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GRE Basics > Arithmetic > Flashcards

Arithmetic Flashcards

integers, fractions, exponents and roots, decimals, real numbers, ratio, percent

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1
Q

What are integers?

A

{…, -2, -1, 0, 1, 2}

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2
Q

Positive integers are

A

greater than 0

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3
Q

negative integers are

A

less than 0

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4
Q

0 is

A

neither positive or negative

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5
Q

When integers are added, subtracted, multiplied or divided the result is always

A

an integer

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6
Q

The sum of two positive integers is

A

positive

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7
Q

The sum of two negative integers is

A

positive

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8
Q

The sum of a positive integer and negative integer is

A

negative

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9
Q

When integers are multiplied, each of the multiplied integers is called a ______ or _____ of the resulting product.

A

factor or divisor

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10
Q

The product of two even integers is an

A

even integer

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11
Q

The product of two odd integers is an

A

odd integer

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12
Q

The product of an even integer and an odd integer is an

A

even integer

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13
Q

What is a prime number?

A

an integer greater than 1 that only has two positive divisors: 1 and itself.

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14
Q

First 10 prime numbers

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

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15
Q

What is a prime divisor?

A

an integer greater than 1 or the product of factors that are prime.

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16
Q

What is a composite number?

A

an integer greater than 2 that is not prime.

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17
Q

The first 10 composite numbers are

A

4, 6, 8, 9, 10, 12, 14, 15, 16, 18

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18
Q

Top of fraction

A

Numerator

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19
Q

Bottom of fraction

A

Denominator

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20
Q

When adding fractions with same denominator, you ____ the numerators and _____ the denominator

A

add the numerators and keep the same denominators

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21
Q

When adding fractions with different denominator, you

A

1) find common denominator (common multiple of two denominators)
2) convert both fractions to equivalent fractions with the same denominator
3) add numerators and keep common denominator

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22
Q

To multiply fractions __________ the two numerators and ____ the two denominators.

A

Multiply the two numerators and the two denominators

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23
Q

To divide one fraction by another

A

1) invert the second fraction (it’s reciprocal-flip it)

2) multiply the first fraction by the inverted fraction

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24
Q

What is a mixed number?

A

integer and fraction

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25
Q

Convert mixed number to a fraction

A

1) convert integer to fraction with same denominator

2) add to existing fraction

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26
Q

What are exponents?

A

repeated multiplication of a number by itself

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27
Q

squaring

A

exponent is 2

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28
Q

when negative numbers are raised in exponents, the result

A

can be positive or negative

29
Q

Negative number raised to even exponent

A

positive

30
Q

negative number raised to an odd exponent

A

negative

31
Q

exponent zero

A

undefined

32
Q

negative exponents

A

make it 1/ the base and square

33
Q

What is a square root?

A

r^2=2

34
Q

All positive numbers

A

have two square roots

one positive, one negative

35
Q

square root of 0 is

A

0

36
Q

all negative numbers

A

have one square root

37
Q

absolute value

A

distance between a number and 0 on the number line.

38
Q

/3/=

A

3

39
Q

/-3/=

A

3

40
Q

/x/=

A

x

41
Q

/-x/=

A

x

42
Q

/0/=

A

0

43
Q

value of any nonzero number is

A

positive

44
Q

r+s=

A

s+r

45
Q

rs=

A

sr

46
Q

(r+s)+t=

A

r+(s+t) and

rs)t=r(st

47
Q

r(s+t)=

A

rs+rt

48
Q

r+0=

A

r

49
Q

(r)(0)=

A

0

50
Q

(r)(1)=

A

r

51
Q

rs=0

A

r=0
s=0
or both

52
Q

Division by 0 is

A

undefined

53
Q

If both r and s are positive then

A

r+s and rs are positive

54
Q

If both r and s are negative then

A

r+s is negative and rs is positive

55
Q

If r is positive and s is negative then

A

rs is negative

56
Q

/r+s/

A

triangle inequality

57
Q

/r//s/=

A

/rs/

58
Q

If r>1 then

A

r^2>r

59
Q

If 0

A

s^2

60
Q

What is a ratio?

A

expresses the relative size of two numbers, usually in a fraction.

61
Q

What is a proportion?

A

equation relating to ratios.

Solve by cross multiplication.

62
Q

What is a percent?

A

ratios that are used to represent parts of a whole (of 100).

63
Q

0.01%

A

0.01/100=0.0001

64
Q

Can be converted to a fraction or decimal by

A

dividing part by whole

65
Q

find 30% of 350

A

30/100 = x/350

66
Q

15 is 60% of what number?

A

15/x = 60/100

67
Q

percent increase

A

amount of increase (larger - smaller)/ base (smaller number

68
Q

percent decrease

A

amount of decrease (larger-smaller)/base (larger number)

GRE Basics (4 decks)

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