Number Values

Question 1

First 12 Prime Numbers

Answer 1

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

Question 2

Base Fraction: One half

Answer 2

1/2, 0.5, 50%

Question 3

Base Fraction: One third

Answer 3

1/3, 0.33. 33.3%

Question 4

Base Fraction: One fourth

Answer 4

1/4, 0.25, 25%

Question 5

Base Fraction: One fifth

Answer 5

1/5, 0.2, 20%

Question 6

Base Fraction: One sixth

Answer 6

1/6, 0.167, 16.7%

Question 7

Base Fraction: One seventh

Answer 7

1/7, 0.143, 14.3%

Question 8

Base Fraction: One eigth

Answer 8

1/8, 0.125, 12.5%

Question 9

Base Fraction: One ninth

Answer 9

1/9, 0.111, 11.1%

Question 10

Base Fraction: One tenth

Answer 10

1/10, 0.1, 10%

Question 11

Faction to Percent: 1/2

Answer 11

50%

Question 12

Faction to Percent: 1/3

Answer 12

0.333, 33.3%

Question 13

Faction to Percent: 2/3

Answer 13

.667, 66.7%

Question 14

First 9 perfect squares

Answer 14

0 (0), 1 (1), 4 (2), 9 (3), 16 (4), 25 (5), 36 (6), 49 (7), 64 (8)

Question 15

Rules of perfect squares

Answer 15

Must end in 0,1,4,5,6,9. CANNOT end in 2,3,7,8

For all perfect squares that are not 0 or 1, all of its prime factors will have even exponents

Question 16

First 9 perfect cubes

Answer 16

0 (0), 1 (1), 8 (2), 27 (3), 64 (4), 125 (5), 216 (6), 343 (7), 512 (8)

Question 17

Rules of perfect cubes

Answer 17

Prime factorization must contain only exponents that are multiples of 3

Question 18

When do decimal equivalents of fractions terminate

Answer 18

Terminate only if the denominator of the reduced fraction has a prime factorization that has only 2s, 5s, or both

If there’s anything other than 2s or 5s, the decimal equivalent will not terminate

Question 19

Patterns of remainders

Answer 19

When a certain divisor is divided into powers of a certain base, a pattern will emerge for each unique combination (i.e. 3 divided into 4, 3^1 has remainder of 3, 3^2 has remainder of 1, 3^3 has remainder of 3, 3^4 has remainder of 1)

Question 20

0 raised to any power

Answer 20

always =0

Question 21

Pattern of base 1

Answer 21

always =1, 1 raised to any power = 1

Question 22

Pattern of base 2

Answer 22

units digit end in pattern of 2, 4, 8, 6

2^4 =16, 2^5 = 32

2^7 = 128, 2^8 = 256

Question 23

Pattern of base 3

Answer 23

units digit end in pattern of 3, 9, 7, 1

3^3 = 27, 3^4 = 81

3^9 - 19,683, 3^10 = 59,049

Question 24

Pattern of base 4

Answer 24

units digit end in pattern of 4, 6 with all odd powers of 4 ending in 4 and all even powers ending in 6

4^3 = 64, 4^4 = 256

4^6 = 4,096, 4^7 = 16,384

Question 25

Pattern of base 5

Answer 25

all end in 5 5^3 = 125, 5^4 = 625

Question 26

Pattern of base 6

Answer 26

all end in 6 6^3 = 216, 6^4 = 1,296

Question 27

Pattern of base 7

Answer 27

units digit end in pattern 7, 9, 3, 1 7^3 = 343, 7^4 = 2,401 7^7 = 823,543, 7^8 = 5,764,801

Question 28

Pattern of base 8

Answer 28

unit digit follow pattern 8, 4, 2, 6 8^3 = 512, 8^4 = 4,096 8^8 = 16,777,216, 8^9 = 134,217,728

Question 29

Pattern of base 9

Answer 29

units digit end in pattern of 9, 1 with all odd powers of 4 ending in 9 and all even powers ending in 1 9^3 = 729, 9^4 = 6561

Question 30

Pattern of base greater than 9

Answer 30

Follow the same units-digit pattern (i.e. 12 follows 2 pattern)

Question 31

Properties of division by 5

Answer 31

When integers with the same digits are divided by 5, the remainder will always be the same Remainder unit digit 1, 6 = 1/5 Remainder unit digit 2, 7 = 2/5 Remainder unit digit 3, 8 = 3/5 Remainder unit digit 4, 9 = 4/5

Question 32

50%

Answer 32

1/2, .5

Question 33

0.667

Answer 33

2/3 or 4/6, 0.667, 66.7%

Question 34

75%

Answer 34

.75, 3/4

Question 35

0.6

Answer 35

3/5, 60%

Question 36

0.8

Answer 36

4/5, 80%

Question 37

0.167

Answer 37

1/6, 16.7%

Question 38

33.3%

Answer 38

1/3 or 2/6 or 3/9

Question 39

66.7%

Answer 39

4/6 or 2/3 or 6/9, 0.667

Question 40

0.833

Answer 40

5/6, 83.3%

Question 41

14.3%

Answer 41

1/7, 0.143

Question 42

0.286

Answer 42

2/7, 28.6%

Question 43

42.9%

Answer 43

3/7, 0.429

Question 44

0.571

Answer 44

57.1%, 4/7

Question 45

0.714

Answer 45

5/7, 71.4%

Question 46

85.7%

Answer 46

0.857, 6/7

Question 47

0.125

Answer 47

1/8, 12/5%

Question 48

0.25

Answer 48

1/4, 2/8, 25%

Question 49

37.5%

Answer 49

3/8, 0.375

Question 50

62.5%

Answer 50

0.625, 5/8

Question 51

75%

Answer 51

3/4 or 6/8, 0.75

Question 52

0.875

Answer 52

87.5%, 7/8

Question 53

11.1%

Answer 53

1/9, 0.111

Question 54

0.222

Answer 54

22.2%, 2/9

Question 55

44.4%

Answer 55

4/9, 0.444

Question 56

0.556

Answer 56

5/9, 55.6%

Question 57

0.778

Answer 57

7/9, 77.8%

Question 58

88.9%

Answer 58

8/9, 0.889

Question 59

0.0909

Answer 59

1/11, 9.09%

Question 60

90.91%

Answer 60

10/11, .9091

Question 61

45.5%

Answer 61

5/11, .455