Fractions, Decimals & Percentages Flashcards

このデッキのカード

1. カード 1

   質問

   In a fraction of one whole, what does the denominator count?

   回答

   The equal parts that make one whole. In 3/7, the whole is divided into seven equal parts.

2. カード 2

   質問

   What does percent mean?

   回答

   Per hundred. A percentage compares an amount with 100 equal parts of the reference whole.

3. カード 3

   質問

   In 0.6, what place does the digit 6 occupy?

   回答

   The tenths place. Its value is 6/10.

4. カード 4

   質問

   How do you reduce a fraction to simplest form?

   回答

   Divide its numerator and denominator by their greatest common factor. The fraction keeps the same value.

5. カード 5

   質問

   Fraction → decimal: which division do you calculate?

   回答

   Numerator ÷ denominator. The denominator must be nonzero.

6. カード 6

   質問

   How do you turn a terminating decimal into a fraction?

   回答

   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.

7. カード 7

   質問

   In 3/7 of one whole, what does the numerator count?

   回答

   Three of the seven equal parts.

8. カード 8

   質問

   Percent → decimal: what do you do with the number before %?

   回答

   Divide it by 100 and remove the % sign.

9. カード 9

   質問

   Does writing 0.60 instead of 0.6 change the numerical value?

   回答

   No. Both equal six tenths. A trailing zero after the decimal does not change the value.

10. カード 10

    質問

    What does the mixed number 2 3/5 mean?

    回答

    2 + 3/5. The space joins a whole-number part and a fractional part; it does not mean multiplication.

11. カード 11

    質問

    Fraction → percent: how do you find the number before %?

    回答

    Divide the numerator by the denominator, then multiply the result by 100. Attach the % sign to that number.

12. カード 12

    質問

    Decimal → percent: how do you find the number before %?

    回答

    Multiply the decimal by 100, then attach the % sign.

13. カード 13

    質問

    In 0.47, what is the value of the digit 7?

    回答

    7/100, or 0.07. The 7 is in the hundredths place.

14. カード 14

    質問

    Percent → fraction: what denominator does % supply?

    回答

    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.

15. カード 15

    質問

    1/2 as a decimal?

    回答

    0.5. One divided by two is five tenths.

16. カード 16

    質問

    1/5 as a percentage?

    回答

    20%. Multiply numerator and denominator by 20 to get 20/100.

17. カード 17

    質問

    3/4 as a decimal?

    回答

    0.75. Three divided by four is seventy-five hundredths.

18. カード 18

    質問

    1/10 as a percentage?

    回答

    10%. One tenth is ten hundredths.

19. カード 19

    質問

    1/4 as a percentage?

    回答

    25%. Four equal quarters each account for 25 out of 100.

20. カード 20

    質問

    50% as a fraction in simplest form?

    回答

    1/2. Reduce 50/100 by dividing both parts by 50.

21. カード 21

    質問

    3/5 as a decimal?

    回答

    0.6. Multiply both parts by 2: 3/5 = 6/10.

22. カード 22

    質問

    0.2 as a fraction in simplest form?

    回答

    1/5. Reduce 2/10 by dividing both parts by 2.

23. カード 23

    質問

    1/8 as a decimal?

    回答

    0.125. One divided by eight terminates after three decimal places.

24. カード 24

    質問

    75% as a fraction in simplest form?

    回答

    3/4. Reduce 75/100 by dividing both parts by 25.

25. カード 25

    質問

    4/5 as a percentage?

    回答

    80%. Each fifth is 20%, so four fifths is 80%.

26. カード 26

    質問

    0.1 as a fraction in simplest form?

    回答

    1/10. The 1 is in the tenths place.

27. カード 27

    質問

    1/20 as a decimal?

    回答

    0.05. Multiply both parts by 5: 1/20 = 5/100.

28. カード 28

    質問

    0.25 as a fraction in simplest form?

    回答

    1/4. Reduce 25/100 by dividing both parts by 25.

29. カード 29

    質問

    60% as a fraction in simplest form?

    回答

    3/5. Reduce 60/100 by dividing both parts by 20.

30. カード 30

    質問

    5/8 as a percentage?

    回答

    62.5%. First divide: 5 ÷ 8 = 0.625. Then multiply by 100.

31. カード 31

    質問

    12.5% as a fraction in simplest form?

    回答

    1/8. Write 12.5/100 = 125/1,000, then simplify.

32. カード 32

    質問

    3/8 as a decimal?

    回答

    0.375. Three divided by eight is 375 thousandths.

33. カード 33

    質問

    0.8 as a fraction in simplest form?

    回答

    4/5. Reduce 8/10 by dividing both parts by 2.

34. カード 34

    質問

    1/25 as a percentage?

    回答

    4%. Multiply numerator and denominator by 4 to get 4/100.

35. カード 35

    質問

    5% as a fraction in simplest form?

    回答

    1/20. Reduce 5/100 by dividing both parts by 5.

36. カード 36

    質問

    2/5 as a decimal?

    回答

    0.4. Multiply both parts by 2: 2/5 = 4/10.

37. カード 37

    質問

    0.625 as a fraction in simplest form?

    回答

    5/8. Reduce 625/1,000 by dividing both parts by 125.

38. カード 38

    質問

    7/8 as a percentage?

    回答

    87.5%. First divide: 7 ÷ 8 = 0.875. Then multiply by 100.

39. カード 39

    質問

    37.5% as a fraction in simplest form?

    回答

    3/8. Write 37.5/100 = 375/1,000, then simplify.

40. カード 40

    質問

    3/20 as a decimal?

    回答

    0.15. Multiply both parts by 5: 3/20 = 15/100.

41. カード 41

    質問

    0.04 as a fraction in simplest form?

    回答

    1/25. Reduce 4/100 by dividing both parts by 4.

42. カード 42

    質問

    40% as a fraction in simplest form?

    回答

    2/5. Reduce 40/100 by dividing both parts by 20.

43. カード 43

    質問

    0.875 as a fraction in simplest form?

    回答

    7/8. Reduce 875/1,000 by dividing both parts by 125.

44. カード 44

    質問

    15% as a fraction in simplest form?

    回答

    3/20. Reduce 15/100 by dividing both parts by 5.

45. カード 45

    質問

    5/4 as a decimal?

    回答

    1.25. One whole plus one quarter is 1 + 0.25.

46. カード 46

    質問

    0.6% as a decimal?

    回答

    0.006. Divide 0.6 by 100; a percentage below 1% is below 0.01 as a decimal.

47. カード 47

    質問

    What distinguishes a repeating decimal from a terminating decimal?

    回答

    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.

48. カード 48

    質問

    2.5 as a percentage?

    回答

    250%. Multiply 2.5 by 100 and attach %.

49. カード 49

    質問

    0% as a decimal?

    回答

    0

    Zero divided by 100 is zero.

50. カード 50

    質問

    1/3 as an exact decimal?

    回答

    0.333… (3 repeats forever). A finite string such as 0.333 is only an approximation.

51. カード 51

    質問

    125% as a fraction in simplest form?

    回答

    5/4. Reduce 125/100; the result exceeds one whole.

52. カード 52

    質問

    1 3/4 as a percentage?

    回答

    175%. Convert the mixed number to 1.75, then multiply by 100.

53. カード 53

    質問

    2/3 as an exact percentage?

    回答

    66 2/3%. Multiplying 2/3 by 100 gives 200/3, or 66 2/3, before the % sign.

54. カード 54

    質問

    0.006 as a percentage?

    回答

    0.6%. Multiply 0.006 by 100 and attach %.

55. カード 55

    質問

    1/6 as a decimal, rounded to three decimal places?

    回答

    0.167. The exact decimal is 0.1666… (6 repeats forever); the next digit rounds the third decimal place up.

56. カード 56

    質問

    0.333… (3 repeats forever) as a fraction in simplest form?

    回答

    1/3. This is exact; 0.333 without the repeating tail is a different number.

57. カード 57

    質問

    1 as a percentage?

    回答

    100%. One whole corresponds to 100 out of 100.

58. カード 58

    質問

    2/3 as a percentage, rounded to one decimal place?

    回答

    66.7%. The exact percentage is 66 2/3%, so round the repeating decimal percentage at the end.

59. カード 59

    質問

    1/12 as an exact percentage?

    回答

    8 1/3%. Compute (1/12) × 100 = 100/12 = 25/3 before attaching %.

60. カード 60

    質問

    0.333 as a fraction in simplest form?

    回答

    333/1,000. It ends after three decimal places and is not exactly 1/3.

61. カード 61

    質問

    How can you compare a fraction, a decimal, and a percentage on one scale?

    回答

    Convert them all to decimals or all to fractions, then compare their numerical values. Keep exact values when rounding could affect the result.

62. カード 62

    質問

    Which is larger: 7/20 or 34%?

    回答

    7/20. It equals 0.35, while 34% equals 0.34.

63. カード 63

    質問

    Which is larger: 0.09 or 0.1?

    回答

    0.1. Write it as 0.10: ten hundredths is greater than nine hundredths.

64. カード 64

    質問

    Are 9/20 and 45% equal?

    回答

    Yes. 9/20 = 45/100 = 45%.

65. カード 65

    質問

    Which is larger: 0.5% or 0.05?

    回答

    0.05. The other value, 0.5%, equals 0.005.

66. カード 66

    質問

    Order from smallest to largest: 0.58, 3/5, 59%.

    回答

    0.58 < 59% < 3/5. As decimals, they are 0.58, 0.59, and 0.60.

67. カード 67

    質問

    Which is larger: 130% or 1 1/4?

    回答

    130%. It equals 1.3, while 1 1/4 equals 1.25.

68. カード 68

    質問

    Which is larger: 1/3 or 33.3%?

    回答

    1/3. The percentage equals exactly 0.333, while 1/3 = 0.333… with 3 repeating forever.

69. カード 69

    質問

    Which is larger: 3/8 or 38%?

    回答

    38%. The fraction equals 0.375, while 38% equals 0.38.

70. カード 70

    質問

    Which is larger: 17/20 or 0.84?

    回答

    17/20. It equals 0.85, which is greater than 0.84.

71. カード 71

    質問

    How do you calculate p% of an amount A?

    回答

    (p ÷ 100) × A. First convert the percentage to a decimal multiplier.

72. カード 72

    質問

    12% of 150?

    回答

    18

    Calculate 0.12 × 150.

73. カード 73

    質問

    How do you find what percentage a part is of a nonzero whole?

    回答

    (part ÷ whole) × 100%. Divide by the whole, not by the part.

74. カード 74

    質問

    A 20% discount leaves what percentage of the original price to pay?

    回答

    80%. Subtract the discount from 100%.

75. カード 75

    質問

    150% of 40?

    回答

    60

    Calculate 1.5 × 40; a percentage above 100% gives more than the original positive amount.

76. カード 76

    質問

    30 is 15% of what number?

    回答

    200

    Divide the part by the decimal percentage: 30 ÷ 0.15.

77. カード 77

    質問

    18 out of 72 is what percentage?

    回答

    25%. Calculate (18 ÷ 72) × 100%.

78. カード 78

    質問

    0.5% of 600?

    回答

    3

    Calculate 0.005 × 600.

79. カード 79

    質問

    To convert 2/7 to a decimal, a learner calculates 7 ÷ 2. What must change?

    回答

    Use 2 ÷ 7. The numerator is divided by the denominator, in that order.

80. カード 80

    質問

    A learner writes 0.42 = 0.42%. What is the correct percentage?

    回答

    42%. Multiply the decimal by 100 before adding %; 0.42% would equal 0.0042.

81. カード 81

    質問

    A learner writes 0.018 = 18/100. What is the correct simplest fraction?

    回答

    9/500. Three decimal places give 18/1,000, which simplifies to 9/500.

82. カード 82

    質問

    Why is “a percentage cannot exceed 100%” incorrect?

    回答

    100% is one reference whole, and an amount can exceed it. For example, 160% of a positive amount is 1.6 times that amount.

83. カード 83

    質問

    A learner reduces 12/20 to 6/20. What is the correct simplest fraction?

    回答

    3/5. Divide both numerator and denominator by 4. Changing only the numerator changes the value.

84. カード 84

    質問

    A learner rounds 1/6 to 0.17 before converting to percent. What is 1/6 as a percentage to one decimal place?

    回答

    16.7%. Convert the exact fraction first: (1/6) × 100 = 16.666… before attaching %. Round only the final percentage.

85. カード 85

    質問

    For the same whole, why is 1/9 smaller than 1/6?

    回答

    Nine equal parts make each part smaller than six equal parts. With the same positive numerator, a larger positive denominator gives a smaller fraction.

86. カード 86

    質問

    Why can 10% of 80 and 10% of 200 be different amounts?

    回答

    The reference whole is different. They are 8 and 20 respectively, even though the percentage is the same.

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Fractions, Decimals & Percentages Flashcards

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