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amount.","correct":true,"explanation":"These forms express how much of a complete quantity is being considered. The whole represents the entire original quantity, while the fraction, decimal or percentage represents a part of it."},{"text":"Fractions, decimals and percentages describe a part of a whole; the whole is the half amount.","correct":false,"explanation":"Half is only one possible part, not the definition of the whole. The whole is the full amount, and fractions, decimals and percentages describe parts of that amount."},{"text":"Fractions, decimals and percentages describe a full amount; the whole is the full amount.","correct":false,"explanation":"This confuses the represented part with the complete quantity. Fractions, decimals and percentages describe a part of a whole, while the whole itself is the full amount."},{"text":"Fractions, decimals and percentages describe a part of a whole; the whole is the numerator.","correct":false,"explanation":"The numerator is the top number in a fraction, not the entire quantity. The whole is the full amount from which the represented part is taken."}]},{"id":"da78ccbe-d2a9-4af7-81b0-fc49285cb905","cardType":"cloze","points":null,"front":"In a fraction, the top number is the [ ] and the bottom number is the [ ].","back":"In a fraction, the top number is the numerator and the bottom number is the denominator.","mcqOptions":[{"text":"In a fraction, the top number is the numerator and the bottom number is the denominator.","correct":true,"explanation":"The numerator counts the selected parts, while the denominator shows how many equal parts make one whole. Their positions are fixed at the top and bottom respectively."},{"text":"In a fraction, the top number is the denominator and the bottom number is the numerator.","correct":false,"explanation":"This reverses the two fraction terms. The numerator is the top number and counts selected parts, while the denominator is the bottom number and gives the total equal parts."},{"text":"In a fraction, the top number is the numerator and the bottom number is the numerator.","correct":false,"explanation":"Only the top number is called the numerator. The bottom number is the denominator, which states how many equal parts form the whole."},{"text":"In a fraction, the top number is the denominator and the bottom number is the denominator.","correct":false,"explanation":"Only the bottom number is called the denominator. The top number is the numerator, which states how many of the equal parts are being considered."}]},{"id":"1e2132dc-92aa-4e1f-a869-fc4202eb9a71","cardType":"cloze","points":null,"front":"A percentage means [ ].","back":"A percentage means out of 100.","mcqOptions":[{"text":"out of 100","correct":true,"explanation":"Percent literally means per hundred, so a percentage states how many parts there are out of 100. For example, 37% means 37 out of 100."},{"text":"out of 10","correct":false,"explanation":"This confuses percentages with tenths. A percentage always means out of 100, although a fraction with denominator 10 can be converted to an equivalent fraction with denominator 100."},{"text":"out of 1","correct":false,"explanation":"Decimals often express a proportion relative to 1, which makes this tempting. A percentage instead means out of 100, so 0.37 is equivalent to 37%."},{"text":"out of 1000","correct":false,"explanation":"This confuses percentages with parts per thousand. A percentage means out of 100; a quantity stated out of 1000 must first be converted to an equivalent amount out of 100."}]},{"id":"4fc8c367-46b4-4bc7-8f33-ba5448904e15","cardType":"cloze","points":null,"front":"To simplify a fraction, divide numerator and denominator by the [ ] without changing its [ ].","back":"To simplify a fraction, divide numerator and denominator by the same number without changing its value.","mcqOptions":[{"text":"To simplify a fraction, divide numerator and denominator by the same number without changing its value.","correct":true,"explanation":"Dividing both parts of a fraction by the same common factor produces an equivalent fraction. Its numbers become smaller, but the proportion and therefore its value remain unchanged."},{"text":"To simplify a fraction, divide numerator and denominator by the different numbers without changing its value.","correct":false,"explanation":"Dividing the numerator and denominator by different numbers usually changes the fraction's value. Both must be divided by the same common factor to produce an equivalent simplified fraction."},{"text":"To simplify a fraction, divide numerator and denominator by the same number without changing its denominator.","correct":false,"explanation":"The denominator normally becomes smaller during simplification, so it does change. Dividing both numbers by the same common factor leaves the fraction's value unchanged instead."},{"text":"To simplify a fraction, divide numerator and denominator by the sum of the numbers without changing its value.","correct":false,"explanation":"The sum of the numerator and denominator is not generally a factor of either number. Simplification requires dividing both by the same common factor, which preserves the fraction's value."}]},{"id":"2c689cb2-fbe5-4f01-ad4f-aa5310038603","cardType":"basic","points":1,"front":"Write 14% as a fraction before simplifying.","back":"$\\frac{14}{100}$","mcqOptions":[{"text":"$\\frac{14}{100}$","correct":true,"explanation":"A percentage means out of 100, so 14% is written directly as $\\frac{14}{100}$. This is the required fraction before dividing both numbers by their common factor."},{"text":"$\\frac{14}{10}$","correct":false,"explanation":"Using 10 as the denominator treats the percentage as tenths and makes the value ten times too large. Since percent means out of 100, the fraction is $\\frac{14}{100}$."},{"text":"$\\frac{100}{14}$","correct":false,"explanation":"This reverses the percentage and its base, producing the reciprocal of the required fraction. The percentage amount is the numerator, so 14% is $\\frac{14}{100}$."},{"text":"$\\frac{14}{1000}$","correct":false,"explanation":"Using 1000 confuses percent with parts per thousand and makes the value ten times too small. Percent means out of 100, giving $\\frac{14}{100}$."}]},{"id":"a74126cf-53c2-4816-bfb4-3fc55245826c","cardType":"basic","points":1,"front":"Simplify $\\frac{14}{100}$.","back":"$\\frac{7}{50}$","mcqOptions":[{"text":"$\\frac{7}{50}$","correct":true,"explanation":"Both 14 and 100 are divisible by 2, giving $14 \\div 2 = 7$ and $100 \\div 2 = 50$. No larger common factor remains."},{"text":"$\\frac{7}{100}$","correct":false,"explanation":"Only dividing the numerator by 2 halves the fraction's value rather than simplifying it equivalently. Divide both numerator and denominator by 2 to obtain $\\frac{7}{50}$."},{"text":"$\\frac{14}{50}$","correct":false,"explanation":"Only dividing the denominator by 2 doubles the fraction's value rather than preserving it. Both parts must be divided by 2, producing $\\frac{7}{50}$."},{"text":"$\\frac{1}{7}$","correct":false,"explanation":"This results from incorrectly cancelling digits or treating the numbers separately rather than using a common factor. Dividing both 14 and 100 by 2 gives $\\frac{7}{50}$."}]},{"id":"ca8f1daf-eefd-49a1-bca7-f4e3ad1ee62e","cardType":"cloze","points":null,"front":"To change a decimal to a percentage, [ ]; the decimal point moves [ ].","back":"To change a decimal to a percentage, multiply by 100; the decimal point moves two places right.","mcqOptions":[{"text":"To change a decimal to a percentage, multiply by 100; the decimal point moves two places right.","correct":true,"explanation":"Percentages are measured out of 100, so multiplying a decimal by 100 gives its percentage value. This multiplication moves the decimal point two places to the right."},{"text":"To change a decimal to a percentage, divide by 100; the decimal point moves two places left.","correct":false,"explanation":"Dividing by 100 converts a percentage back to a decimal, so this reverses the required operation. Decimal to percentage requires multiplying by 100 and moving two places right."},{"text":"To change a decimal to a percentage, multiply by 100; the decimal point moves two places left.","correct":false,"explanation":"The stated operation and movement contradict each other: multiplying by 100 moves the decimal point right, not left. A decimal becomes a percentage by moving it two places right."},{"text":"To change a decimal to a percentage, multiply by 10; the decimal point moves one place right.","correct":false,"explanation":"Multiplying by 10 only moves the decimal point one place and gives a result ten times too small. Percentage conversion requires multiplying by 100 and moving two places right."}]},{"id":"cbc7e496-ebe6-4849-b0ec-37a508d07c13","cardType":"basic","points":1,"front":"Convert 0.37 to a percentage.","back":"37%","mcqOptions":[{"text":"37%","correct":true,"explanation":"Multiplying 0.37 by 100 moves the decimal point two places to the right, giving 37. Therefore, the equivalent percentage is 37%."},{"text":"3.7%","correct":false,"explanation":"This moves the decimal point only one place right, equivalent to multiplying by 10. Converting a decimal to a percentage requires multiplying by 100, so 0.37 becomes 37%."},{"text":"0.37%","correct":false,"explanation":"This simply adds a percentage sign without changing the numerical value, making the result 100 times too small. Multiplying 0.37 by 100 gives 37%."},{"text":"370%","correct":false,"explanation":"This moves the decimal point three places right, equivalent to multiplying by 1000. Percentage conversion multiplies by only 100, so the correct result is 37%."}]},{"id":"cbc5c2f6-8ff4-4245-98c5-0e3054d53e4d","cardType":"basic","points":1,"front":"Convert 0.3 to a percentage.","back":"30%","mcqOptions":[{"text":"30%","correct":true,"explanation":"Converting a decimal to a percentage means multiplying by 100. 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The correct conversion moves it two places right, so 0.3 equals 30%."}]},{"id":"14232de6-9f4c-4577-8264-8849291d2bbf","cardType":"cloze","points":null,"front":"To change a percentage to a decimal, [ ]; the decimal point moves [ ].","back":"To change a percentage to a decimal, divide by 100; the decimal point moves two places left.","mcqOptions":[{"text":"To change a percentage to a decimal, divide by 100; the decimal point moves two places left.","correct":true,"explanation":"A percentage means an amount out of 100, so dividing by 100 converts it to a decimal. This is equivalent to moving the decimal point two places left."},{"text":"To change a percentage to a decimal, multiply by 100; the decimal point moves two places right.","correct":false,"explanation":"Multiplying by 100 converts a decimal to a percentage, so this reverses the required process. A percentage becomes a decimal by dividing by 100 and moving two places left."},{"text":"To change a percentage to a decimal, divide by 10; the decimal point moves one place left.","correct":false,"explanation":"Dividing by 10 moves the decimal point only one place, making the result ten times too large. Percentages are divided by 100, moving the point two places left."},{"text":"To change a percentage to a decimal, divide by 1000; the decimal point moves three places left.","correct":false,"explanation":"Dividing by 1000 moves the decimal point one place too far and makes the result ten times too small. The correct divisor is 100, giving two places left."}]},{"id":"1d6e4519-3aed-4093-a9fb-6e28606ddaa8","cardType":"basic","points":1,"front":"Convert 7% to a decimal.","back":"0.07","mcqOptions":[{"text":"0.07","correct":true,"explanation":"Dividing 7 by 100 moves the decimal point two places left. Therefore, 7% represents seven hundredths and is written as 0.07."},{"text":"0.7","correct":false,"explanation":"This represents seven tenths, which is 70%, not 7%. Dividing 7 by 100 requires moving the decimal point two places left, giving 0.07."},{"text":"0.007","correct":false,"explanation":"Moving the decimal point three places left divides by 1000 and produces a value ten times too small. Dividing 7 by 100 gives 0.07."},{"text":"7.00","correct":false,"explanation":"Writing 7 as a decimal does not account for the meaning of the percent sign. Since percent means out of 100, 7% must be divided by 100 to give 0.07."}]},{"id":"654fa034-b26c-4279-a47d-997d13f9a7a0","cardType":"basic","points":1,"front":"Convert 4% to a decimal.","back":"0.04","mcqOptions":[{"text":"0.04","correct":true,"explanation":"The percent sign means out of 100, so 4% is $\\frac{4}{100}$. Dividing 4 by 100 moves the decimal point two places left to 0.04."},{"text":"0.4","correct":false,"explanation":"This is four tenths and equals 40%, so the decimal point has moved only one place. Dividing 4 by 100 moves it two places left, giving 0.04."},{"text":"0.004","correct":false,"explanation":"This results from dividing by 1000 rather than 100, making the decimal ten times too small. Since percent means out of 100, 4% equals 0.04."},{"text":"4.00","correct":false,"explanation":"Removing the percent sign without dividing leaves a value 100 times too large. Converting 4% to a decimal requires dividing by 100, which gives 0.04."}]},{"id":"8f2a43dd-722e-42b8-a0fa-622fb7959bb4","cardType":"basic","points":1,"front":"Write 0.025 as a fraction before simplifying.","back":"$\\frac{25}{1000}$","mcqOptions":[{"text":"$\\frac{25}{1000}$","correct":true,"explanation":"There are three digits after the decimal point, so 0.025 represents 25 thousandths. It is therefore written as $\\frac{25}{1000}$ before simplifying."},{"text":"$\\frac{25}{100}$","correct":false,"explanation":"A denominator of 100 represents hundredths and would give 0.25. Since 0.025 has three decimal places, it represents 25 thousandths, so the fraction is $\\frac{25}{1000}$."},{"text":"$\\frac{25}{10000}$","correct":false,"explanation":"A denominator of 10000 treats 25 as ten-thousandths and gives 0.0025, which is ten times too small. Three decimal places require the denominator 1000."},{"text":"$\\frac{25}{100000}$","correct":false,"explanation":"Using 100000 as the denominator interprets 25 as hundred-thousandths, producing 0.00025. The three decimal places in 0.025 require $\\frac{25}{1000}$."}]},{"id":"0164610d-d84f-4a9e-a694-46ab67e3c003","cardType":"basic","points":1,"front":"Simplify $\\frac{25}{1000}$.","back":"$\\frac{1}{40}$","mcqOptions":[{"text":"$\\frac{1}{40}$","correct":true,"explanation":"The highest common factor of 25 and 1000 is 25. Dividing both by 25 gives $\\frac{25 \\div 25}{1000 \\div 25}=\\frac{1}{40}$."},{"text":"$\\frac{1}{4}$","correct":false,"explanation":"Dividing the numerator by 25 but the denominator by 250 changes the fraction's value. Both parts must be divided by 25, producing $\\frac{1}{40}$."},{"text":"$\\frac{1}{25}$","correct":false,"explanation":"This denominator results from an incorrect division of 1000. Dividing both numerator and denominator by their common factor 25 gives a denominator of 40, so the answer is $\\frac{1}{40}$."},{"text":"$\\frac{1}{400}$","correct":false,"explanation":"Dividing 25 by 25 but dividing 1000 by only 2.5 does not preserve the fraction. Applying the same division by 25 to both parts gives $\\frac{1}{40}$."}]},{"id":"0431ea84-9d06-46fe-bdb0-764aea9d90a8","cardType":"basic","points":1,"front":"What operation does a fraction bar mean?","back":"Divide","mcqOptions":[{"text":"Divide","correct":true,"explanation":"A fraction bar instructs you to divide the numerator by the denominator. For example, $\\frac{6}{3}$ means $6 \\div 3$, which equals 2."},{"text":"Multiply","correct":false,"explanation":"Multiplication may be used when working with fractions, but the fraction bar itself represents division. The numerator is divided by the denominator, so $\\frac{6}{3}$ means $6 \\div 3$."},{"text":"Add","correct":false,"explanation":"The numerator and denominator are not added together. A fraction bar means division, with the value found by dividing the numerator by the denominator."},{"text":"Subtract","correct":false,"explanation":"The fraction bar does not mean finding the difference between the numerator and denominator. It represents division, so the numerator must be divided by the denominator."}]},{"id":"33354477-5838-4657-8f76-9398f1522da2","cardType":"basic","points":2,"front":"Convert $\\frac{4}{5}$ to a decimal using tenths.","back":"$\\frac{4}{5}=\\frac{8}{10}=0.8$","mcqOptions":[{"text":"$\\frac{4}{5}=\\frac{8}{10}=0.8$","correct":true,"explanation":"Multiplying both numerator and denominator by 2 creates the equivalent fraction $\\frac{8}{10}$. Eight tenths is written as the decimal 0.8."},{"text":"$\\frac{4}{5}=\\frac{4}{10}=0.4$","correct":false,"explanation":"Doubling only the denominator changes the fraction's value rather than creating an equivalent fraction. Both parts must be doubled, giving $\\frac{8}{10}=0.8$."},{"text":"$\\frac{4}{5}=\\frac{8}{100}=0.08$","correct":false,"explanation":"The denominator has been multiplied by 20 while the numerator has only been multiplied by 2, so the fractions are not equivalent. Using tenths gives $\\frac{8}{10}=0.8$."},{"text":"$\\frac{4}{5}=\\frac{6}{10}=0.6$","correct":false,"explanation":"Adding the same amount to the numerator and denominator does not preserve a fraction's value. Multiplying both by 2 gives the equivalent fraction $\\frac{8}{10}=0.8$."}]},{"id":"acb74d51-217a-4120-975e-b8ce0e5be135","cardType":"basic","points":1,"front":"Convert $\\frac{11}{20}$ to a percentage.","back":"55%","mcqOptions":[{"text":"55%","correct":true,"explanation":"Multiplying by 100 converts the fraction to a percentage: $\\frac{11}{20}\\times 100=55$, so the fraction is 55%."},{"text":"45%","correct":false,"explanation":"Dividing 11 by 20 gives 0.55, not 0.45. Multiplying 0.55 by 100 gives the correct percentage, 55%."},{"text":"0.55%","correct":false,"explanation":"The decimal 0.55 must be multiplied by 100 when converting to a percentage. Omitting that step gives 0.55 instead of the correct 55%."},{"text":"220%","correct":false,"explanation":"Multiplying 11 by 20 does not convert the fraction to a percentage. Instead, $11\\div20=0.55$, which is equal to 55%."}]},{"id":"7a5e5f6a-b9f1-48ea-bd37-34e33e84d589","cardType":"basic","points":1,"front":"If a fraction’s denominator is multiplied by 5, what must happen to the numerator?","back":"Multiply the numerator by 5 too.","mcqOptions":[{"text":"Multiply the numerator by 5 too.","correct":true,"explanation":"Multiplying the numerator and denominator by the same non-zero number produces an equivalent fraction, so multiplying the denominator by 5 requires multiplying the numerator by 5."},{"text":"Divide the numerator by 5 too.","correct":false,"explanation":"Dividing the numerator while multiplying the denominator makes the fraction 25 times smaller. To preserve its value, multiply the numerator by 5 too."},{"text":"Leave the numerator unchanged.","correct":false,"explanation":"Leaving the numerator unchanged makes the fraction five times smaller because only the denominator increases. Multiply the numerator by 5 too to form an equivalent fraction."},{"text":"Add 5 to the numerator too.","correct":false,"explanation":"Adding 5 does not apply the same scale factor as multiplying the denominator by 5. The numerator must also be multiplied by 5."}]},{"id":"a820661c-3f28-4f1d-ba4e-2fd261cd55f6","cardType":"basic","points":2,"front":"Is 16% greater than 0.2?","back":"No: 16% = $0.16$, and $0.16 < 0.20$.","mcqOptions":[{"text":"No: 16% = $0.16$, and $0.16 < 0.20$.","correct":true,"explanation":"Dividing 16 by 100 converts 16% to 0.16. Since 0.16 is less than 0.20, 16% is not greater than 0.2."},{"text":"Yes: 16% = $1.6$, and $1.6 > 0.20$.","correct":false,"explanation":"Converting a percentage to a decimal requires dividing by 100, not 10. Therefore, 16% is 0.16, which is less than 0.20."},{"text":"Yes: 16% = $0.16$, and $0.16 > 0.20$.","correct":false,"explanation":"The decimal conversion is correct, but the inequality sign is reversed. Since 16 hundredths is less than 20 hundredths, the correct answer is no."},{"text":"Yes: 16% = $0.16$, and $16 > 0.2$.","correct":false,"explanation":"This compares a percentage number with a decimal without putting them on the same scale. Converting 16% gives 0.16, which is less than 0.2."}]},{"id":"c2de4a89-fccb-44ae-b58f-5ce14bb0e820","cardType":"basic","points":2,"front":"Which is larger: 0.9 or 75%?","back":"0.9, because 0.9 = 90%.","mcqOptions":[{"text":"0.9, because 0.9 = 90%.","correct":true,"explanation":"Multiplying 0.9 by 100 converts it to 90%. Since 90% is greater than 75%, 0.9 is the larger value."},{"text":"75%, because 0.9 = 9%.","correct":false,"explanation":"The decimal point must move two places when converting a decimal to a percentage. Thus, 0.9 equals 90%, not 9%, and is larger than 75%."},{"text":"75%, because 75% = 7.5.","correct":false,"explanation":"Dividing 75 by 100 gives 0.75, not 7.5. Comparing 0.75 with 0.9 shows that 0.9 is the larger value."},{"text":"They are equal, because 0.9 = 75%.","correct":false,"explanation":"The values are not equal because 0.9 corresponds to 90%, whereas 75% corresponds to 0.75. Therefore, 0.9 is larger."}]},{"id":"7f4a6581-e228-442a-9ced-3c8f154183aa","cardType":"basic","points":2,"front":"Which is smaller: 0.405 or 42%?","back":"0.405, because 42% = 0.420.","mcqOptions":[{"text":"0.405, because 42% = 0.420.","correct":true,"explanation":"Converting 42% to a decimal gives 0.42, conventionally written as 0.420 for comparison. Since 0.405 is less than 0.420, it is smaller."},{"text":"42%, because 42% = 0.042.","correct":false,"explanation":"Dividing 42 by 100 gives 0.42, not 0.042. Comparing 0.405 with 0.420 shows that 0.405 is actually the smaller value."},{"text":"42%, because 0.405 = 405%.","correct":false,"explanation":"Multiplying 0.405 by 100 gives 40.5%, not 405%. Since 40.5% is less than 42%, the smaller value is 0.405."},{"text":"They are equal, because 0.405 = 42%.","correct":false,"explanation":"The decimal 0.405 is equivalent to 40.5%, not 42%. Since 40.5% is below 42%, the two values are unequal and 0.405 is smaller."}]},{"id":"e6f5918b-0a4d-4520-a489-a3da0cd28a71","cardType":"basic","points":3,"front":"Maya saves 38%. Leo spends $\\frac{3}{5}$ and saves the rest. Who saves more?","back":"Leo: the rest is $\\frac{2}{5}=40%$.","mcqOptions":[{"text":"Leo: the rest is $\\frac{2}{5}=40%$.","correct":true,"explanation":"Leo saves the fraction he does not spend: $1-\\frac{3}{5}=\\frac{2}{5}$. This equals 40%, which is greater than Maya’s 38%."},{"text":"Maya: the rest is $\\frac{2}{5}=0.4%$.","correct":false,"explanation":"The fraction $\\frac{2}{5}$ equals 0.4, or 40%, not 0.4%. Leo therefore saves 40%, which is more than Maya’s 38%."},{"text":"Maya: the rest is $\\frac{1}{5}=20%$.","correct":false,"explanation":"Subtracting $\\frac{3}{5}$ from one gives $\\frac{2}{5}$, not $\\frac{1}{5}$. Leo saves 40%, so he saves more than Maya."},{"text":"They save the same: $\\frac{2}{5}=38%$.","correct":false,"explanation":"The fraction $\\frac{2}{5}$ converts to 40%, not 38%. Leo therefore saves two percentage points more than Maya, so their savings are not equal."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Fractions, Decimals and Percentages","title":"Fractions, Decimals and Percentages Flashcards","topbar":{"backHref":"/gcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"577e9414-30c8-4f3b-af4b-7f61b2dca99b","walled":"$L39"}],"$L3a","$L3b"]