Fractions, Decimals & Percentages Flashcards
86 flashcards on fraction, decimal and percent conversions, exact and rounded equivalents, mixed-value comparisons, and common mistakes.
Über dieses Lernkartenset
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.
Karten in diesem Lernkartenset
Karte 1
Frage
In a fraction of one whole, what does the denominator count?
Antwort
The equal parts that make one whole. In 3/7, the whole is divided into seven equal parts.
Karte 2
Frage
What does percent mean?
Antwort
Per hundred. A percentage compares an amount with 100 equal parts of the reference whole.
Karte 3
Frage
In 0.6, what place does the digit 6 occupy?
Antwort
The tenths place. Its value is 6/10.
Karte 4
Frage
How do you reduce a fraction to simplest form?
Antwort
Divide its numerator and denominator by their greatest common factor. The fraction keeps the same value.
Karte 5
Frage
Fraction → decimal: which division do you calculate?
Antwort
Numerator ÷ denominator. The denominator must be nonzero.
Karte 6
Frage
How do you turn a terminating decimal into a fraction?
Antwort
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.
Karte 7
Frage
In 3/7 of one whole, what does the numerator count?
Antwort
Three of the seven equal parts.
Karte 8
Frage
Percent → decimal: what do you do with the number before %?
Antwort
Divide it by 100 and remove the % sign.
Karte 9
Frage
Does writing 0.60 instead of 0.6 change the numerical value?
Antwort
No. Both equal six tenths. A trailing zero after the decimal does not change the value.
Karte 10
Frage
What does the mixed number 2 3/5 mean?
Antwort
2 + 3/5. The space joins a whole-number part and a fractional part; it does not mean multiplication.
Karte 11
Frage
Fraction → percent: how do you find the number before %?
Antwort
Divide the numerator by the denominator, then multiply the result by 100. Attach the % sign to that number.
Karte 12
Frage
Decimal → percent: how do you find the number before %?
Antwort
Multiply the decimal by 100, then attach the % sign.
Karte 13
Frage
In 0.47, what is the value of the digit 7?
Antwort
7/100, or 0.07. The 7 is in the hundredths place.
Karte 14
Frage
Percent → fraction: what denominator does % supply?
Antwort
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.
Karte 15
Frage
1/2 as a decimal?
Antwort
0.5. One divided by two is five tenths.
Karte 16
Frage
1/5 as a percentage?
Antwort
20%. Multiply numerator and denominator by 20 to get 20/100.
Karte 17
Frage
3/4 as a decimal?
Antwort
0.75. Three divided by four is seventy-five hundredths.
Karte 18
Frage
1/10 as a percentage?
Antwort
10%. One tenth is ten hundredths.
Karte 19
Frage
1/4 as a percentage?
Antwort
25%. Four equal quarters each account for 25 out of 100.
Karte 20
Frage
50% as a fraction in simplest form?
Antwort
1/2. Reduce 50/100 by dividing both parts by 50.
Karte 21
Frage
3/5 as a decimal?
Antwort
0.6. Multiply both parts by 2: 3/5 = 6/10.
Karte 22
Frage
0.2 as a fraction in simplest form?
Antwort
1/5. Reduce 2/10 by dividing both parts by 2.
Karte 23
Frage
1/8 as a decimal?
Antwort
0.125. One divided by eight terminates after three decimal places.
Karte 24
Frage
75% as a fraction in simplest form?
Antwort
3/4. Reduce 75/100 by dividing both parts by 25.
Karte 25
Frage
4/5 as a percentage?
Antwort
80%. Each fifth is 20%, so four fifths is 80%.
Karte 26
Frage
0.1 as a fraction in simplest form?
Antwort
1/10. The 1 is in the tenths place.
Karte 27
Frage
1/20 as a decimal?
Antwort
0.05. Multiply both parts by 5: 1/20 = 5/100.
Karte 28
Frage
0.25 as a fraction in simplest form?
Antwort
1/4. Reduce 25/100 by dividing both parts by 25.
Karte 29
Frage
60% as a fraction in simplest form?
Antwort
3/5. Reduce 60/100 by dividing both parts by 20.
Karte 30
Frage
5/8 as a percentage?
Antwort
62.5%. First divide: 5 ÷ 8 = 0.625. Then multiply by 100.
Karte 31
Frage
12.5% as a fraction in simplest form?
Antwort
1/8. Write 12.5/100 = 125/1,000, then simplify.
Karte 32
Frage
3/8 as a decimal?
Antwort
0.375. Three divided by eight is 375 thousandths.
Karte 33
Frage
0.8 as a fraction in simplest form?
Antwort
4/5. Reduce 8/10 by dividing both parts by 2.
Karte 34
Frage
1/25 as a percentage?
Antwort
4%. Multiply numerator and denominator by 4 to get 4/100.
Karte 35
Frage
5% as a fraction in simplest form?
Antwort
1/20. Reduce 5/100 by dividing both parts by 5.
Karte 36
Frage
2/5 as a decimal?
Antwort
0.4. Multiply both parts by 2: 2/5 = 4/10.
Karte 37
Frage
0.625 as a fraction in simplest form?
Antwort
5/8. Reduce 625/1,000 by dividing both parts by 125.
Karte 38
Frage
7/8 as a percentage?
Antwort
87.5%. First divide: 7 ÷ 8 = 0.875. Then multiply by 100.
Karte 39
Frage
37.5% as a fraction in simplest form?
Antwort
3/8. Write 37.5/100 = 375/1,000, then simplify.
Karte 40
Frage
3/20 as a decimal?
Antwort
0.15. Multiply both parts by 5: 3/20 = 15/100.
Karte 41
Frage
0.04 as a fraction in simplest form?
Antwort
1/25. Reduce 4/100 by dividing both parts by 4.
Karte 42
Frage
40% as a fraction in simplest form?
Antwort
2/5. Reduce 40/100 by dividing both parts by 20.
Karte 43
Frage
0.875 as a fraction in simplest form?
Antwort
7/8. Reduce 875/1,000 by dividing both parts by 125.
Karte 44
Frage
15% as a fraction in simplest form?
Antwort
3/20. Reduce 15/100 by dividing both parts by 5.
Karte 45
Frage
5/4 as a decimal?
Antwort
1.25. One whole plus one quarter is 1 + 0.25.
Karte 46
Frage
0.6% as a decimal?
Antwort
0.006. Divide 0.6 by 100; a percentage below 1% is below 0.01 as a decimal.
Karte 47
Frage
What distinguishes a repeating decimal from a terminating decimal?
Antwort
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.
Karte 48
Frage
2.5 as a percentage?
Antwort
250%. Multiply 2.5 by 100 and attach %.
Karte 49
Frage
0% as a decimal?
Antwort
0
Zero divided by 100 is zero.
Karte 50
Frage
1/3 as an exact decimal?
Antwort
0.333… (3 repeats forever). A finite string such as 0.333 is only an approximation.
Karte 51
Frage
125% as a fraction in simplest form?
Antwort
5/4. Reduce 125/100; the result exceeds one whole.
Karte 52
Frage
1 3/4 as a percentage?
Antwort
175%. Convert the mixed number to 1.75, then multiply by 100.
Karte 53
Frage
2/3 as an exact percentage?
Antwort
66 2/3%. Multiplying 2/3 by 100 gives 200/3, or 66 2/3, before the % sign.
Karte 54
Frage
0.006 as a percentage?
Antwort
0.6%. Multiply 0.006 by 100 and attach %.
Karte 55
Frage
1/6 as a decimal, rounded to three decimal places?
Antwort
0.167. The exact decimal is 0.1666… (6 repeats forever); the next digit rounds the third decimal place up.
Karte 56
Frage
0.333… (3 repeats forever) as a fraction in simplest form?
Antwort
1/3. This is exact; 0.333 without the repeating tail is a different number.
Karte 57
Frage
1 as a percentage?
Antwort
100%. One whole corresponds to 100 out of 100.
Karte 58
Frage
2/3 as a percentage, rounded to one decimal place?
Antwort
66.7%. The exact percentage is 66 2/3%, so round the repeating decimal percentage at the end.
Karte 59
Frage
1/12 as an exact percentage?
Antwort
8 1/3%. Compute (1/12) × 100 = 100/12 = 25/3 before attaching %.
Karte 60
Frage
0.333 as a fraction in simplest form?
Antwort
333/1,000. It ends after three decimal places and is not exactly 1/3.
Karte 61
Frage
How can you compare a fraction, a decimal, and a percentage on one scale?
Antwort
Convert them all to decimals or all to fractions, then compare their numerical values. Keep exact values when rounding could affect the result.
Karte 62
Frage
Which is larger: 7/20 or 34%?
Antwort
7/20. It equals 0.35, while 34% equals 0.34.
Karte 63
Frage
Which is larger: 0.09 or 0.1?
Antwort
0.1. Write it as 0.10: ten hundredths is greater than nine hundredths.
Karte 64
Frage
Are 9/20 and 45% equal?
Antwort
Yes. 9/20 = 45/100 = 45%.
Karte 65
Frage
Which is larger: 0.5% or 0.05?
Antwort
0.05. The other value, 0.5%, equals 0.005.
Karte 66
Frage
Order from smallest to largest: 0.58, 3/5, 59%.
Antwort
0.58 < 59% < 3/5. As decimals, they are 0.58, 0.59, and 0.60.
Karte 67
Frage
Which is larger: 130% or 1 1/4?
Antwort
130%. It equals 1.3, while 1 1/4 equals 1.25.
Karte 68
Frage
Which is larger: 1/3 or 33.3%?
Antwort
1/3. The percentage equals exactly 0.333, while 1/3 = 0.333… with 3 repeating forever.
Karte 69
Frage
Which is larger: 3/8 or 38%?
Antwort
38%. The fraction equals 0.375, while 38% equals 0.38.
Karte 70
Frage
Which is larger: 17/20 or 0.84?
Antwort
17/20. It equals 0.85, which is greater than 0.84.
Karte 71
Frage
How do you calculate p% of an amount A?
Antwort
(p ÷ 100) × A. First convert the percentage to a decimal multiplier.
Karte 72
Frage
12% of 150?
Antwort
18
Calculate 0.12 × 150.
Karte 73
Frage
How do you find what percentage a part is of a nonzero whole?
Antwort
(part ÷ whole) × 100%. Divide by the whole, not by the part.
Karte 74
Frage
A 20% discount leaves what percentage of the original price to pay?
Antwort
80%. Subtract the discount from 100%.
Karte 75
Frage
150% of 40?
Antwort
60
Calculate 1.5 × 40; a percentage above 100% gives more than the original positive amount.
Karte 76
Frage
30 is 15% of what number?
Antwort
200
Divide the part by the decimal percentage: 30 ÷ 0.15.
Karte 77
Frage
18 out of 72 is what percentage?
Antwort
25%. Calculate (18 ÷ 72) × 100%.
Karte 78
Frage
0.5% of 600?
Antwort
3
Calculate 0.005 × 600.
Karte 79
Frage
To convert 2/7 to a decimal, a learner calculates 7 ÷ 2. What must change?
Antwort
Use 2 ÷ 7. The numerator is divided by the denominator, in that order.
Karte 80
Frage
A learner writes 0.42 = 0.42%. What is the correct percentage?
Antwort
42%. Multiply the decimal by 100 before adding %; 0.42% would equal 0.0042.
Karte 81
Frage
A learner writes 0.018 = 18/100. What is the correct simplest fraction?
Antwort
9/500. Three decimal places give 18/1,000, which simplifies to 9/500.
Karte 82
Frage
Why is “a percentage cannot exceed 100%” incorrect?
Antwort
100% is one reference whole, and an amount can exceed it. For example, 160% of a positive amount is 1.6 times that amount.
Karte 83
Frage
A learner reduces 12/20 to 6/20. What is the correct simplest fraction?
Antwort
3/5. Divide both numerator and denominator by 4. Changing only the numerator changes the value.
Karte 84
Frage
A learner rounds 1/6 to 0.17 before converting to percent. What is 1/6 as a percentage to one decimal place?
Antwort
16.7%. Convert the exact fraction first: (1/6) × 100 = 16.666… before attaching %. Round only the final percentage.
Karte 85
Frage
For the same whole, why is 1/9 smaller than 1/6?
Antwort
Nine equal parts make each part smaller than six equal parts. With the same positive numerator, a larger positive denominator gives a smaller fraction.
Karte 86
Frage
Why can 10% of 80 and 10% of 200 be different amounts?
Antwort
The reference whole is different. They are 8 and 20 respectively, even though the percentage is the same.
86 Karten
Fractions, Decimals & Percentages Flashcards
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