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GMAT > 1. Fractions & Decimals > Flashcards

1. Fractions & Decimals Flashcards

1
Q

Number on top of a fraction

A

Numerator

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2
Q

Number on bottom of a fraction

A

Denominator

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3
Q

0 / 3

A

0

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4
Q

3 / 0

A

undefined

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5
Q

How are fractions properly expressed?

A

in their lowest or simplest terms

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6
Q

What is a mixed numeral

A

The combination of a whole number and a faction

Ex: 6⅔

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7
Q

How to convert a mixed numeral into a fraction?

A
  1. Multiply the denominator by the whole number
  2. Add the numerator
  3. Place the sum over the denominator
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8
Q

How to convert a fraction into a mixed numeral?

A
  1. Divide the numerator by the denominator

2. Place the remainder over the denominator

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9
Q

Before adding and subtracting fractions

A

be sure to simplify the factions first if possible

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10
Q

To add whole numbers and fractions

A
  1. combine the two into a mixed numeral

2. convert the mixed numeral

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11
Q

When multiplying large or complex number

A
  1. rip up the numerators and denominators
  2. cancel out the common terms
  3. express what remains as a fraction
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12
Q

If all the terms in the numerator or denominator cancel out

A

be sure to leave a 1 in their place

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13
Q

To divide two fractions

A
  1. Flip the second fraction

2. multiply the two together

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14
Q

When dividing large or complex numbers

A
  1. rip up the numerators and denominators
  2. cancel out the common terms
  3. express what remains as a fraction
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15
Q

What is a complex fraction?

A

Any fraction that contains addition or subtraction in either the numerator or denominator

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16
Q

What is a simple fraction?

A

No addition or subtraction in numerator or denominator?

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17
Q

Can terms within complex fractions be cancelled?

A

No, NEVER.

Only within simple fractions

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18
Q

What is the Complex Numerator Shortcut?

A

If the numerator of a fraction contains addition or subtraction, the fraction can be split to simplify the arithmetic

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19
Q

Can the denominator of a complex fraction be split?

A

No, NEVER.

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20
Q

When adding, subtracting, multiplying or dividing mixed numerals

A

always convert the mixed numerals into fractions before performing the operation

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21
Q

Reciprocals (definition)

A

Any two numbers who product equals 1

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22
Q

Numbers that are not “flips” mays also be reciprocals

A

Especially w/ square roots

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23
Q

How many reciprocals can fractions have?

A

More than one

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24
Q

Fractions within fractions

A

Multiply the numerator by the “flip” of the denominator

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25
Q

Fractions within the Denominator

A

Put the numerator over one and multiplying the numerator by the “flip” of the denominator

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26
Q

Fractions within the Nominator

A

Put the denominator over one and multiplying the numerator by the “flip” of the denominator

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27
Q

What are fractions with multiple “levels”?

A

Complex fractions that contain fraction sin either the numerator or the denominator

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28
Q

How to solve complex fractions with multiple “levels”?

A

Work on “level” at a time, starting with the bottom “level” and progressing upwards

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29
Q

What are the properties of fractions (2)

A
  1. If the num = 0, that fraction = 0

2. If the den = 0, that faction is undefined

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30
Q

Proper fractions (definition)

A

Any fraction whose numerator is smaller than its denominator is known

0 < x/y < 1

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31
Q

0 < x/y < 1

A

Value of positive proper fractions

32
Q

Multiplying any number by a whole number yields

A

a product equal or larger than the original number

33
Q

Squaring any number by a whole number yields

A

a product equal to or larger than the original number

34
Q

Dividing any number by a whole number yields

A

a quotient equal to or smaller than the original number

35
Q

Taking the square root of any number by a whole number yields

A

a root equal to or smaller than the original number

36
Q

Multiplying any number by a proper fraction yields

A

a product smaller than the original number

37
Q

Squaring any number by a proper fraction yields

A

a product smaller than the original number

38
Q

Taking the square root of any number by a proper fraction yields

A

a root larger than the original number

39
Q

Dividing any number by a proper fraction yields

A

a quotient larger than the original number

40
Q

k = -3/7

Which one is bigger? k^2 or k^4

A

k^2 > k^4

The more we multiply a fraction between 0 and 1, the smaller it gets

41
Q

What are the different ways to compare any two fractions? (3)

A
  1. Cross-multiplying
  2. Approximating
  3. Picking a Litmus
42
Q

Cross-multiplying

A

Cross-multiply the num and den.
Multiply from the bottom up, and write each product over the corresponding numerator.
The fraction under the larger product will always be larger

43
Q

Approximating

A

If num and den too large to multiply easily, identify approximate equivalents that are easy to work with

44
Q

How to rank fractions?

A
  1. Pick a Litmus
    ¼, ⅓, ½, ⅔, ¾
  2. Determine which fractions are bigger than the litmus and which are smaller
45
Q

FUQ

A

Fractions with Unspecified Quantities

46
Q

How to solve FUGs?

A
  1. Pick numbers

2. Let the unspecified quantity equal the product of the den of the fractions involved

47
Q

Properties of Num and Den

A
  1. Increasing the num increases the value of the fraction, while increasing the den decreases the value of the fraction
  2. Increasing the num and the den by the same amount brings the value of a fraction closer to 1, while decreasing the num and the den by the same amount moves the value of a fraction away from 1
48
Q

Zeroes can be added and removed from the end of a decimal without altering the value of the decimal

A

Not true for whole numbers

4.2 = 4.20 = 4.200
23 ≠ 230 ≠ 2300

49
Q

Difference thousands and thousandths?

A

1000 vs 0,001

50
Q

Rounding decimals

A

Limiting a value of a decimal to a specified place value

51
Q

How to round digit

A
  1. Find rounding digit
  2. Look at the digit immediately to its right
  3. IF less than 5, leave rounding digit unchanged and drop all the digits to its right
    IF 5 or greater, add one to the rounding digit and drop all digits to its right
52
Q

Power of 10

A

Any number formed by multiplying one or more tens together

53
Q

Multiplying by a power of 10 shifts the decimal point of any number to the right

A

Multiplying by a number greater than 1 makes a number larger.
The number of shifts to the right will equal the number of the zeroes in the power of 10

54
Q

Multiplying by a power of 10 shifts the decimal point of any number to the ______

A

right

Multiplying by a number greater than 1 makes a number larger.
The number of shifts to the right will equal the number of the zeroes in the power of 10

55
Q

Dividing by a power of 10 shifts the decimal point of any number to the _____

A

left
as dividing by a number created than 1 makes a number smaller
The number of shifts to the left will equal the number of zeroes in the power of 10

56
Q

Powers of 10 written in the form of 10^-n work in the opposite manner of regular powers of 10

A

Multiplying by 10^-n will shift the decimal point to the left, and dividing by 10^-n will shift the decimal point to the right

57
Q

Approximation - know when to round

A

Decimal problems that contain words such as “approximately”, “nearest” and “closest” can usually be solved through approximation

58
Q

Know when not to round

A
  1. numbers can easily be reduced

2. doesn’t not contain the word approximately

59
Q

How to divide decimals (2)

A
  1. Long division

2. Slide approach

60
Q

Slide approach (3)

A
  1. Put the division in fraction form
  2. Slide the decimal point an equal number of times in both the num and the den
  3. until neither the num nor the den contains a decimal
61
Q

Decimal property 0 < x < 1

A

Numbers 0 < x < 1 always behave in the opposite manner of numbers larger than 1 when it comes to multiplying/dividing

x > 1 : 25 = 10
x < 1 : 20.5 = 1

Idem for squaring, square root, mult., div.

62
Q

Converting decimals to fractions

A

To convert a decimal into a fraction, place the digits of that decimal over a 1 with a number of zeroes equal to the number of decimal places in the decimal

63
Q

Ways to convert fractions to decimals (3)

A
  1. Long division
  2. Conversion Chart
  3. Set the Den equal to a power of 10
64
Q

1/6

A

0.16

65
Q

1/7

A

0.14

66
Q

11/9

A

0.11

67
Q

1/11

A

0.09

68
Q

1/99

A

0.01

69
Q

Setting the Den equal to a power of 10

A

See them equal to a power of 10 such as 10, 100 or 1000

Ex: 17/50 * 2/2 = 34/100 = 0.34

70
Q

A repeating decimal

A

Any decimals whose digits repeat in a FIXED pattern without end

Represented by horizontal line

71
Q

Converting repeating decimals to fractions

A

Set the repeating decimal to x and multiply both sides of the equation by a power of 10

! Let the number of zeroes in the power of 10 equal the length of the repeating sequence (provide two equations that can be subtracted to determine your fraction)

72
Q

Fractional equivalent of 0.5757

A
  1. Since 0.57 2 digits -> multiply by 100
  2. 100x = 57.57
  3. Subtract both :
    100x = 57.57
    - x = 0.57
    __________
    99x = 57
  4. Solve
    x = 57/99
    x = 319 / 333
    x = 19/33
73
Q

Terminating decimals

A

Decimals that do end

! Adding more zeroes to the end does NOT make it non-terminating, since 0 can always be removed

74
Q

Non-terminating decimals

A

Any decimal that never ends

! Adding more zeroes to the end does NOT make it non-terminating, since 0 can always be removed

75
Q

Which prime factors need to be included in the denominator to terminate?

A

2 and 5

3/10 ; 21/50 ; 7/100

76
Q

How to determine the number of consecutive zeroes that an integer has to the LEFT of its decimal point

A

count the number of “10”s it contains

2 and 5

77
Q

How to determine the number of consecutive zeroes that an integer has to the RIGHT of its decimal point

A
  1. Simplify the faction and count the number of 10s left in the denominator
  2. Determine the product of any numbers that do not produce a “10”
    _ less than 10 - no 10
    _ less than 100 - one 10
    _ less than 1000 -two 10

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