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