Fractions, Decimals & Percentages Flashcards
86 flashcards on fraction, decimal and percent conversions, exact and rounded equivalents, mixed-value comparisons, and common mistakes.
دربارهٔ این دسته
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.
کارتهای این دسته
کارت ۱
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In a fraction of one whole, what does the denominator count?
پاسخ
The equal parts that make one whole. In 3/7, the whole is divided into seven equal parts.
کارت ۲
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What does percent mean?
پاسخ
Per hundred. A percentage compares an amount with 100 equal parts of the reference whole.
کارت ۳
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In 0.6, what place does the digit 6 occupy?
پاسخ
The tenths place. Its value is 6/10.
کارت ۴
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How do you reduce a fraction to simplest form?
پاسخ
Divide its numerator and denominator by their greatest common factor. The fraction keeps the same value.
کارت ۵
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Fraction → decimal: which division do you calculate?
پاسخ
Numerator ÷ denominator. The denominator must be nonzero.
کارت ۶
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How do you turn a terminating decimal into a fraction?
پاسخ
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.
کارت ۷
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In 3/7 of one whole, what does the numerator count?
پاسخ
Three of the seven equal parts.
کارت ۸
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Percent → decimal: what do you do with the number before %?
پاسخ
Divide it by 100 and remove the % sign.
کارت ۹
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Does writing 0.60 instead of 0.6 change the numerical value?
پاسخ
No. Both equal six tenths. A trailing zero after the decimal does not change the value.
کارت ۱۰
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What does the mixed number 2 3/5 mean?
پاسخ
2 + 3/5. The space joins a whole-number part and a fractional part; it does not mean multiplication.
کارت ۱۱
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Fraction → percent: how do you find the number before %?
پاسخ
Divide the numerator by the denominator, then multiply the result by 100. Attach the % sign to that number.
کارت ۱۲
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Decimal → percent: how do you find the number before %?
پاسخ
Multiply the decimal by 100, then attach the % sign.
کارت ۱۳
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In 0.47, what is the value of the digit 7?
پاسخ
7/100, or 0.07. The 7 is in the hundredths place.
کارت ۱۴
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Percent → fraction: what denominator does % supply?
پاسخ
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.
کارت ۱۵
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1/2 as a decimal?
پاسخ
0.5. One divided by two is five tenths.
کارت ۱۶
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1/5 as a percentage?
پاسخ
20%. Multiply numerator and denominator by 20 to get 20/100.
کارت ۱۷
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3/4 as a decimal?
پاسخ
0.75. Three divided by four is seventy-five hundredths.
کارت ۱۸
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1/10 as a percentage?
پاسخ
10%. One tenth is ten hundredths.
کارت ۱۹
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1/4 as a percentage?
پاسخ
25%. Four equal quarters each account for 25 out of 100.
کارت ۲۰
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50% as a fraction in simplest form?
پاسخ
1/2. Reduce 50/100 by dividing both parts by 50.
کارت ۲۱
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3/5 as a decimal?
پاسخ
0.6. Multiply both parts by 2: 3/5 = 6/10.
کارت ۲۲
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0.2 as a fraction in simplest form?
پاسخ
1/5. Reduce 2/10 by dividing both parts by 2.
کارت ۲۳
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1/8 as a decimal?
پاسخ
0.125. One divided by eight terminates after three decimal places.
کارت ۲۴
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75% as a fraction in simplest form?
پاسخ
3/4. Reduce 75/100 by dividing both parts by 25.
کارت ۲۵
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4/5 as a percentage?
پاسخ
80%. Each fifth is 20%, so four fifths is 80%.
کارت ۲۶
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0.1 as a fraction in simplest form?
پاسخ
1/10. The 1 is in the tenths place.
کارت ۲۷
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1/20 as a decimal?
پاسخ
0.05. Multiply both parts by 5: 1/20 = 5/100.
کارت ۲۸
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0.25 as a fraction in simplest form?
پاسخ
1/4. Reduce 25/100 by dividing both parts by 25.
کارت ۲۹
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60% as a fraction in simplest form?
پاسخ
3/5. Reduce 60/100 by dividing both parts by 20.
کارت ۳۰
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5/8 as a percentage?
پاسخ
62.5%. First divide: 5 ÷ 8 = 0.625. Then multiply by 100.
کارت ۳۱
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12.5% as a fraction in simplest form?
پاسخ
1/8. Write 12.5/100 = 125/1,000, then simplify.
کارت ۳۲
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3/8 as a decimal?
پاسخ
0.375. Three divided by eight is 375 thousandths.
کارت ۳۳
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0.8 as a fraction in simplest form?
پاسخ
4/5. Reduce 8/10 by dividing both parts by 2.
کارت ۳۴
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1/25 as a percentage?
پاسخ
4%. Multiply numerator and denominator by 4 to get 4/100.
کارت ۳۵
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5% as a fraction in simplest form?
پاسخ
1/20. Reduce 5/100 by dividing both parts by 5.
کارت ۳۶
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2/5 as a decimal?
پاسخ
0.4. Multiply both parts by 2: 2/5 = 4/10.
کارت ۳۷
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0.625 as a fraction in simplest form?
پاسخ
5/8. Reduce 625/1,000 by dividing both parts by 125.
کارت ۳۸
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7/8 as a percentage?
پاسخ
87.5%. First divide: 7 ÷ 8 = 0.875. Then multiply by 100.
کارت ۳۹
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37.5% as a fraction in simplest form?
پاسخ
3/8. Write 37.5/100 = 375/1,000, then simplify.
کارت ۴۰
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3/20 as a decimal?
پاسخ
0.15. Multiply both parts by 5: 3/20 = 15/100.
کارت ۴۱
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0.04 as a fraction in simplest form?
پاسخ
1/25. Reduce 4/100 by dividing both parts by 4.
کارت ۴۲
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40% as a fraction in simplest form?
پاسخ
2/5. Reduce 40/100 by dividing both parts by 20.
کارت ۴۳
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0.875 as a fraction in simplest form?
پاسخ
7/8. Reduce 875/1,000 by dividing both parts by 125.
کارت ۴۴
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15% as a fraction in simplest form?
پاسخ
3/20. Reduce 15/100 by dividing both parts by 5.
کارت ۴۵
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5/4 as a decimal?
پاسخ
1.25. One whole plus one quarter is 1 + 0.25.
کارت ۴۶
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0.6% as a decimal?
پاسخ
0.006. Divide 0.6 by 100; a percentage below 1% is below 0.01 as a decimal.
کارت ۴۷
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What distinguishes a repeating decimal from a terminating decimal?
پاسخ
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.
کارت ۴۸
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2.5 as a percentage?
پاسخ
250%. Multiply 2.5 by 100 and attach %.
کارت ۴۹
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0% as a decimal?
پاسخ
0
Zero divided by 100 is zero.
کارت ۵۰
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1/3 as an exact decimal?
پاسخ
0.333… (3 repeats forever). A finite string such as 0.333 is only an approximation.
کارت ۵۱
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125% as a fraction in simplest form?
پاسخ
5/4. Reduce 125/100; the result exceeds one whole.
کارت ۵۲
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1 3/4 as a percentage?
پاسخ
175%. Convert the mixed number to 1.75, then multiply by 100.
کارت ۵۳
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2/3 as an exact percentage?
پاسخ
66 2/3%. Multiplying 2/3 by 100 gives 200/3, or 66 2/3, before the % sign.
کارت ۵۴
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0.006 as a percentage?
پاسخ
0.6%. Multiply 0.006 by 100 and attach %.
کارت ۵۵
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1/6 as a decimal, rounded to three decimal places?
پاسخ
0.167. The exact decimal is 0.1666… (6 repeats forever); the next digit rounds the third decimal place up.
کارت ۵۶
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0.333… (3 repeats forever) as a fraction in simplest form?
پاسخ
1/3. This is exact; 0.333 without the repeating tail is a different number.
کارت ۵۷
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1 as a percentage?
پاسخ
100%. One whole corresponds to 100 out of 100.
کارت ۵۸
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2/3 as a percentage, rounded to one decimal place?
پاسخ
66.7%. The exact percentage is 66 2/3%, so round the repeating decimal percentage at the end.
کارت ۵۹
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1/12 as an exact percentage?
پاسخ
8 1/3%. Compute (1/12) × 100 = 100/12 = 25/3 before attaching %.
کارت ۶۰
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0.333 as a fraction in simplest form?
پاسخ
333/1,000. It ends after three decimal places and is not exactly 1/3.
کارت ۶۱
پرسش
How can you compare a fraction, a decimal, and a percentage on one scale?
پاسخ
Convert them all to decimals or all to fractions, then compare their numerical values. Keep exact values when rounding could affect the result.
کارت ۶۲
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Which is larger: 7/20 or 34%?
پاسخ
7/20. It equals 0.35, while 34% equals 0.34.
کارت ۶۳
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Which is larger: 0.09 or 0.1?
پاسخ
0.1. Write it as 0.10: ten hundredths is greater than nine hundredths.
کارت ۶۴
پرسش
Are 9/20 and 45% equal?
پاسخ
Yes. 9/20 = 45/100 = 45%.
کارت ۶۵
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Which is larger: 0.5% or 0.05?
پاسخ
0.05. The other value, 0.5%, equals 0.005.
کارت ۶۶
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Order from smallest to largest: 0.58, 3/5, 59%.
پاسخ
0.58 < 59% < 3/5. As decimals, they are 0.58, 0.59, and 0.60.
کارت ۶۷
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Which is larger: 130% or 1 1/4?
پاسخ
130%. It equals 1.3, while 1 1/4 equals 1.25.
کارت ۶۸
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Which is larger: 1/3 or 33.3%?
پاسخ
1/3. The percentage equals exactly 0.333, while 1/3 = 0.333… with 3 repeating forever.
کارت ۶۹
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Which is larger: 3/8 or 38%?
پاسخ
38%. The fraction equals 0.375, while 38% equals 0.38.
کارت ۷۰
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Which is larger: 17/20 or 0.84?
پاسخ
17/20. It equals 0.85, which is greater than 0.84.
کارت ۷۱
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How do you calculate p% of an amount A?
پاسخ
(p ÷ 100) × A. First convert the percentage to a decimal multiplier.
کارت ۷۲
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12% of 150?
پاسخ
18
Calculate 0.12 × 150.
کارت ۷۳
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How do you find what percentage a part is of a nonzero whole?
پاسخ
(part ÷ whole) × 100%. Divide by the whole, not by the part.
کارت ۷۴
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A 20% discount leaves what percentage of the original price to pay?
پاسخ
80%. Subtract the discount from 100%.
کارت ۷۵
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150% of 40?
پاسخ
60
Calculate 1.5 × 40; a percentage above 100% gives more than the original positive amount.
کارت ۷۶
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30 is 15% of what number?
پاسخ
200
Divide the part by the decimal percentage: 30 ÷ 0.15.
کارت ۷۷
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18 out of 72 is what percentage?
پاسخ
25%. Calculate (18 ÷ 72) × 100%.
کارت ۷۸
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0.5% of 600?
پاسخ
3
Calculate 0.005 × 600.
کارت ۷۹
پرسش
To convert 2/7 to a decimal, a learner calculates 7 ÷ 2. What must change?
پاسخ
Use 2 ÷ 7. The numerator is divided by the denominator, in that order.
کارت ۸۰
پرسش
A learner writes 0.42 = 0.42%. What is the correct percentage?
پاسخ
42%. Multiply the decimal by 100 before adding %; 0.42% would equal 0.0042.
کارت ۸۱
پرسش
A learner writes 0.018 = 18/100. What is the correct simplest fraction?
پاسخ
9/500. Three decimal places give 18/1,000, which simplifies to 9/500.
کارت ۸۲
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Why is “a percentage cannot exceed 100%” incorrect?
پاسخ
100% is one reference whole, and an amount can exceed it. For example, 160% of a positive amount is 1.6 times that amount.
کارت ۸۳
پرسش
A learner reduces 12/20 to 6/20. What is the correct simplest fraction?
پاسخ
3/5. Divide both numerator and denominator by 4. Changing only the numerator changes the value.
کارت ۸۴
پرسش
A learner rounds 1/6 to 0.17 before converting to percent. What is 1/6 as a percentage to one decimal place?
پاسخ
16.7%. Convert the exact fraction first: (1/6) × 100 = 16.666… before attaching %. Round only the final percentage.
کارت ۸۵
پرسش
For the same whole, why is 1/9 smaller than 1/6?
پاسخ
Nine equal parts make each part smaller than six equal parts. With the same positive numerator, a larger positive denominator gives a smaller fraction.
کارت ۸۶
پرسش
Why can 10% of 80 and 10% of 200 be different amounts?
پاسخ
The reference whole is different. They are 8 and 20 respectively, even though the percentage is the same.
۸۶ کارت
Fractions, Decimals & Percentages Flashcards
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