Fractions, Decimals & Percentages Flashcards
86 flashcards on fraction, decimal and percent conversions, exact and rounded equivalents, mixed-value comparisons, and common mistakes.
About this deck
Practice 86 English flashcards on fractions, decimals, and percentages. Build fluent recall of common equivalents, then use that knowledge to compare values, calculate short percentage problems, and spot conversion mistakes.
The cards teach all six conversion procedures: fraction to decimal, fraction to percentage, decimal to fraction, decimal to percentage, percentage to fraction, and percentage to decimal. Fifteen familiar proper fractions have a decimal or percentage prompt plus a separate recall prompt that returns to the fraction from one of those forms. The set adds mixed numbers, values above one, percentages below 1% and above 100%, and selected repeating-decimal equivalents. Exact answers and rounded answers are distinguished, with the required precision stated on each rounding prompt.
Comparisons ask you to choose the larger value, recognize equality, or order three mixed representations. Short applications practice percentage of an amount, part as a percentage of a whole, recovering a whole from a known percentage, and the percentage left after a discount. Error cards check division direction, place value, simplification, percentage notation, premature rounding, and the reference whole.
Learn the notation and conversion methods first. Familiar equivalents come next, with related prompts separated, followed by extended conversions, comparisons, and applications. Say or write the answer before turning the card, then work fresh problems outside the deck. Each card has one short retrieval task and an answer with brief reasoning.
This is focused foundational practice for secondary-school and adult learners. It does not include every possible direction for every number: selected reverse prompts give useful retrieval practice without a full permutation table. Negative-number ordering, full fraction arithmetic, recurring-decimal algebra, ratio and unit conversions, dosage calculations, and long multistep exercises are outside its scope. It is not a complete course or exam preparation program.
Questions, answers, examples, sequence, and metadata were independently authored with AI assistance. Arithmetic was checked directly; general definitions were cross-checked against freely available decimal, percentage, and repeating-decimal references. No textbook, examination, or competitor-deck wording or diagrams were copied. Mathematical facts are common knowledge. The original text and generated cover are released under CC0 1.0 to the extent applicable rights exist. This is an independent resource, unaffiliated with any school or examination provider.
Cards in this deck
Card 1
Question
In a fraction of one whole, what does the denominator count?
Answer
The equal parts that make one whole. In 3/7, the whole is divided into seven equal parts.
Card 2
Question
What does percent mean?
Answer
Per hundred. A percentage compares an amount with 100 equal parts of the reference whole.
Card 3
Question
In 0.6, what place does the digit 6 occupy?
Answer
The tenths place. Its value is 6/10.
Card 4
Question
How do you reduce a fraction to simplest form?
Answer
Divide its numerator and denominator by their greatest common factor. The fraction keeps the same value.
Card 5
Question
Fraction → decimal: which division do you calculate?
Answer
Numerator ÷ denominator. The denominator must be nonzero.
Card 6
Question
How do you turn a terminating decimal into a fraction?
Answer
Use place value: write the digits over 10, 100, 1,000, and so on, then simplify. For example, 0.032 = 32/1,000 = 4/125.
Card 7
Question
In 3/7 of one whole, what does the numerator count?
Answer
Three of the seven equal parts.
Card 8
Question
Percent → decimal: what do you do with the number before %?
Answer
Divide it by 100 and remove the % sign.
Card 9
Question
Does writing 0.60 instead of 0.6 change the numerical value?
Answer
No. Both equal six tenths. A trailing zero after the decimal does not change the value.
Card 10
Question
What does the mixed number 2 3/5 mean?
Answer
2 + 3/5. The space joins a whole-number part and a fractional part; it does not mean multiplication.
Card 11
Question
Fraction → percent: how do you find the number before %?
Answer
Divide the numerator by the denominator, then multiply the result by 100. Attach the % sign to that number.
Card 12
Question
Decimal → percent: how do you find the number before %?
Answer
Multiply the decimal by 100, then attach the % sign.
Card 13
Question
In 0.47, what is the value of the digit 7?
Answer
7/100, or 0.07. The 7 is in the hundredths place.
Card 14
Question
Percent → fraction: what denominator does % supply?
Answer
100
Put the number before % over 100. If the numerator has a decimal, multiply both parts by the same power of 10 to get integers, then simplify.
Card 15
Question
1/2 as a decimal?
Answer
0.5. One divided by two is five tenths.
Card 16
Question
1/5 as a percentage?
Answer
20%. Multiply numerator and denominator by 20 to get 20/100.
Card 17
Question
3/4 as a decimal?
Answer
0.75. Three divided by four is seventy-five hundredths.
Card 18
Question
1/10 as a percentage?
Answer
10%. One tenth is ten hundredths.
Card 19
Question
1/4 as a percentage?
Answer
25%. Four equal quarters each account for 25 out of 100.
Card 20
Question
50% as a fraction in simplest form?
Answer
1/2. Reduce 50/100 by dividing both parts by 50.
Card 21
Question
3/5 as a decimal?
Answer
0.6. Multiply both parts by 2: 3/5 = 6/10.
Card 22
Question
0.2 as a fraction in simplest form?
Answer
1/5. Reduce 2/10 by dividing both parts by 2.
Card 23
Question
1/8 as a decimal?
Answer
0.125. One divided by eight terminates after three decimal places.
Card 24
Question
75% as a fraction in simplest form?
Answer
3/4. Reduce 75/100 by dividing both parts by 25.
Card 25
Question
4/5 as a percentage?
Answer
80%. Each fifth is 20%, so four fifths is 80%.
Card 26
Question
0.1 as a fraction in simplest form?
Answer
1/10. The 1 is in the tenths place.
Card 27
Question
1/20 as a decimal?
Answer
0.05. Multiply both parts by 5: 1/20 = 5/100.
Card 28
Question
0.25 as a fraction in simplest form?
Answer
1/4. Reduce 25/100 by dividing both parts by 25.
Card 29
Question
60% as a fraction in simplest form?
Answer
3/5. Reduce 60/100 by dividing both parts by 20.
Card 30
Question
5/8 as a percentage?
Answer
62.5%. First divide: 5 ÷ 8 = 0.625. Then multiply by 100.
Card 31
Question
12.5% as a fraction in simplest form?
Answer
1/8. Write 12.5/100 = 125/1,000, then simplify.
Card 32
Question
3/8 as a decimal?
Answer
0.375. Three divided by eight is 375 thousandths.
Card 33
Question
0.8 as a fraction in simplest form?
Answer
4/5. Reduce 8/10 by dividing both parts by 2.
Card 34
Question
1/25 as a percentage?
Answer
4%. Multiply numerator and denominator by 4 to get 4/100.
Card 35
Question
5% as a fraction in simplest form?
Answer
1/20. Reduce 5/100 by dividing both parts by 5.
Card 36
Question
2/5 as a decimal?
Answer
0.4. Multiply both parts by 2: 2/5 = 4/10.
Card 37
Question
0.625 as a fraction in simplest form?
Answer
5/8. Reduce 625/1,000 by dividing both parts by 125.
Card 38
Question
7/8 as a percentage?
Answer
87.5%. First divide: 7 ÷ 8 = 0.875. Then multiply by 100.
Card 39
Question
37.5% as a fraction in simplest form?
Answer
3/8. Write 37.5/100 = 375/1,000, then simplify.
Card 40
Question
3/20 as a decimal?
Answer
0.15. Multiply both parts by 5: 3/20 = 15/100.
Card 41
Question
0.04 as a fraction in simplest form?
Answer
1/25. Reduce 4/100 by dividing both parts by 4.
Card 42
Question
40% as a fraction in simplest form?
Answer
2/5. Reduce 40/100 by dividing both parts by 20.
Card 43
Question
0.875 as a fraction in simplest form?
Answer
7/8. Reduce 875/1,000 by dividing both parts by 125.
Card 44
Question
15% as a fraction in simplest form?
Answer
3/20. Reduce 15/100 by dividing both parts by 5.
Card 45
Question
5/4 as a decimal?
Answer
1.25. One whole plus one quarter is 1 + 0.25.
Card 46
Question
0.6% as a decimal?
Answer
0.006. Divide 0.6 by 100; a percentage below 1% is below 0.01 as a decimal.
Card 47
Question
What distinguishes a repeating decimal from a terminating decimal?
Answer
A repeating decimal continues with a fixed digit or block of digits repeating forever, such as 0.272727… . A terminating decimal can be written with finitely many decimal places.
Card 48
Question
2.5 as a percentage?
Answer
250%. Multiply 2.5 by 100 and attach %.
Card 49
Question
0% as a decimal?
Answer
0
Zero divided by 100 is zero.
Card 50
Question
1/3 as an exact decimal?
Answer
0.333… (3 repeats forever). A finite string such as 0.333 is only an approximation.
Card 51
Question
125% as a fraction in simplest form?
Answer
5/4. Reduce 125/100; the result exceeds one whole.
Card 52
Question
1 3/4 as a percentage?
Answer
175%. Convert the mixed number to 1.75, then multiply by 100.
Card 53
Question
2/3 as an exact percentage?
Answer
66 2/3%. Multiplying 2/3 by 100 gives 200/3, or 66 2/3, before the % sign.
Card 54
Question
0.006 as a percentage?
Answer
0.6%. Multiply 0.006 by 100 and attach %.
Card 55
Question
1/6 as a decimal, rounded to three decimal places?
Answer
0.167. The exact decimal is 0.1666… (6 repeats forever); the next digit rounds the third decimal place up.
Card 56
Question
0.333… (3 repeats forever) as a fraction in simplest form?
Answer
1/3. This is exact; 0.333 without the repeating tail is a different number.
Card 57
Question
1 as a percentage?
Answer
100%. One whole corresponds to 100 out of 100.
Card 58
Question
2/3 as a percentage, rounded to one decimal place?
Answer
66.7%. The exact percentage is 66 2/3%, so round the repeating decimal percentage at the end.
Card 59
Question
1/12 as an exact percentage?
Answer
8 1/3%. Compute (1/12) × 100 = 100/12 = 25/3 before attaching %.
Card 60
Question
0.333 as a fraction in simplest form?
Answer
333/1,000. It ends after three decimal places and is not exactly 1/3.
Card 61
Question
How can you compare a fraction, a decimal, and a percentage on one scale?
Answer
Convert them all to decimals or all to fractions, then compare their numerical values. Keep exact values when rounding could affect the result.
Card 62
Question
Which is larger: 7/20 or 34%?
Answer
7/20. It equals 0.35, while 34% equals 0.34.
Card 63
Question
Which is larger: 0.09 or 0.1?
Answer
0.1. Write it as 0.10: ten hundredths is greater than nine hundredths.
Card 64
Question
Are 9/20 and 45% equal?
Answer
Yes. 9/20 = 45/100 = 45%.
Card 65
Question
Which is larger: 0.5% or 0.05?
Answer
0.05. The other value, 0.5%, equals 0.005.
Card 66
Question
Order from smallest to largest: 0.58, 3/5, 59%.
Answer
0.58 < 59% < 3/5. As decimals, they are 0.58, 0.59, and 0.60.
Card 67
Question
Which is larger: 130% or 1 1/4?
Answer
130%. It equals 1.3, while 1 1/4 equals 1.25.
Card 68
Question
Which is larger: 1/3 or 33.3%?
Answer
1/3. The percentage equals exactly 0.333, while 1/3 = 0.333… with 3 repeating forever.
Card 69
Question
Which is larger: 3/8 or 38%?
Answer
38%. The fraction equals 0.375, while 38% equals 0.38.
Card 70
Question
Which is larger: 17/20 or 0.84?
Answer
17/20. It equals 0.85, which is greater than 0.84.
Card 71
Question
How do you calculate p% of an amount A?
Answer
(p ÷ 100) × A. First convert the percentage to a decimal multiplier.
Card 72
Question
12% of 150?
Answer
18
Calculate 0.12 × 150.
Card 73
Question
How do you find what percentage a part is of a nonzero whole?
Answer
(part ÷ whole) × 100%. Divide by the whole, not by the part.
Card 74
Question
A 20% discount leaves what percentage of the original price to pay?
Answer
80%. Subtract the discount from 100%.
Card 75
Question
150% of 40?
Answer
60
Calculate 1.5 × 40; a percentage above 100% gives more than the original positive amount.
Card 76
Question
30 is 15% of what number?
Answer
200
Divide the part by the decimal percentage: 30 ÷ 0.15.
Card 77
Question
18 out of 72 is what percentage?
Answer
25%. Calculate (18 ÷ 72) × 100%.
Card 78
Question
0.5% of 600?
Answer
3
Calculate 0.005 × 600.
Card 79
Question
To convert 2/7 to a decimal, a learner calculates 7 ÷ 2. What must change?
Answer
Use 2 ÷ 7. The numerator is divided by the denominator, in that order.
Card 80
Question
A learner writes 0.42 = 0.42%. What is the correct percentage?
Answer
42%. Multiply the decimal by 100 before adding %; 0.42% would equal 0.0042.
Card 81
Question
A learner writes 0.018 = 18/100. What is the correct simplest fraction?
Answer
9/500. Three decimal places give 18/1,000, which simplifies to 9/500.
Card 82
Question
Why is “a percentage cannot exceed 100%” incorrect?
Answer
100% is one reference whole, and an amount can exceed it. For example, 160% of a positive amount is 1.6 times that amount.
Card 83
Question
A learner reduces 12/20 to 6/20. What is the correct simplest fraction?
Answer
3/5. Divide both numerator and denominator by 4. Changing only the numerator changes the value.
Card 84
Question
A learner rounds 1/6 to 0.17 before converting to percent. What is 1/6 as a percentage to one decimal place?
Answer
16.7%. Convert the exact fraction first: (1/6) × 100 = 16.666… before attaching %. Round only the final percentage.
Card 85
Question
For the same whole, why is 1/9 smaller than 1/6?
Answer
Nine equal parts make each part smaller than six equal parts. With the same positive numerator, a larger positive denominator gives a smaller fraction.
Card 86
Question
Why can 10% of 80 and 10% of 200 be different amounts?
Answer
The reference whole is different. They are 8 and 20 respectively, even though the percentage is the same.
86 cards
Fractions, Decimals & Percentages Flashcards
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