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In this fraction, the bottom number is 5."},{"text":"3","correct":false,"explanation":"The number 3 is the numerator, which counts the selected parts. The denominator is the bottom number, so the correct answer is 5."},{"text":"2","correct":false,"explanation":"Subtracting the numerator from the denominator gives 2, but subtraction is irrelevant here. The denominator is read directly from the bottom of the fraction, giving 5."},{"text":"15","correct":false,"explanation":"Multiplying the numerator and denominator gives 15, but that does not identify either part of the fraction. The denominator is the bottom number, 5."}]},{"id":"df1d14aa-2bf9-464b-85c3-6877a555a500","cardType":"basic","points":1,"front":"What does the word percent literally mean?","back":"Out of 100","mcqOptions":[{"text":"Out of 100","correct":true,"explanation":"The word “percent” comes from the Latin meaning “per hundred”. A percentage therefore describes a quantity as a number of parts out of 100."},{"text":"Out of 10","correct":false,"explanation":"This confuses percentages with tenths. “Percent” means per hundred, so a percentage expresses a number of parts out of 100."},{"text":"Out of 1","correct":false,"explanation":"A proportion may be expressed out of one, but that is not the literal meaning of “percent”. The word means out of 100."},{"text":"Out of 1000","correct":false,"explanation":"This would describe parts per thousand rather than percent. The prefix and root in “percent” indicate that the quantity is measured out of 100."}]},{"id":"906a9a55-06da-4ac5-8645-2a5da4a7a555","cardType":"basic","points":1,"front":"How is a percentage converted into a decimal?","back":"Divide by 100","mcqOptions":[{"text":"Divide by 100","correct":true,"explanation":"A percentage is a quantity out of 100, so dividing its numerical value by 100 converts it to an equivalent decimal."},{"text":"Multiply by 100","correct":false,"explanation":"Multiplying by 100 converts a decimal into a percentage, so this reverses the required conversion. To change a percentage into a decimal, divide by 100."},{"text":"Divide by 10","correct":false,"explanation":"Dividing by 10 moves the decimal point only one place left. Percentage-to-decimal conversion requires two places, which is equivalent to dividing by 100."},{"text":"Add 100","correct":false,"explanation":"Adding 100 changes the value rather than expressing the same proportion in decimal form. The percentage must instead be divided by 100."}]},{"id":"6ee7caf3-1593-4323-8edc-1d1646e76c24","cardType":"basic","points":2,"front":"Why is 0.06 smaller than 0.6?","back":"0.06 is 6 hundredths, while 0.6 is 6 tenths.","mcqOptions":[{"text":"0.06 is 6 hundredths, while 0.6 is 6 tenths.","correct":true,"explanation":"Hundredths are ten times smaller than tenths. Therefore 6 hundredths equals 0.06, whereas 6 tenths equals 0.6, making 0.06 smaller."},{"text":"0.06 is 6 tenths, while 0.6 is 6 hundredths.","correct":false,"explanation":"This reverses the place values: 0.06 represents 6 hundredths and 0.6 represents 6 tenths. Since hundredths are smaller than tenths, 0.06 is smaller."},{"text":"0.06 is 6 thousandths, while 0.6 is 6 hundredths.","correct":false,"explanation":"The decimal places have been shifted incorrectly. The 6 in 0.06 occupies the hundredths column, while the 6 in 0.6 occupies the tenths column."},{"text":"0.06 is 6 hundredths, while 0.6 is 6 ones.","correct":false,"explanation":"The 6 in 0.6 is not in the ones column; it is in the tenths column. Meanwhile, 0.06 contains 6 hundredths, which is smaller."}]},{"id":"d6c67138-800c-40ba-b2a3-ec68aa03d364","cardType":"basic","points":1,"front":"What is 4% written as a decimal?","back":"0.04","mcqOptions":[{"text":"0.04","correct":true,"explanation":"Converting a percentage to a decimal requires division by 100. Dividing 4 by 100 moves the decimal point two places left, producing 0.04."},{"text":"0.4","correct":false,"explanation":"Moving the decimal point only one place left divides by 10, not 100. Dividing 4 by 100 gives the correct decimal, 0.04."},{"text":"0.004","correct":false,"explanation":"Moving the decimal point three places left divides by 1000, making the result ten times too small. For 4%, divide by 100 to obtain 0.04."},{"text":"4.0","correct":false,"explanation":"Leaving 4 as a whole-number value does not account for “percent”, which means out of 100. Dividing by 100 gives 0.04."}]},{"id":"e3a60ff5-c517-4eff-8fde-06a4b5184425","cardType":"basic","points":1,"front":"How do you convert a decimal into a percentage?","back":"Multiply by 100","mcqOptions":[{"text":"Multiply by 100","correct":true,"explanation":"A decimal represents a proportion of one, while a percentage represents the equivalent proportion out of 100. Multiplying by 100 performs this conversion."},{"text":"Divide by 100","correct":false,"explanation":"Dividing by 100 is the reverse process used to convert a percentage into a decimal. To convert a decimal into a percentage, multiply by 100."},{"text":"Multiply by 10","correct":false,"explanation":"Multiplying by 10 moves the decimal point only one place and gives a value ten times too small. Percentage conversion requires multiplication by 100."},{"text":"Divide by 10","correct":false,"explanation":"Dividing by 10 moves the value in the wrong direction and by only one place. A decimal is converted to a percentage by multiplying by 100."}]},{"id":"9c75431f-7e1a-45f3-aa34-aeae0398c421","cardType":"basic","points":2,"front":"What is the decimal equivalent of $\\frac{2}{5}$?","back":"0.4","mcqOptions":[{"text":"0.4","correct":true,"explanation":"Dividing the numerator by the denominator gives the decimal value: $2 \\div 5 = 0.4$. Equivalently, multiplying both parts by 2 gives $\\frac{4}{10}$."},{"text":"0.25","correct":false,"explanation":"This results from reversing the decimal digits associated with the calculation. Dividing the numerator by the denominator correctly gives $2 \\div 5 = 0.4$."},{"text":"0.04","correct":false,"explanation":"This is ten times too small, as though the denominator were 50 rather than 5. The correct calculation is $2 \\div 5 = 0.4$."},{"text":"0.6","correct":false,"explanation":"This is the decimal equivalent of $\\frac{3}{5}$, not $\\frac{2}{5}$. Dividing 2 by 5 gives the correct value, 0.4."}]},{"id":"d51726c5-b75d-4fc1-859f-fb66a6d32133","cardType":"basic","points":2,"front":"Convert $\\frac{3}{50}$ to a percentage.","back":"6%","mcqOptions":[{"text":"6%","correct":true,"explanation":"Multiplying $\\frac{3}{50}$ by 100% gives $\\frac{300}{50}\\% = 6\\%$. Equivalently, the fraction simplifies to $\\frac{6}{100}$."},{"text":"3%","correct":false,"explanation":"This treats the denominator as though it were 100 without adjusting the numerator. Doubling both parts gives $\\frac{6}{100}$, so the correct percentage is 6%."},{"text":"0.06%","correct":false,"explanation":"This uses the decimal 0.06 but then incorrectly attaches a percent sign without multiplying by 100. Since 0.06 as a percentage is 6%, that is the correct answer."},{"text":"60%","correct":false,"explanation":"This moves the decimal point one place too far when converting 0.06 to a percentage. Multiplication by 100 gives 6%, not 60%."}]},{"id":"a6e2e2c4-3358-4ee9-930f-48373f863d09","cardType":"basic","points":1,"front":"When is a fraction considered to be in its simplest form?","back":"When the numerator and denominator have no common factors except 1.","mcqOptions":[{"text":"When the numerator and denominator have no common factors except 1.","correct":true,"explanation":"With no common factor greater than 1, there is no number by which both parts can be divided, so the fraction cannot be simplified further."},{"text":"When the numerator is smaller than the denominator.","correct":false,"explanation":"A numerator smaller than the denominator makes a fraction proper, not necessarily simplified. A fraction is simplest when its numerator and denominator have no common factors except 1."},{"text":"When the numerator and denominator are both even numbers.","correct":false,"explanation":"If both numbers are even, they share a factor of 2 and the fraction can still be reduced. Simplest form requires no common factors except 1."},{"text":"When the numerator and denominator have no common multiples except 1.","correct":false,"explanation":"This confuses factors with multiples; numbers generally have infinitely many common multiples. Simplest form means the numerator and denominator have no common factors greater than 1."}]},{"id":"ccb60e4a-7426-46df-a56b-9744e1a4bf2a","cardType":"basic","points":2,"front":"What are the decimal and percentage equivalents of $\\frac{3}{4}$?","back":"

0.75
75%

","mcqOptions":[{"text":"

0.75
75%

","correct":true,"explanation":"The fraction bar means division, so 3 divided by 4 equals 0.75. Multiplying the decimal by 100 converts it to the equivalent percentage, 75%."},{"text":"

0.25
25%

","correct":false,"explanation":"These are the equivalents of one quarter, the part remaining after three quarters. Dividing 3 by 4 gives 0.75, and multiplying by 100 gives 75%."},{"text":"

0.34
34%

","correct":false,"explanation":"Placing the numerator and denominator beside each other does not perform the required division. Calculating 3 divided by 4 gives 0.75, which is equivalent to 75%."},{"text":"

","correct":false,"explanation":"Rounding 0.75 to one decimal place gives 0.8, but that is not its exact equivalent. The exact decimal and percentage are 0.75 and 75%."}]},{"id":"abd1e511-31ff-4e9e-b078-e3ab2cdd2848","cardType":"basic","points":2,"front":"Which is larger: 16% or 0.2?","back":"0.2 (because 16% is only 0.16)","mcqOptions":[{"text":"0.2 (because 16% is only 0.16)","correct":true,"explanation":"Dividing 16 by 100 converts 16% to 0.16. Comparing the decimals shows that 0.20 is greater than 0.16, so 0.2 is larger."},{"text":"16% (because 0.2 is only 2%)","correct":false,"explanation":"This comes from moving the decimal point only one place when converting to a percentage. In fact, 0.2 equals 20%, so 0.2 is larger than 16%."},{"text":"They are equal (because both represent 20%)","correct":false,"explanation":"Although 0.2 does represent 20%, 16% represents 0.16 rather than 20%. Therefore the two values are unequal, and 0.2 is the larger value."},{"text":"16% (because 0.2 is only 0.02)","correct":false,"explanation":"This incorrectly divides 0.2 by 10 during the comparison. The decimal is already 0.20, while 16% equals 0.16, making 0.2 the larger value."}]},{"id":"369b89a9-d34d-4c2e-98c6-eda1c4c20383","cardType":"basic","points":2,"front":"If Sam spends $\\frac{3}{5}$ of his money, what percentage does he have left?","back":"40%","mcqOptions":[{"text":"40%","correct":true,"explanation":"Spending three fifths leaves two fifths of the original amount. Since two fifths equals 0.4, multiplying by 100 shows that 40% remains."},{"text":"60%","correct":false,"explanation":"This is the percentage Sam spends, not the percentage remaining. He has two fifths left, and multiplying two fifths by 100 gives 40%."},{"text":"20%","correct":false,"explanation":"This treats the remaining numerator, 2, as two tenths rather than two fifths. Since two fifths equals 0.4, Sam has 40% of his money left."},{"text":"25%","correct":false,"explanation":"This mistakenly treats the remaining two fifths as one quarter. The correct remaining fraction is two fifths, which equals 0.4 or 40%."}]},{"id":"9f94519b-d449-4e23-aff2-8f2787d647b7","cardType":"basic","points":1,"front":"What is 30% written as a decimal?","back":"0.3","mcqOptions":[{"text":"0.3","correct":true,"explanation":"Percent means out of 100, so 30% is 30 divided by 100. Moving the decimal point two places left gives 0.3."},{"text":"3","correct":false,"explanation":"Dividing 30 by only 10 gives 3, but percentages are amounts out of 100. Dividing 30 by 100 gives the correct decimal, 0.3."},{"text":"0.03","correct":false,"explanation":"This moves the decimal point three places rather than two, producing the decimal for 3%. Dividing 30 by 100 gives 0.3."},{"text":"30","correct":false,"explanation":"Leaving the number unchanged ignores that a percentage must be divided by 100 to become a decimal. Therefore 30% is 0.3, not 30."}]},{"id":"8e28be44-d29e-45fd-ab52-ffac51fcbc9e","cardType":"basic","points":1,"front":"What is usually the easiest form to use when ordering mixed fractions, decimals, and percentages?","back":"Decimals","mcqOptions":[{"text":"Decimals","correct":true,"explanation":"Converting every value to a decimal gives them a common form. Their place values can then be aligned, making direct comparison and ordering straightforward."},{"text":"Fractions","correct":false,"explanation":"Fractions can be compared, but unlike denominators often require extra conversion or common denominators. Converting all the values to decimals usually makes their sizes easiest to compare."},{"text":"Percentages","correct":false,"explanation":"Percentages can be used for ordering, but mixed forms are usually quickest to compare after converting them to decimals, which align naturally by place value."},{"text":"Mixed numbers","correct":false,"explanation":"Mixed numbers are unsuitable for values originally given as percentages and decimals and often require extra conversion. Decimals usually provide the clearest common form for ordering."}]},{"id":"3ed6068d-f6a6-480d-a9c4-5308ed0917ff","cardType":"cloze","points":null,"front":"The decimal 0.3 represents [ ].","back":"The decimal 0.3 represents 3 tenths.","mcqOptions":[{"text":"3 tenths","correct":true,"explanation":"The first digit after the decimal point is in the tenths column. Therefore a 3 in that position represents three parts out of ten."},{"text":"3 hundredths","correct":false,"explanation":"Three hundredths is written as 0.03 because the digit 3 occupies the hundredths place. In 0.3, it occupies the tenths place, so the value is 3 tenths."},{"text":"30 tenths","correct":false,"explanation":"Thirty tenths equals 3, so it is ten times larger than 0.3. The single digit 3 immediately after the decimal point represents 3 tenths."},{"text":"3 thousandths","correct":false,"explanation":"Three thousandths is written as 0.003 because the 3 is in the third decimal place. In 0.3, the 3 is in the tenths place."}]},{"id":"ccb27323-7e24-4dd6-9fe7-e9c1ad03b976","cardType":"cloze","points":null,"front":"A fraction bar (as in $\\frac{3}{4}$) represents the mathematical operation of [ ].","back":"A fraction bar (as in $\\frac{3}{4}$) represents the mathematical operation of division.","mcqOptions":[{"text":"division","correct":true,"explanation":"A fraction bar means divide the numerator by the denominator. Thus three quarters represents the calculation 3 divided by 4, which equals 0.75."},{"text":"multiplication","correct":false,"explanation":"The fraction bar does not instruct you to multiply the two numbers. It means that the numerator is divided by the denominator, so three quarters means 3 divided by 4."},{"text":"subtraction","correct":false,"explanation":"Subtracting the denominator from the numerator would give a difference, not a fraction’s value. A fraction bar represents division of the numerator by the denominator."},{"text":"addition","correct":false,"explanation":"Adding the numerator and denominator does not evaluate a fraction. The bar indicates division, so three quarters is found by dividing 3 by 4."}]},{"id":"6859bca8-a538-48e8-b636-ac8a22904376","cardType":"cloze","points":null,"front":"To convert 0.06 to a percentage, [ ] it by 100 to get 6%.","back":"To convert 0.06 to a percentage, multiply it by 100 to get 6%.","mcqOptions":[{"text":"multiply","correct":true,"explanation":"Multiplying a decimal by 100 moves its digits two places to the left relative to the decimal point, so 0.06 becomes 6%."},{"text":"divide","correct":false,"explanation":"Dividing by 100 converts a percentage to a decimal, not a decimal to a percentage. The correct operation is to multiply 0.06 by 100."},{"text":"add","correct":false,"explanation":"Adding 100 does not perform a decimal-to-percentage conversion. A decimal is converted to a percentage by multiplying it by 100."},{"text":"subtract","correct":false,"explanation":"Subtracting 100 changes the value rather than expressing it as a percentage. The correct conversion multiplies the decimal by 100."}]},{"id":"ce2dc5f2-7468-49d2-8ac0-b2aa02377c6d","cardType":"cloze","points":null,"front":"To convert 0.06 to a percentage, multiply it by 100 to get [ ].","back":"To convert 0.06 to a percentage, multiply it by 100 to get 6%.","mcqOptions":[{"text":"6%","correct":true,"explanation":"Multiplying 0.06 by 100 moves the digits two places, giving 6. Therefore, 0.06 is equivalent to 6%."},{"text":"0.6%","correct":false,"explanation":"This results from moving the decimal point only one place rather than two. Multiplying 0.06 by 100 gives 6%, not 0.6%."},{"text":"60%","correct":false,"explanation":"This moves the decimal point three places, effectively multiplying by 1000. Multiplying 0.06 by 100 gives the correct percentage of 6%."},{"text":"600%","correct":false,"explanation":"This effectively multiplies 0.06 by 10,000, making the result 100 times too large. Multiplication by 100 gives 6%."}]},{"id":"23473bdc-3f97-4a40-a795-706fda0a6449","cardType":"cloze","points":null,"front":"The decimal [ ] represents 3 thousandths.","back":"The decimal 0.003 represents 3 thousandths.","mcqOptions":[{"text":"0.003","correct":true,"explanation":"The third digit after the decimal point is the thousandths digit. Placing 3 there gives 0.003, which represents three thousandths."},{"text":"0.03","correct":false,"explanation":"This places 3 in the hundredths column, so it represents three hundredths. Three thousandths requires 3 in the third decimal place: 0.003."},{"text":"0.0003","correct":false,"explanation":"This places 3 in the ten-thousandths column, making the value ten times too small. Three thousandths is written as 0.003."},{"text":"3.000","correct":false,"explanation":"This places 3 in the ones column, so it represents three whole units. Three thousandths is written with 3 in the third decimal place: 0.003."}]},{"id":"3cbad882-58b1-4329-b910-936d1f7504db","cardType":"cloze","points":null,"front":"$$100\\%$ of a value is equivalent to [ ].","back":"$$100\\%$ of a value is equivalent to one whole.","mcqOptions":[{"text":"one whole","correct":true,"explanation":"The word percent means “out of 100”, so 100% means 100 out of 100. This is equal to one complete whole."},{"text":"one half","correct":false,"explanation":"One half is equivalent to 50%, not 100%. A percentage of 100% represents the entire original value, which is one whole."},{"text":"one tenth","correct":false,"explanation":"One tenth is equivalent to 10%, not 100%. Taking 100% of a value gives all of that value, or one whole."},{"text":"two wholes","correct":false,"explanation":"Two wholes correspond to 200%, because the original value is counted twice. Taking 100% gives the original value once, which is one whole."}]},{"id":"744b9073-15ed-457a-9b12-e7ad3981265c","cardType":"cloze","points":null,"front":"To write 17% as a fraction, you write the value over a denominator of [ ].","back":"To write 17% as a fraction, you write the value over a denominator of 100.","mcqOptions":[{"text":"100","correct":true,"explanation":"Percent means “per hundred”, so 17% means 17 parts out of 100. It is therefore written as the fraction 17/100."},{"text":"10","correct":false,"explanation":"Using 10 as the denominator confuses percentages with tenths and would make 17/10. Since percent means “per hundred”, the denominator must be 100."},{"text":"17","correct":false,"explanation":"Using 17 as the denominator would produce 17/17, which equals one whole. The percentage 17% means 17 out of 100."},{"text":"1000","correct":false,"explanation":"Using 1000 confuses percentage with parts per thousand and would make the fraction ten times too small. Percentages are written over 100."}]}]}],"examCountdown":null,"heading":"Fractions, Decimals and Percentages","title":"Fractions, Decimals and Percentages Flashcards","topbar":{"backHref":"/igcse/maths/oxford-aqa/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"355f4b62-7432-49a6-a907-1470fb84ec3d","walled":"$L39"}],"$L3a","$L3b"]