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The numerator is the top number, showing how many parts are being considered."},{"text":"left","correct":false,"explanation":"Fractions are described using positions above and below the fraction bar, not left and right. The numerator is the top number."},{"text":"larger","correct":false,"explanation":"The numerator is not defined by its size and may be larger or smaller than the denominator. It is the top number in the fraction."}]},{"id":"9e18317a-f942-40de-8f23-b563a255ca91","cardType":"cloze","points":null,"front":"In a fraction, the denominator is the [ ] number.","back":"In a fraction, the denominator is the bottom number.","mcqOptions":[{"text":"bottom","correct":true,"explanation":"The denominator is written below the fraction bar, so it is the bottom number in a fraction."},{"text":"top","correct":false,"explanation":"The top number is the numerator, not the denominator. The denominator is the bottom number and usually shows the total number of equal parts."},{"text":"right","correct":false,"explanation":"Fractions use positions above and below the fraction bar, not right and left. The denominator is the bottom number."},{"text":"smaller","correct":false,"explanation":"The denominator is not defined by being smaller and can have any value appropriate to the fraction. It is identified as the bottom number."}]},{"id":"80a4e7f3-1d40-442d-b755-9cb02696f3e3","cardType":"basic","points":1,"front":"If 3 out of 8 equal parts are shaded, what fraction is shaded?","back":"$\\frac{3}{8}$","mcqOptions":[{"text":"$\\frac{3}{8}$","correct":true,"explanation":"The numerator records the 3 shaded parts, while the denominator records all 8 equal parts, giving $\\frac{3}{8}$."},{"text":"$\\frac{8}{3}$","correct":false,"explanation":"This reverses the numerator and denominator. The 3 shaded parts belong in the numerator and the 8 total parts belong in the denominator, giving $\\frac{3}{8}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"This incorrectly uses the 5 unshaded parts as the denominator. The denominator must count all 8 equal parts, so the shaded fraction is $\\frac{3}{8}$."},{"text":"$\\frac{5}{8}$","correct":false,"explanation":"This gives the fraction that is unshaded because $8-3=5$. The question asks for the 3 shaded parts out of 8, so the answer is $\\frac{3}{8}$."}]},{"id":"d21a98d7-a6a4-4fd4-8e5e-49793e55c894","cardType":"basic","points":1,"front":"For a fraction of a group, what goes in the numerator?","back":"The number of chosen objects.","mcqOptions":[{"text":"The number of chosen objects.","correct":true,"explanation":"The numerator counts the objects with the required property, so it contains the number of chosen objects in the group."},{"text":"The total number of objects.","correct":false,"explanation":"The total number of objects belongs in the denominator. The numerator counts only the chosen objects that meet the condition in the question."},{"text":"The number of unchosen objects.","correct":false,"explanation":"Counting unchosen objects gives the complementary fraction rather than the requested fraction. The numerator must be the number of chosen objects."},{"text":"The number of different objects.","correct":false,"explanation":"The numerator does not count how many types of object there are. It counts the individual objects selected by the condition in the question."}]},{"id":"05b88821-085e-44c2-adaa-d6bdf3542e81","cardType":"basic","points":1,"front":"For a fraction of a group, what goes in the denominator?","back":"The total number of objects.","mcqOptions":[{"text":"The total number of objects.","correct":true,"explanation":"The denominator represents the whole group, so it contains the total number of objects being considered."},{"text":"The number of chosen objects.","correct":false,"explanation":"The chosen objects are counted in the numerator. The denominator must represent the whole group, so it is the total number of objects."},{"text":"The number of unchosen objects.","correct":false,"explanation":"The unchosen objects form only part of the group, not the whole. The denominator is the total number of objects, including chosen and unchosen ones."},{"text":"The number of different objects.","correct":false,"explanation":"The denominator counts every individual object, not the number of object types. It must contain the total number of objects in the group."}]},{"id":"33ace9a6-84e6-4466-bba4-1ed8e14b5efc","cardType":"basic","points":1,"front":"In a fraction question, what does “the rest” mean you should do?","back":"Subtract from the total.","mcqOptions":[{"text":"Subtract from the total.","correct":true,"explanation":"“The rest” means the amount remaining after the known part is removed, so subtract the known amount from the total."},{"text":"Add to the total.","correct":false,"explanation":"Adding would make the amount exceed the original total. To find “the rest”, subtract the known part from the total."},{"text":"Divide by the total.","correct":false,"explanation":"Division may be used later to form a fraction, but it does not find the remaining amount. First subtract the known part from the total."},{"text":"Multiply by the total.","correct":false,"explanation":"Multiplication does not find what remains and usually increases the quantity. “The rest” is found by subtracting the known amount from the total."}]},{"id":"ccc33d50-0e31-45d4-bff3-74fa41d3d614","cardType":"basic","points":2,"front":"There are 13 pencils; 8 are black and the rest are orange. What fraction are orange?","back":"$\\frac{5}{13}$","mcqOptions":[{"text":"$\\frac{5}{13}$","correct":true,"explanation":"There are $13-8=5$ orange pencils. The orange pencils are therefore 5 of the 13 pencils, giving $\\frac{5}{13}$."},{"text":"$\\frac{8}{13}$","correct":false,"explanation":"This is the fraction of pencils that are black. There are $13-8=5$ orange pencils, so the orange fraction is $\\frac{5}{13}$."},{"text":"$\\frac{5}{8}$","correct":false,"explanation":"Although there are 5 orange pencils, the denominator must be the total number of pencils, not the number of black pencils. The answer is $\\frac{5}{13}$."},{"text":"$\\frac{13}{5}$","correct":false,"explanation":"This reverses the part and the total. The 5 orange pencils go in the numerator and all 13 pencils go in the denominator, giving $\\frac{5}{13}$."}]},{"id":"c12414e6-fcb8-4a94-b120-32c6417eea56","cardType":"cloze","points":null,"front":"Equivalent fractions have the same [ ], even if they look different.","back":"Equivalent fractions have the same value, even if they look different.","mcqOptions":[{"text":"value","correct":true,"explanation":"Equivalent fractions represent the same proportion or number, so they have the same value even when their numerators and denominators differ."},{"text":"numerator","correct":false,"explanation":"Equivalent fractions can have different numerators; for example, $\\frac{1}{2}$ and $\\frac{2}{4}$. What remains the same is their value."},{"text":"denominator","correct":false,"explanation":"Equivalent fractions can have different denominators because both parts may be multiplied or divided by the same number. Their value, not their denominator, stays the same."},{"text":"appearance","correct":false,"explanation":"Equivalent fractions often look different because their numerators and denominators are different. They are equivalent because they represent the same value."}]},{"id":"1f082bac-1e5d-4dcf-a1ac-4ec175f0e8d6","cardType":"basic","points":1,"front":"How can you make an equivalent fraction?","back":"Multiply or divide the numerator and denominator by the same number.","mcqOptions":[{"text":"Multiply or divide the numerator and denominator by the same number.","correct":true,"explanation":"Applying the same non-zero multiplier or divisor to both parts preserves the fraction’s value because the numerator-to-denominator ratio remains unchanged."},{"text":"Multiply or divide the numerator and denominator by different numbers.","correct":false,"explanation":"Using different numbers changes the numerator-to-denominator ratio. An equivalent fraction is made by multiplying or dividing both parts by the same non-zero number."},{"text":"Add or subtract the same number from the numerator and denominator.","correct":false,"explanation":"Adding or subtracting equal amounts generally changes a fraction’s value. Equivalence is maintained by multiplying or dividing the numerator and denominator by the same non-zero number."},{"text":"Multiply or divide the numerator but leave the denominator unchanged.","correct":false,"explanation":"Changing only the numerator changes the fraction’s value. Both the numerator and denominator must be multiplied or divided by the same non-zero number."}]},{"id":"6bc8413e-ab33-4780-b77e-7d5e4e51a125","cardType":"basic","points":1,"front":"Which is not equivalent to $\\frac{3}{5}$: $\\frac{6}{10}$, $\\frac{9}{15}$, $\\frac{12}{20}$, $\\frac{15}{30}$, $\\frac{18}{30}$?","back":"$\\frac{15}{30}$","mcqOptions":[{"text":"$\\frac{15}{30}$","correct":true,"explanation":"Dividing the numerator and denominator by 15 gives $\\frac{1}{2}$, not $\\frac{3}{5}$, so this is the fraction that is not equivalent."},{"text":"$\\frac{6}{10}$","correct":false,"explanation":"This is formed by multiplying both parts of $\\frac{3}{5}$ by 2, so it is equivalent. The non-equivalent fraction is $\\frac{15}{30}=\\frac{1}{2}$."},{"text":"$\\frac{9}{15}$","correct":false,"explanation":"This is formed by multiplying both parts of $\\frac{3}{5}$ by 3, so it is equivalent. The non-equivalent fraction is $\\frac{15}{30}=\\frac{1}{2}$."},{"text":"$\\frac{18}{30}$","correct":false,"explanation":"Dividing both parts by 6 gives $\\frac{3}{5}$, so this fraction is equivalent. The non-equivalent fraction is $\\frac{15}{30}=\\frac{1}{2}$."}]},{"id":"39d3dda2-28ab-4c2c-ba3d-8f5607819837","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 common factor preserves the fraction’s value while producing an equivalent fraction with smaller terms."},{"text":"larger number","correct":false,"explanation":"Dividing both terms by whichever number is larger will not generally produce whole numbers. They must be divided by the same number that is a common factor."},{"text":"smaller number","correct":false,"explanation":"The smaller term is not necessarily a factor of the larger term. Simplification requires dividing the numerator and denominator by the same common factor."},{"text":"next prime number","correct":false,"explanation":"The next prime number may not divide either term exactly. The numerator and denominator must instead be divided by the same common factor."}]},{"id":"7d8a0a0f-bc11-4b92-9221-b4bd4938a879","cardType":"cloze","points":null,"front":"A fraction is in simplest form when the numerator and denominator have no common factor apart from [ ].","back":"A fraction is in simplest form when the numerator and denominator have no common factor apart from 1.","mcqOptions":[{"text":"1","correct":true,"explanation":"A fraction is fully simplified when the greatest common factor of its numerator and denominator is 1, so no further common division is possible."},{"text":"0","correct":false,"explanation":"Zero is not a factor used to test simplest form, and division by zero is undefined. The numerator and denominator must have no common factor apart from 1."},{"text":"2","correct":false,"explanation":"If both terms share a factor of 2, they can still be divided by 2, so the fraction is not simplest. Their only common factor must be 1."},{"text":"10","correct":false,"explanation":"A common factor of 10 would allow both terms to be divided again. In simplest form, the numerator and denominator have no common factor apart from 1."}]},{"id":"f5522f2a-ee6b-4eeb-8e9d-84ef8e51da13","cardType":"basic","points":1,"front":"Simplify $\\frac{36}{48}$.","back":"$\\frac{3}{4}$","mcqOptions":[{"text":"$\\frac{3}{4}$","correct":true,"explanation":"The greatest common factor of 36 and 48 is 12. Dividing both terms by 12 gives $\\frac{36\\div12}{48\\div12}=\\frac{3}{4}$."},{"text":"$\\frac{6}{8}$","correct":false,"explanation":"Dividing both terms by 6 gives an equivalent fraction, but it is not fully simplified because both terms still share 2. Dividing again gives $\\frac{3}{4}$."},{"text":"$\\frac{4}{6}$","correct":false,"explanation":"This results from dividing the numerator and denominator inconsistently, so it changes the fraction’s value. Dividing both original terms by 12 gives $\\frac{3}{4}$."},{"text":"$\\frac{4}{5}$","correct":false,"explanation":"Dividing 36 by 9 and 48 by a different amount changes the fraction’s value. Both terms should be divided by 12, giving $\\frac{3}{4}$."}]},{"id":"be45f88d-638f-4996-9e18-a5dcc1725ac0","cardType":"basic","points":1,"front":"For an increase as a fraction of last year’s cost, what is the denominator?","back":"The original amount.","mcqOptions":[{"text":"The original amount.","correct":true,"explanation":"An increase as a fraction of last year’s cost compares the change with the starting value, so the original amount is used as the denominator."},{"text":"The new amount.","correct":false,"explanation":"Using the new amount measures the increase relative to the final cost rather than last year’s cost. The required denominator is the original amount."},{"text":"The increase amount.","correct":false,"explanation":"The increase belongs in the numerator because it is the quantity being compared. The denominator is the original amount, representing last year’s cost."},{"text":"The average amount.","correct":false,"explanation":"Averaging the old and new costs gives neither the required reference value nor the stated comparison. The denominator must be the original amount."}]},{"id":"b5c9d7c0-5a09-4389-9141-b08c4722f99c","cardType":"basic","points":2,"front":"A bus pass rises from £30 to £42. What is the increase as a simplified fraction of last year’s cost?","back":"$\\frac{2}{5}$","mcqOptions":[{"text":"$\\frac{2}{5}$","correct":true,"explanation":"The increase is $£42-£30=£12$. Comparing this with the original £30 gives $\\frac{12}{30}$, which simplifies to $\\frac{2}{5}$."},{"text":"$\\frac{2}{7}$","correct":false,"explanation":"This comes from comparing the £12 increase with the new £42 cost. The denominator should be the original £30, giving $\\frac{12}{30}=\\frac{2}{5}$."},{"text":"$\\frac{7}{5}$","correct":false,"explanation":"This compares the new cost, £42, with the old cost, £30, rather than finding the increase. The required fraction is $\\frac{12}{30}=\\frac{2}{5}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"This does not use the £12 increase produced by subtracting £30 from £42. The correct comparison is $\\frac{12}{30}$, which simplifies to $\\frac{2}{5}$."}]},{"id":"f9964b3a-185f-4a8e-ab61-8ec68671f3bc","cardType":"cloze","points":null,"front":"To order fractions, first change them to a [ ].","back":"To order fractions, first change them to a common denominator.","mcqOptions":[{"text":"common denominator","correct":true,"explanation":"Equivalent fractions with a common denominator can be ordered by comparing their numerators directly, since each fraction is then divided into equal-sized parts."},{"text":"mixed number","correct":false,"explanation":"Converting fractions to mixed numbers does not create equally sized fractional parts and is impossible for proper fractions without writing zero wholes. Use a common denominator instead."},{"text":"unit fraction","correct":false,"explanation":"Rewriting every fraction as a unit fraction would usually change its value because unit fractions have numerator 1. Equivalent fractions should instead be given a common denominator."},{"text":"whole number","correct":false,"explanation":"Most fractions cannot be changed into whole numbers without rounding, which loses their exact values. They should be converted to equivalent fractions with a common denominator."}]},{"id":"a27d2986-006f-4fb4-9072-d806340e03b4","cardType":"basic","points":1,"front":"Once fractions have the same denominator, which part decides which is smaller?","back":"The numerator; smaller numerator means smaller fraction.","mcqOptions":[{"text":"The numerator; smaller numerator means smaller fraction.","correct":true,"explanation":"When fractions have the same denominator, each part is the same size, so the fraction with fewer parts has the smaller numerator and is smaller."},{"text":"The denominator; smaller denominator means smaller fraction.","correct":false,"explanation":"This reverses the role of the denominator. With equal denominators, compare the numerators because they count how many equal parts are present; the smaller numerator gives the smaller fraction."},{"text":"The numerator; larger numerator means smaller fraction.","correct":false,"explanation":"The comparison direction is reversed. Equal denominators mean a larger numerator represents more equal parts, so the larger numerator gives the larger fraction, not the smaller one."},{"text":"The denominator; larger denominator means smaller fraction.","correct":false,"explanation":"A larger denominator does usually make unit fractions smaller, but that is not the rule when denominators are already equal. In that case, compare the numerators."}]},{"id":"49de8655-85de-4f11-a393-0c366389dcb8","cardType":"basic","points":3,"front":"Put in ascending order: $\\frac{1}{4}$, $\\frac{2}{5}$, $\\frac{3}{10}$, $\\frac{1}{2}$, $\\frac{1}{5}$.","back":"$\\frac{1}{5}$, $\\frac{1}{4}$, $\\frac{3}{10}$, $\\frac{2}{5}$, $\\frac{1}{2}$","mcqOptions":[{"text":"$\\frac{1}{5}$, $\\frac{1}{4}$, $\\frac{3}{10}$, $\\frac{2}{5}$, $\\frac{1}{2}$","correct":true,"explanation":"Their decimal values are $0.2$, $0.25$, $0.3$, $0.4$, and $0.5$, respectively, so this list increases from the smallest fraction to the largest."},{"text":"$\\frac{1}{4}$, $\\frac{1}{5}$, $\\frac{3}{10}$, $\\frac{2}{5}$, $\\frac{1}{2}$","correct":false,"explanation":"This puts $\\frac{1}{4}$ before $\\frac{1}{5}$, but $0.25$ is greater than $0.2$. The correct ascending order starts $\\frac{1}{5}$, $\\frac{1}{4}$, then $\\frac{3}{10}$, $\\frac{2}{5}$, $\\frac{1}{2}$."},{"text":"$\\frac{1}{5}$, $\\frac{1}{4}$, $\\frac{2}{5}$, $\\frac{3}{10}$, $\\frac{1}{2}$","correct":false,"explanation":"The middle pair is reversed: $\\frac{2}{5}=0.4$ is greater than $\\frac{3}{10}=0.3$. The correct order places $\\frac{3}{10}$ before $\\frac{2}{5}$."},{"text":"$\\frac{1}{2}$, $\\frac{2}{5}$, $\\frac{3}{10}$, $\\frac{1}{4}$, $\\frac{1}{5}$","correct":false,"explanation":"This is descending order rather than ascending order, beginning with the largest fraction. Ascending order must begin with $\\frac{1}{5}$ and end with $\\frac{1}{2}$."}]},{"id":"c79ebfcc-4b99-4e07-8816-1223de349c16","cardType":"basic","points":1,"front":"To decide which fraction is closer to a target, what should you compare?","back":"Compare the gaps from the target.","mcqOptions":[{"text":"Compare the gaps from the target.","correct":true,"explanation":"A fraction is closer when its distance from the target is smaller. Comparing the gaps shows which fraction has the least difference from the target value."},{"text":"Compare the numerators.","correct":false,"explanation":"Numerators alone cannot show closeness when denominators differ, because the fraction's value depends on both parts. Compare each fraction's gap from the target instead."},{"text":"Compare the denominators.","correct":false,"explanation":"A denominator only describes the number of equal parts and does not directly measure distance from the target. The correct comparison is the size of each gap from the target."},{"text":"Compare the fractions’ products with the target.","correct":false,"explanation":"Multiplying fractions by the target does not measure how far apart they are and can give misleading results. Subtract each fraction from the target and compare the gaps."}]},{"id":"a7fa9c35-3b71-475c-a51f-c0f4eae12fb0","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 gap from $\\frac{1}{2}$ is $\\frac{1}{10}$ for $\\frac{2}{5}$, while the gap is $\\frac{1}{8}$ for $\\frac{5}{8}$. Since $\\frac{1}{10}<\\frac{1}{8}$, $\\frac{2}{5}$ is closer."},{"text":"$\\frac{5}{8}$","correct":false,"explanation":"This may seem closer because $\\frac{5}{8}$ is only slightly above $\\frac{1}{2}$, but its gap is $\\frac{1}{8}$. The gap for $\\frac{2}{5}$ is $\\frac{1}{10}$, so $\\frac{2}{5}$ is closer."},{"text":"$\\frac{1}{2}$","correct":false,"explanation":"The target itself would have zero gap, but it is not one of the two fractions being compared. Between the given choices, $\\frac{2}{5}$ is closer because its gap is $\\frac{1}{10}$."},{"text":"$\\frac{3}{5}$","correct":false,"explanation":"This is a tempting estimate because it is close to $\\frac{1}{2}$, but it is not one of the options being compared. The given fraction with the smaller gap is $\\frac{2}{5}$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Writing, Simplifying and Ordering Fractions","title":"Writing, Simplifying and Ordering Fractions Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"df3e6931-6d72-439e-a690-a25eb88e7056","walled":"$L39"}],"$L3a","$L3b"]