":false,"explanation":"This incorrectly uses the number of non-yellow counters as the denominator. The denominator must be all 20 counters, giving $\\frac{6}{20}$."},{"text":"$\\frac{20}{6}$","correct":false,"explanation":"This reverses part and total. The 6 yellow counters belong in the numerator and all 20 counters belong in the denominator, giving $\\frac{6}{20}$."}]},{"id":"3e57f07a-44dc-50f9-e8bb-0e62e9962938","cardType":"basic","points":1,"front":"20 counters, 6 yellow: what fraction are yellow in simplest form?","back":"$\\frac{3}{10}$","mcqOptions":[{"text":"$\\frac{3}{10}$","correct":true,"explanation":"The fraction is initially $\\frac{6}{20}$. Dividing both the numerator and denominator by their highest common factor, 2, gives the simplest form $\\frac{3}{10}$."},{"text":"$\\frac{7}{10}$","correct":false,"explanation":"This is the simplified fraction of counters that are not yellow, since $20-6=14$ and $\\frac{14}{20}=\\frac{7}{10}$. The yellow fraction is $\\frac{3}{10}$."},{"text":"$\\frac{3}{7}$","correct":false,"explanation":"This compares the 6 yellow counters with the 14 non-yellow counters instead of the total. Using 20 as the denominator and simplifying gives $\\frac{3}{10}$."},{"text":"$\\frac{6}{10}$","correct":false,"explanation":"This halves only the denominator, which changes the fraction’s value. Dividing both 6 and 20 by 2 gives the correct simplest form, $\\frac{3}{10}$."}]},{"id":"c6dff985-c06f-04e7-4698-57bfd10c55c8","cardType":"basic","points":1,"front":"15 pens, 6 red, rest green: how many pens are green?","back":"9","mcqOptions":[{"text":"9","correct":true,"explanation":"The 15 pens consist of 6 red pens and the remaining green pens. Subtracting gives $15-6=9$, so there are 9 green pens."},{"text":"6","correct":false,"explanation":"This repeats the number of red pens rather than finding the remainder. Subtracting the 6 red pens from all 15 pens gives 9 green pens."},{"text":"21","correct":false,"explanation":"This comes from adding 15 and 6, even though the red pens are already included in the total. The green count is $15-6=9$."},{"text":"11","correct":false,"explanation":"This results from an incorrect subtraction of 6 from 15. The correct calculation is $15-6=9$, so 9 of the pens are green."}]},{"id":"b8b2c30f-5eeb-9895-4299-b39a901bd6ef","cardType":"basic","points":2,"front":"15 pens, 6 red, rest green: what fraction are green in simplest form?","back":"$\\frac{3}{5}$","mcqOptions":[{"text":"$\\frac{3}{5}$","correct":true,"explanation":"There are $15-6=9$ green pens, so the fraction is $\\frac{9}{15}$. Dividing both numbers by 3 gives the simplest form $\\frac{3}{5}$."},{"text":"$\\frac{2}{5}$","correct":false,"explanation":"This is the fraction of pens that are red, because $\\frac{6}{15}=\\frac{2}{5}$. The green fraction is $\\frac{9}{15}=\\frac{3}{5}$."},{"text":"$\\frac{3}{4}$","correct":false,"explanation":"This incorrectly compares the 9 green pens with the 12 obtained by adding green and half the red count. The correct part-over-total calculation gives $\\frac{3}{5}$."},{"text":"$\\frac{5}{3}$","correct":false,"explanation":"This reverses the simplified fraction, producing an improper fraction greater than 1 even though green pens are only part of the total. The correct fraction is $\\frac{3}{5}$."}]},{"id":"e18700e3-9ed3-d3ff-8a1d-74e63951a3ff","cardType":"cloze","points":null,"front":"To simplify a fraction, divide the numerator and denominator by the [ ].","back":"To simplify a fraction, divide the numerator and denominator by the same number.","mcqOptions":[{"text":"same number","correct":true,"explanation":"Dividing the numerator and denominator by the same non-zero common factor preserves the fraction’s value. Using the highest common factor produces simplest form in one step."},{"text":"two different numbers","correct":false,"explanation":"Dividing by different numbers changes the fraction’s value rather than simplifying it equivalently. Both the numerator and denominator must be divided by the same common factor."},{"text":"numerator only","correct":false,"explanation":"Dividing both parts by the numerator alone is generally impossible unless it also divides the denominator exactly. A fraction is simplified using the same common factor."},{"text":"denominator only","correct":false,"explanation":"Focusing only on the denominator does not preserve the fraction’s value and may not produce whole numbers. Both parts must be divided by the same common factor."}]},{"id":"460c906a-543c-04f4-b753-e357aa23f664","cardType":"basic","points":1,"front":"Simplify $\\frac{24}{32}$.","back":"$\\frac{3}{4}$","mcqOptions":[{"text":"$\\frac{3}{4}$","correct":true,"explanation":"The highest common factor of 24 and 32 is 8. Dividing both numbers by 8 gives $\\frac{24\\div8}{32\\div8}=\\frac{3}{4}$."},{"text":"$\\frac{4}{3}$","correct":false,"explanation":"This inverts the simplified fraction. Since 24 is less than 32, the answer must remain less than 1; dividing both by 8 gives $\\frac{3}{4}$."},{"text":"$\\frac{3}{8}$","correct":false,"explanation":"This comes from dividing the numerator and denominator by different numbers, which changes the fraction’s value. Dividing both by 8 gives $\\frac{3}{4}$."},{"text":"$\\frac{2}{3}$","correct":false,"explanation":"This may result from subtracting 8 repeatedly rather than dividing by a common factor. Simplification requires dividing 24 and 32 by 8, giving $\\frac{3}{4}$."}]},{"id":"b6cd52bf-fff1-38bc-97d1-0420a925c500","cardType":"cloze","points":null,"front":"A fraction is in simplest form when its numerator and denominator have no common factor except [ ].","back":"A fraction is in simplest form when its numerator and denominator have no common factor except 1.","mcqOptions":[{"text":"1","correct":true,"explanation":"Every whole number has 1 as a factor. A fraction is in simplest form when 1 is the only positive factor shared by its numerator and denominator."},{"text":"0","correct":false,"explanation":"Zero is not a factor of positive integers because division by zero is undefined. The only common factor allowed in a fraction’s simplest form is 1."},{"text":"2","correct":false,"explanation":"If both numbers have 2 as a factor, they can still be divided by 2, so the fraction is not fully simplified. The only permitted common factor is 1."},{"text":"10","correct":false,"explanation":"A shared factor of 10 would mean both numbers could be divided by 10, so further simplification is possible. In simplest form, their only common factor is 1."}]},{"id":"2040796a-fdde-96d6-92f4-0f483f73331e","cardType":"basic","points":1,"front":"If the numerator and denominator are both even, what divisor should you try first?","back":"2","mcqOptions":[{"text":"2","correct":true,"explanation":"Every even integer is divisible by 2, so both parts can always be divided by 2 before checking whether the fraction simplifies further."},{"text":"4","correct":false,"explanation":"Being even does not guarantee divisibility by 4 - for example, 6 is even but not divisible by 4. The first guaranteed divisor is 2."},{"text":"6","correct":false,"explanation":"Divisibility by 6 requires divisibility by both 2 and 3, while evenness guarantees only divisibility by 2. Therefore, try 2 first."},{"text":"8","correct":false,"explanation":"An even number need not be divisible by 8 - for example, 10 is not. Both even parts are always divisible by 2, so start there."}]},{"id":"c0aadac8-64c5-d54a-2d32-bbc5f09f37cb","cardType":"basic","points":1,"front":"If the numerator and denominator both end in 0 or 5, what divisor should you try first?","back":"5","mcqOptions":[{"text":"5","correct":true,"explanation":"Any whole number ending in 0 or 5 is divisible by 5, so 5 is a guaranteed common divisor to try when both parts have these endings."},{"text":"10","correct":false,"explanation":"Numbers ending in 0 are divisible by 10, but numbers ending in 5 are not. Since either ending is allowed, the guaranteed divisor is 5."},{"text":"3","correct":false,"explanation":"Ending in 0 or 5 does not establish divisibility by 3; that depends on the sum of the digits. The guaranteed divisor is 5."},{"text":"25","correct":false,"explanation":"Only some numbers ending in 0 or 5 are divisible by 25 - for example, 30 is not. All such numbers are divisible by 5."}]},{"id":"9375855d-000f-587d-0d2e-171c48421897","cardType":"basic","points":1,"front":"Last year £30, this year £42: what is the increase?","back":"£12","mcqOptions":[{"text":"£12","correct":true,"explanation":"Subtract the original cost from the new cost: £42 - £30 = £12. Therefore, the cost has increased by £12."},{"text":"£10","correct":false,"explanation":"This results from comparing only the tens digits and ignores the remaining units. Subtracting the complete amounts gives £42 - £30 = £12."},{"text":"£32","correct":false,"explanation":"This subtracts £10 from £42 rather than subtracting the original £30. The increase is found using £42 - £30 = £12."},{"text":"£72","correct":false,"explanation":"This adds the two costs instead of finding their difference. An increase is calculated by subtracting the old value: £42 - £30 = £12."}]},{"id":"7e10b8f0-5f89-8b99-8f6f-49b1cecfce8a","cardType":"basic","points":2,"front":"A cost rises from £30 to £42. As a fraction of last year’s cost, what is the increase in simplest form?","back":"$\\frac{2}{5}$","mcqOptions":[{"text":"$\\frac{2}{5}$","correct":true,"explanation":"The increase is £42 - £30 = £12. As a fraction of the original £30, this is $rac{12}{30}$, which simplifies to $rac{2}{5}$."},{"text":"$\\frac{2}{7}$","correct":false,"explanation":"This divides the £12 increase by the new cost of £42, giving $rac{12}{42}=rac{2}{7}$. The question requires division by the original £30, giving $rac{2}{5}$."},{"text":"$\\frac{7}{5}$","correct":false,"explanation":"This represents the new cost as a fraction of the old cost: $rac{42}{30}=rac{7}{5}$. The increase alone is $rac{12}{30}=rac{2}{5}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"This treats £18 as the increase, but the actual difference is £42 - £30 = £12. Thus the required fraction is $rac{12}{30}=rac{2}{5}$."}]},{"id":"7167b475-1ab5-a862-472d-00319807ff8c","cardType":"cloze","points":null,"front":"Equivalent fractions have the [ ].","back":"Equivalent fractions have the same value.","mcqOptions":[{"text":"same value","correct":true,"explanation":"Equivalent fractions may use different numerators and denominators, but they represent the same proportion or point on the number line, so they have the same value."},{"text":"same numerator","correct":false,"explanation":"Equivalent fractions usually have different numerators because both parts have been scaled by a common factor. Their defining feature is that they have the same value."},{"text":"same denominator","correct":false,"explanation":"Equivalent fractions can have different denominators, such as $rac{1}{2}$ and $rac{2}{4}$. They are equivalent because they have the same value."},{"text":"same appearance","correct":false,"explanation":"Equivalent fractions often look different because their numerators and denominators have been scaled. What makes them equivalent is that they represent the same value."}]},{"id":"43ce6fca-7e6e-fd74-4a7c-821a2a35c04c","cardType":"basic","points":2,"front":"Which is not equivalent to $\\frac{2}{3}$: $\\frac{8}{12}$, $\\frac{10}{15}$, $\\frac{14}{21}$, $\\frac{15}{24}$, $\\frac{18}{27}$?","back":"$\\frac{15}{24}$","mcqOptions":[{"text":"$\\frac{15}{24}$","correct":true,"explanation":"Simplifying gives $rac{15}{24}=rac{5}{8}$, which is not $rac{2}{3}$. The other listed fractions all simplify to $rac{2}{3}$."},{"text":"$\\frac{8}{12}$","correct":false,"explanation":"Dividing both parts by 4 gives $rac{8}{12}=rac{2}{3}$, so this fraction is equivalent. The non-equivalent fraction is $rac{15}{24}=rac{5}{8}$."},{"text":"$\\frac{10}{15}$","correct":false,"explanation":"Dividing the numerator and denominator by 5 gives $rac{10}{15}=rac{2}{3}$. The fraction that does not simplify to $rac{2}{3}$ is $rac{15}{24}$."},{"text":"$\\frac{14}{21}$","correct":false,"explanation":"Dividing both parts by 7 gives $rac{14}{21}=rac{2}{3}$, so it is equivalent. Instead, $rac{15}{24}$ simplifies to $rac{5}{8}$."}]},{"id":"40e197d9-9e63-190c-50c1-39fda496cb35","cardType":"cloze","points":null,"front":"To make an equivalent fraction, multiply or divide the numerator and denominator by the [ ].","back":"To make an equivalent fraction, multiply or divide the numerator and denominator by the same number.","mcqOptions":[{"text":"same number","correct":true,"explanation":"Multiplying or dividing both parts by the same non-zero number preserves the numerator-to-denominator ratio, so the resulting fraction has the same value."},{"text":"two different numbers","correct":false,"explanation":"Using different multipliers or divisors changes the ratio between the numerator and denominator. Both parts must be multiplied or divided by the same number."},{"text":"numerator and denominator respectively","correct":false,"explanation":"Scaling the numerator by the numerator and the denominator by the denominator generally changes the fraction’s value. Both parts require the same multiplier or divisor."},{"text":"two consecutive numbers","correct":false,"explanation":"Using consecutive numbers applies unequal scale factors to the numerator and denominator, changing their ratio. An equivalent fraction requires the same number for both parts."}]},{"id":"e8e377be-331e-8ead-2dc8-cfe13ee63f6d","cardType":"basic","points":1,"front":"With the same denominator, which is smaller: $\\frac{3}{20}$ or $\\frac{7}{20}$?","back":"$\\frac{3}{20}$","mcqOptions":[{"text":"$\\frac{3}{20}$","correct":true,"explanation":"When denominators are equal, the fraction with the smaller numerator is smaller. Since 3 is less than 7, $rac{3}{20}$ is smaller."},{"text":"$\\frac{7}{20}$","correct":false,"explanation":"This reverses the comparison of the numerators. With equal denominators, 7 twentieths is greater than 3 twentieths, so the smaller fraction is $rac{3}{20}$."},{"text":"$\\frac{3}{7}$","correct":false,"explanation":"This incorrectly combines the two numerators and is not one of the fractions being compared. With equal denominators, $rac{3}{20}$ is smaller because 3 < 7."},{"text":"$\\frac{20}{7}$","correct":false,"explanation":"This inverts $rac{7}{20}$ and produces a value greater than 1, rather than comparing the given fractions. The smaller given fraction is $rac{3}{20}$."}]},{"id":"0eeb5579-157d-490a-7054-c9bf92705c20","cardType":"basic","points":1,"front":"For denominators 4, 10, 5 and 2, what common denominator is used in the notes?","back":"20","mcqOptions":[{"text":"20","correct":true,"explanation":"The lowest common multiple of 4, 10, 5 and 2 is 20, so each fraction can be rewritten with denominator 20."},{"text":"10","correct":false,"explanation":"Although 10 is divisible by 10, 5 and 2, it is not divisible by 4. The common denominator used is 20."},{"text":"4","correct":false,"explanation":"Using the largest original denominator does not guarantee a common denominator, since 4 does not divide into 10. The notes use 20."},{"text":"40","correct":false,"explanation":"Although 40 is a possible common denominator, it is not the denominator used in the notes. The lowest common denominator is 20."}]},{"id":"a66167f6-18ce-0731-1b8f-ca5830727b9c","cardType":"basic","points":3,"front":"Order from smallest: $\\frac{1}{4}$, $\\frac{3}{10}$, $\\frac{2}{5}$, $\\frac{1}{2}$.","back":"$\\frac{1}{4},\\ \\frac{3}{10},\\ \\frac{2}{5},\\ \\frac{1}{2}$","mcqOptions":[{"text":"$\\frac{1}{4},\\ \\frac{3}{10},\\ \\frac{2}{5},\\ \\frac{1}{2}$","correct":true,"explanation":"Using denominator 20 gives $\\frac{5}{20}$, $\\frac{6}{20}$, $\\frac{8}{20}$ and $\\frac{10}{20}$, so the fractions are already listed from smallest to largest."},{"text":"$\\frac{1}{2},\\ \\frac{2}{5},\\ \\frac{3}{10},\\ \\frac{1}{4}$","correct":false,"explanation":"This places the fractions in decreasing rather than increasing order. With denominator 20, the correct numerators are 5, 6, 8 and 10 from smallest to largest."},{"text":"$\\frac{3}{10},\\ \\frac{1}{4},\\ \\frac{2}{5},\\ \\frac{1}{2}$","correct":false,"explanation":"Comparing only the original numerators wrongly places $\\frac{3}{10}$ below $\\frac{1}{4}$. Their equivalents are $\\frac{6}{20}$ and $\\frac{5}{20}$, so $\\frac{1}{4}$ is smaller."},{"text":"$\\frac{1}{4},\\ \\frac{3}{10},\\ \\frac{1}{2},\\ \\frac{2}{5}$","correct":false,"explanation":"A larger denominator does not automatically mean a larger fraction. Since $\\frac{2}{5}=\\frac{8}{20}$ and $\\frac{1}{2}=\\frac{10}{20}$, $\\frac{2}{5}$ must come first."}]},{"id":"b3e0d4b1-7961-619c-3a2f-94cba5849171","cardType":"cloze","points":null,"front":"For a “closer to” question, the fraction with the [ ] from the target is closer.","back":"For a “closer to” question, the fraction with the smaller distance from the target is closer.","mcqOptions":[{"text":"smaller distance","correct":true,"explanation":"Closeness is measured by the absolute difference between each fraction and the target. The fraction with the smaller distance therefore lies nearer to the target."},{"text":"larger distance","correct":false,"explanation":"A larger distance means the fraction is farther from the target, not closer. The correct comparison selects the fraction with the smaller distance."},{"text":"positive difference","correct":false,"explanation":"The sign only shows which side of the target a fraction lies on; it does not determine closeness. The smaller absolute distance identifies the closer fraction."},{"text":"negative difference","correct":false,"explanation":"A negative difference means the fraction lies below the target, but it may still be far away. Closeness depends on the smaller distance from the target."}]},{"id":"9121ab62-3633-11e3-a132-e0b50a25f9f5","cardType":"basic","points":2,"front":"Which is closer to 1: $\\frac{5}{4}$ or $\\frac{4}{5}$?","back":"$\\frac{4}{5}$","mcqOptions":[{"text":"$\\frac{4}{5}$","correct":true,"explanation":"The distances from 1 are $\\frac{1}{5}$ for $\\frac{4}{5}$ and $\\frac{1}{4}$ for $\\frac{5}{4}$. Since $\\frac{1}{5}<\\frac{1}{4}$, $\\frac{4}{5}$ is closer."},{"text":"$\\frac{5}{4}$","correct":false,"explanation":"Being above 1 does not make a fraction closer. Its distance is $\\frac{1}{4}$, while $\\frac{4}{5}$ is only $\\frac{1}{5}$ from 1."},{"text":"They are equally close","correct":false,"explanation":"Reciprocal fractions are not necessarily equally distant from 1. Their distances are $\\frac{1}{4}$ and $\\frac{1}{5}$, so $\\frac{4}{5}$ is closer."},{"text":"Neither fraction","correct":false,"explanation":"Both fractions can be compared by subtracting them from 1 and taking absolute values. The smaller distance is $\\frac{1}{5}$, belonging to $\\frac{4}{5}$."}]},{"id":"d697a978-e20a-4a87-fcee-1b9bf3e5b4f0","cardType":"basic","points":2,"front":"Which is closer to $\\frac{1}{2}$: $\\frac{2}{5}$ or $\\frac{5}{8}$?","back":"$\\frac{2}{5}$","mcqOptions":[{"text":"$\\frac{2}{5}$","correct":true,"explanation":"The distances from $\\frac{1}{2}$ are $\\frac{1}{10}$ for $\\frac{2}{5}$ and $\\frac{1}{8}$ for $\\frac{5}{8}$. Since $\\frac{1}{10}<\\frac{1}{8}$, $\\frac{2}{5}$ is closer."},{"text":"$\\frac{5}{8}$","correct":false,"explanation":"Comparing decimal values gives distances of $0.1$ for $\\frac{2}{5}$ and $0.125$ for $\\frac{5}{8}$. Therefore $\\frac{2}{5}$, not $\\frac{5}{8}$, is closer."},{"text":"They are equally close","correct":false,"explanation":"The fractions lie on opposite sides of $\\frac{1}{2}$, but their distances are unequal. Since $\\frac{1}{10}<\\frac{1}{8}$, $\\frac{2}{5}$ is closer."},{"text":"Neither fraction","correct":false,"explanation":"Both distances can be calculated exactly, so a closer fraction can be identified. The distance $\\frac{1}{10}$ makes $\\frac{2}{5}$ closer than $\\frac{5}{8}$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Writing, Simplifying and Ordering Fractions","title":"Writing, Simplifying and Ordering Fractions Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"1d05be5b-108a-4c66-9e0b-ea9c9880c171","walled":"$L38"}],"$L39","$L3a"]