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It shows that 3 of the equal parts making up the whole have been selected."},{"text":"3 equal parts make the whole.","correct":false,"explanation":"This confuses the numerator with the denominator, which tells how many equal parts make the whole. The numerator 3 shows that 3 parts are selected."},{"text":"3 parts are unselected.","correct":false,"explanation":"The numerator counts the parts that are selected, not those left over. In this fraction, 3 equal parts out of the 5 are selected."},{"text":"3 wholes are selected.","correct":false,"explanation":"The numerator counts selected equal parts of one whole, rather than a number of wholes. Here, it means that 3 parts are selected."}]},{"id":"5fe4f26f-10da-f547-401e-a181ea54f2e3","cardType":"basic","points":1,"front":"In $\\frac{3}{5}$, what does the denominator 5 tell you?","back":"The whole is split into 5 equal parts.","mcqOptions":[{"text":"The whole is split into 5 equal parts.","correct":true,"explanation":"The denominator is the bottom number and gives the total number of equal parts in the whole. Therefore, the whole is divided into 5 equal parts."},{"text":"The whole is split into 3 equal parts.","correct":false,"explanation":"This uses the numerator instead of the denominator to count the total parts. The denominator 5 means that the whole is split into 5 equal parts."},{"text":"The whole has 5 selected parts.","correct":false,"explanation":"This confuses the denominator with the numerator. The denominator shows that there are 5 equal parts altogether, while the numerator shows how many are selected."},{"text":"The whole is split into 5 unequal parts.","correct":false,"explanation":"Fractions divide a whole into equal parts, not unequal ones. The denominator 5 means that the whole is split into 5 equal parts."}]},{"id":"703ced54-b865-f637-bc37-03c60a650814","cardType":"cloze","points":null,"front":"A fraction is in [ ] when its numerator and denominator cannot both be divided by the same whole number bigger than 1.","back":"A fraction is in simplest form when its numerator and denominator cannot both be divided by the same whole number bigger than 1.","mcqOptions":[{"text":"simplest form","correct":true,"explanation":"A fraction is in simplest form when no whole number greater than 1 divides both its numerator and denominator, so it cannot be reduced further."},{"text":"improper form","correct":false,"explanation":"Improper describes a fraction whose numerator is at least as large as its denominator. The stated condition instead defines a fraction in simplest form."},{"text":"mixed form","correct":false,"explanation":"Mixed form combines a whole number with a proper fraction. A fraction that cannot be reduced by a common factor is in simplest form."},{"text":"decimal form","correct":false,"explanation":"Decimal form expresses a value using decimal notation rather than a fraction. The condition about having no common factor defines simplest form."}]},{"id":"d022266f-8b86-5635-aca7-53e3502c7d13","cardType":"basic","points":1,"front":"Simplify $\\frac{12}{18}$.","back":"$$\\frac{2}{3}$","mcqOptions":[{"text":"$$\\frac{2}{3}$","correct":true,"explanation":"The highest common factor of 12 and 18 is 6. Dividing both numbers by 6 gives $12 \\div 6=2$ and $18 \\div 6=3$."},{"text":"$$\\frac{6}{9}$","correct":false,"explanation":"Dividing both numbers by 2 gives an equivalent fraction, but it is not fully simplified because 6 and 9 are both divisible by 3. The answer is $\\frac{2}{3}$."},{"text":"$$\\frac{3}{2}$","correct":false,"explanation":"This reverses the simplified numerator and denominator, producing the reciprocal. Dividing 12 and 18 by their common factor 6 gives $\\frac{2}{3}$."},{"text":"$$\\frac{4}{9}$","correct":false,"explanation":"This results from dividing the numerator and denominator by different numbers, which changes the fraction’s value. Dividing both by 6 gives $\\frac{2}{3}$."}]},{"id":"5e1f5c56-4f51-3f30-13a1-fd8b46999955","cardType":"cloze","points":null,"front":"Equivalent fractions have the [ ] even though they [ ].","back":"Equivalent fractions have the same value even though they look different.","mcqOptions":[{"text":"Equivalent fractions have the same value even though they look different.","correct":true,"explanation":"Equivalent fractions represent the same proportion or amount, although their numerators and denominators differ. For example, $\\frac{1}{2}$ and $\\frac{2}{4}$ look different but are equal."},{"text":"Equivalent fractions have the same numerator even though they have different denominators.","correct":false,"explanation":"Keeping the same numerator while changing the denominator normally changes the fraction’s value. Equivalent fractions must have the same value, even though they look different."},{"text":"Equivalent fractions have the different values even though they look different.","correct":false,"explanation":"This mistakes equivalent for merely different-looking fractions. Equivalent fractions have the same value because the numerator and denominator have been scaled by the same factor."},{"text":"Equivalent fractions have the same denominator even though they represent different amounts.","correct":false,"explanation":"Fractions representing different amounts are not equivalent, and equivalent fractions do not need the same denominator. They have the same value even though they look different."}]},{"id":"f12c3d3d-f27b-0c88-7949-d05545ab2ad1","cardType":"basic","points":1,"front":"What must you do to the numerator and denominator to make an equivalent fraction?","back":"Multiply or divide both by the same number.","mcqOptions":[{"text":"Multiply or divide both by the same number.","correct":true,"explanation":"Applying the same non-zero multiplier or divisor to both the numerator and denominator preserves their ratio, creating a fraction with the same value."},{"text":"Add or subtract both by the same number.","correct":false,"explanation":"Adding or subtracting the same number does not usually preserve the ratio between numerator and denominator. To make an equivalent fraction, multiply or divide both by the same number."},{"text":"Multiply only the numerator by the same number.","correct":false,"explanation":"Changing only the numerator changes the fraction’s value rather than creating an equivalent fraction. Both numerator and denominator must be multiplied or divided by the same number."},{"text":"Multiply or divide them by different numbers.","correct":false,"explanation":"Using different factors changes the ratio between numerator and denominator. Equivalent fractions are made by multiplying or dividing both by the same number."}]},{"id":"724521e1-cbc2-6bc4-3517-b6387a2a3f7c","cardType":"basic","points":1,"front":"Work out $\\frac{2}{7}+\\frac{3}{7}$.","back":"$$\\frac{5}{7}$","mcqOptions":[{"text":"$$\\frac{5}{7}$","correct":true,"explanation":"The denominators are already the same, so add the numerators and keep the denominator: $\\frac{2}{7}+\\frac{3}{7}=\\frac{2+3}{7}=\\frac{5}{7}$."},{"text":"$$\\frac{5}{14}$","correct":false,"explanation":"This incorrectly adds the denominators as well as the numerators. With equal denominators, keep 7 as the denominator and add only the numerators to get $\\frac{5}{7}$."},{"text":"$$\\frac{6}{7}$","correct":false,"explanation":"This multiplies the numerators instead of adding them. Since the denominators match, calculate $2+3=5$ and keep the denominator 7, giving $\\frac{5}{7}$."},{"text":"$$\\frac{1}{7}$","correct":false,"explanation":"This subtracts the numerators rather than adding them. The calculation requires $2+3=5$, while the common denominator remains 7, so the answer is $\\frac{5}{7}$."}]},{"id":"2a0096b7-74a0-26b1-c623-68f11fda6adb","cardType":"cloze","points":null,"front":"Fractions with different denominators must be changed to a [ ] before adding or subtracting.","back":"Fractions with different denominators must be changed to a common denominator before adding or subtracting.","mcqOptions":[{"text":"common denominator","correct":true,"explanation":"A common denominator divides each whole into parts of the same size. Once the denominators match, the numerators can be added or subtracted correctly."},{"text":"common numerator","correct":false,"explanation":"Matching numerators does not make the parts the same size, so it does not prepare fractions for addition or subtraction. The fractions need a common denominator."},{"text":"lowest denominator","correct":false,"explanation":"The denominator does not simply need to be made as small as possible. Both fractions need the same, or common, denominator before their numerators can be combined."},{"text":"mixed number","correct":false,"explanation":"Converting fractions to mixed numbers does not ensure that their fractional parts have equal-sized pieces. Fractions with different denominators must first use a common denominator."}]},{"id":"1c223c92-af7f-520c-db95-7fbde388a731","cardType":"basic","points":2,"front":"Work out $\\frac{1}{6}+\\frac{2}{3}$.","back":"$$\\frac{5}{6}$","mcqOptions":[{"text":"$$\\frac{5}{6}$","correct":true,"explanation":"Converting $\\frac{2}{3}$ to sixths gives $\\frac{4}{6}$. Adding the numerators then gives $\\frac{1}{6}+\\frac{4}{6}=\\frac{5}{6}$."},{"text":"$$\\frac{3}{6}$","correct":false,"explanation":"Adding the numerators while keeping 6 as the denominator ignores that $\\frac{2}{3}$ equals $\\frac{4}{6}$. The correct sum is $\\frac{5}{6}$."},{"text":"$$\\frac{3}{9}$","correct":false,"explanation":"Adding both numerators and denominators is not a valid rule for fraction addition. Using sixths gives $\\frac{1}{6}+\\frac{4}{6}=\\frac{5}{6}$."},{"text":"$$\\frac{7}{6}$","correct":false,"explanation":"An improper result comes from converting or combining the fractions incorrectly. Since $\\frac{2}{3}=\\frac{4}{6}$, the correct total is $\\frac{5}{6}$."}]},{"id":"6de4dcd8-e515-4c69-b9ba-6472db2b7694","cardType":"basic","points":2,"front":"Work out $\\frac{5}{8}-\\frac{1}{4}$.","back":"$$\\frac{3}{8}$","mcqOptions":[{"text":"$$\\frac{3}{8}$","correct":true,"explanation":"Convert $\\frac{1}{4}$ to $\\frac{2}{8}$, then subtract the numerators: $\\frac{5}{8}-\\frac{2}{8}=\\frac{3}{8}$."},{"text":"$$\\frac{4}{4}$","correct":false,"explanation":"Subtracting the numerator and denominator separately is not valid for fractions. Convert $\\frac{1}{4}$ to $\\frac{2}{8}$, giving the correct answer $\\frac{3}{8}$."},{"text":"$$\\frac{1}{2}$","correct":false,"explanation":"This results from treating $\\frac{1}{4}$ as $\\frac{1}{8}$. The equivalent fraction is $\\frac{2}{8}$, so the correct difference is $\\frac{3}{8}$."},{"text":"$$\\frac{7}{8}$","correct":false,"explanation":"Adding $\\frac{2}{8}$ instead of subtracting it reverses the required operation. The calculation is $\\frac{5}{8}-\\frac{2}{8}=\\frac{3}{8}$."}]},{"id":"6c2591bf-2432-30c5-e073-93b9bdab70f9","cardType":"basic","points":1,"front":"For denominators 4 and 12, what common denominator shortcut can you use?","back":"Use 12, the bigger multiple.","mcqOptions":[{"text":"Use 12, the bigger multiple.","correct":true,"explanation":"Because 12 is already a multiple of 4, it is the lowest common denominator. There is no need to multiply the two denominators together."},{"text":"Use 4, the smaller factor.","correct":false,"explanation":"Although 4 is the smaller denominator, 12 cannot be rewritten as an integer number of fourths. The suitable common denominator is 12 because both denominators divide into it."},{"text":"Use 8, the difference doubled.","correct":false,"explanation":"Adding or doubling denominators does not generally produce a common denominator. Here 8 is not divisible by 12, while 12 is divisible by both 4 and 12."},{"text":"Use 16, the two denominators added.","correct":false,"explanation":"Adding the denominators gives 16, but 16 is not a multiple of 12. The shortcut is to use 12 because it is already a multiple of 4."}]},{"id":"e32785e4-e779-9514-8b1a-273ed89e2fe5","cardType":"cloze","points":null,"front":"To multiply fractions, multiply the [ ] together and the [ ] together.","back":"To multiply fractions, multiply the numerators together and the denominators together.","mcqOptions":[{"text":"To multiply fractions, multiply the numerators together and the denominators together.","correct":true,"explanation":"Fraction multiplication is performed straight across: multiply the top numbers to obtain the new numerator and the bottom numbers to obtain the new denominator."},{"text":"To multiply fractions, multiply the denominators together and the denominators together.","correct":false,"explanation":"Using the denominators for both products ignores the original numerators. The top numbers must be multiplied together, followed by the bottom numbers."},{"text":"To multiply fractions, multiply the numerators together and the numerators together.","correct":false,"explanation":"Using the numerators for both products ignores the original denominators. Multiply the numerators for the new top and the denominators for the new bottom."},{"text":"To multiply fractions, multiply the diagonal terms together and the diagonal terms together.","correct":false,"explanation":"Diagonal multiplication is associated with comparing or solving some fraction equations, not ordinary fraction multiplication. Multiply the numerators together and the denominators together."}]},{"id":"70cfd373-d9e6-5b66-2dda-1f4b250a1af9","cardType":"basic","points":2,"front":"Work out $\\frac{2}{5}\\times\\frac{3}{4}$ in simplest form.","back":"$$\\frac{3}{10}$","mcqOptions":[{"text":"$$\\frac{3}{10}$","correct":true,"explanation":"Multiply straight across to get $\\frac{6}{20}$. Dividing both numerator and denominator by 2 simplifies this to $\\frac{3}{10}$."},{"text":"$$\\frac{5}{9}$","correct":false,"explanation":"Adding the numerators and denominators instead of multiplying gives this result. Multiplication gives $\\frac{6}{20}$, which simplifies correctly to $\\frac{3}{10}$."},{"text":"$$\\frac{6}{5}$","correct":false,"explanation":"Multiplying only the numerators and retaining a denominator loses the factor of 4. The complete product is $\\frac{6}{20}$, which simplifies to $\\frac{3}{10}$."},{"text":"$$\\frac{3}{20}$","correct":false,"explanation":"This is the unsimplified product with the numerator calculated incorrectly as 3 rather than $2\\times3=6$. The correctly simplified product is $\\frac{3}{10}$."}]},{"id":"0ea6a504-2775-86e2-e376-ee9970d9b38b","cardType":"cloze","points":null,"front":"To divide by a fraction, multiply by its [ ].","back":"To divide by a fraction, multiply by its reciprocal.","mcqOptions":[{"text":"reciprocal","correct":true,"explanation":"The reciprocal is formed by swapping a fraction’s numerator and denominator. Multiplying by this reciprocal is equivalent to dividing by the original fraction."},{"text":"denominator","correct":false,"explanation":"Multiplying by only the denominator does not invert the entire fraction. Division by a fraction is replaced by multiplication by its reciprocal."},{"text":"numerator","correct":false,"explanation":"Using only the numerator ignores the denominator and does not represent division by the fraction. The whole fraction must be inverted to form its reciprocal."},{"text":"negative","correct":false,"explanation":"The negative changes a number’s sign and is its additive inverse, not its multiplicative inverse. Fraction division requires multiplication by the reciprocal."}]},{"id":"f7629066-1eca-f708-d616-c020b2efebeb","cardType":"basic","points":1,"front":"In keep-change-flip, which fraction is flipped?","back":"The second fraction only.","mcqOptions":[{"text":"The second fraction only.","correct":true,"explanation":"Keep the first fraction unchanged, change division to multiplication, and flip only the second fraction to form its reciprocal."},{"text":"The first fraction only.","correct":false,"explanation":"Flipping the first fraction changes the dividend rather than replacing division by the divisor. Keep the first fraction and flip only the second fraction."},{"text":"The two fractions together.","correct":false,"explanation":"Taking both reciprocals changes the value of the calculation. In keep-change-flip, the first fraction stays unchanged and only the second fraction is flipped."},{"text":"The smaller fraction only.","correct":false,"explanation":"The choice is determined by the order of division, not by denominator size. The divisor is the second fraction, so only that fraction is flipped."}]},{"id":"773325b3-255b-1270-9180-4827acf7ae12","cardType":"basic","points":2,"front":"Work out $\\frac{2}{9}\\div\\frac{4}{5}$ in simplest form.","back":"$$\\frac{5}{18}$","mcqOptions":[{"text":"$$\\frac{5}{18}$","correct":true,"explanation":"Change division to multiplication and flip $\\frac{4}{5}$: $\\frac{2}{9}\\times\\frac{5}{4}=\\frac{10}{36}$, which simplifies to $\\frac{5}{18}$."},{"text":"$$\\frac{8}{45}$","correct":false,"explanation":"Multiplying the fractions without flipping the divisor gives $\\frac{8}{45}$. Division requires multiplying $\\frac{2}{9}$ by $\\frac{5}{4}$, producing $\\frac{5}{18}$."},{"text":"$$\\frac{18}{5}$","correct":false,"explanation":"Flipping the first fraction instead of the second reverses the wrong part of the calculation. Keep $\\frac{2}{9}$ and flip $\\frac{4}{5}$ to obtain $\\frac{5}{18}$."},{"text":"$$\\frac{10}{36}$","correct":false,"explanation":"This is equivalent to the correct value but is not in simplest form as requested. Dividing its numerator and denominator by 2 gives $\\frac{5}{18}$."}]},{"id":"fbc6011f-bb31-fe0c-b4c6-c56d6be872c8","cardType":"cloze","points":null,"front":"To calculate with mixed numbers, it is usually easiest to change them into [ ] first.","back":"To calculate with mixed numbers, it is usually easiest to change them into improper fractions first.","mcqOptions":[{"text":"improper fractions","correct":true,"explanation":"Improper fractions are easier to calculate with because each mixed number becomes a single fraction, allowing the usual methods for adding, subtracting, multiplying or dividing fractions."},{"text":"proper fractions","correct":false,"explanation":"A mixed number greater than one cannot be represented by a proper fraction of equal value. It should first be converted into an improper fraction."},{"text":"equivalent fractions","correct":false,"explanation":"Equivalent fractions are useful for finding common denominators, but this conversion specifically changes mixed numbers into improper fractions before carrying out the calculation."},{"text":"unit fractions","correct":false,"explanation":"A unit fraction has a numerator of one, so it cannot generally represent a mixed number by itself. Mixed numbers should be changed into improper fractions."}]},{"id":"847f39f2-8d89-7ed0-8633-b12fccd90646","cardType":"basic","points":1,"front":"Change $2\\frac{1}{5}$ into an improper fraction.","back":"$$\\frac{11}{5}$","mcqOptions":[{"text":"$$\\frac{11}{5}$","correct":true,"explanation":"Multiply the whole number by the denominator and add the numerator: $2\\times5+1=11$. The denominator remains $5$, giving $\\frac{11}{5}$."},{"text":"$$\\frac{10}{5}$","correct":false,"explanation":"This includes only $2\\times5$ and forgets to add the original numerator. Adding the extra $1$ gives the correct numerator $11$, so the answer is $\\frac{11}{5}$."},{"text":"$$\\frac{7}{5}$","correct":false,"explanation":"Adding the whole number directly to the numerator gives $2+1=3$, not $7$. The required calculation is $2\\times5+1=11$, giving $\\frac{11}{5}$."},{"text":"$$\\frac{11}{6}$","correct":false,"explanation":"The denominator should not be increased when converting a mixed number. The numerator becomes $2\\times5+1=11$, while the denominator stays $5$, giving $\\frac{11}{5}$."}]},{"id":"3fd41863-5c32-b01f-d6a9-4119cf63772b","cardType":"basic","points":2,"front":"Work out $2\\frac{1}{3}+1\\frac{1}{6}$.","back":"$$3\\frac{1}{2}$","mcqOptions":[{"text":"$$3\\frac{1}{2}$","correct":true,"explanation":"Use sixths: $\\frac{1}{3}=\\frac{2}{6}$, so the fractional parts total $\\frac{3}{6}=\\frac{1}{2}$. The whole-number parts total $3$, giving $3\\frac{1}{2}$."},{"text":"$$3\\frac{2}{9}$","correct":false,"explanation":"Adding the numerators and denominators separately incorrectly gives $\\frac{2}{9}$. Using a common denominator gives $\\frac{2}{6}+\\frac{1}{6}=\\frac{1}{2}$, so the answer is $3\\frac{1}{2}$."},{"text":"$$3\\frac{1}{3}$","correct":false,"explanation":"This effectively omits the additional $\\frac{1}{6}$. Since $\\frac{1}{3}=\\frac{2}{6}$, the fractional total is $\\frac{3}{6}=\\frac{1}{2}$, producing $3\\frac{1}{2}$."},{"text":"$$4\\frac{1}{2}$","correct":false,"explanation":"The whole-number parts are $2+1=3$, not $4$. The fractional parts add to $\\frac{1}{2}$, so the correct total is $3\\frac{1}{2}$."}]},{"id":"8544b3dc-af23-d6b2-3944-a1f4b7192e33","cardType":"basic","points":3,"front":"Work out $1\\frac{1}{2}\\times1\\frac{2}{3}$. Give a mixed number.","back":"$$2\\frac{1}{2}$","mcqOptions":[{"text":"$$2\\frac{1}{2}$","correct":true,"explanation":"Convert the mixed numbers to improper fractions: $\\frac{3}{2}\\times\\frac{5}{3}=\\frac{15}{6}=\\frac{5}{2}$. Converting back gives $2\\frac{1}{2}$."},{"text":"$$1\\frac{1}{3}$","correct":false,"explanation":"This comes from multiplying the whole and fractional parts separately, which is not valid for mixed numbers. Converting first gives $\\frac{3}{2}\\times\\frac{5}{3}=\\frac{5}{2}=2\\frac{1}{2}$."},{"text":"$$3\\frac{1}{6}$","correct":false,"explanation":"This is the result of adding the mixed numbers instead of multiplying them. For multiplication, convert first: $\\frac{3}{2}\\times\\frac{5}{3}=\\frac{5}{2}=2\\frac{1}{2}$."},{"text":"$$2\\frac{1}{3}$","correct":false,"explanation":"This confuses the fractional part after simplifying the product. The product is $\\frac{15}{6}=\\frac{5}{2}$, whose remainder is $\\frac{1}{2}$, so it equals $2\\frac{1}{2}$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Component 1"},"heading":"Fractions","title":"Fractions Flashcards","topbar":{"backHref":"/gcse/maths/eduqas/flashcards"},"topicSidebar":"$L36"}]}],"topicId":"64b03626-ee84-4bde-bc78-e70bdd4f12d4","walled":"$L37"}],"$L38","$L39"]