Arithmetic - items to memorize

Question 1

Reciprocals:

• between -1 and 0
• between 0 and 1

Answer 1

Between -1 and 0: reciprocals are less than the number

Between 0 and 1: reciprocals are greater than the number

Question 2

Squares:

• between -1 and 0
• between 0 and 1

Answer 2

Between -1 and 0: squares are greater than the number

Between 0 and 1: squares are less than the number

Question 3

Odd/even rules:

• odd + odd
• even + even
• odd + even
• odd * odd
• even * even
• odd * even
• even / even

Answer 3

• odd + odd = even
• even + even = even
• odd + even = odd
• odd * odd = odd
• even * even = even
• odd * even = even
• even / even = can be either

Question 4

Multiple (definition)

Answer 4

An integer that is divisible by another integer

i.e. 12 is a multiple of 3

Question 5

Factor (definition)

Answer 5

Divisors, positive integers that evenly divide into a number

i.e. 5 is a factor of 10

Question 6

Divisibility rules (2-11)

Answer 6

2: even, or last digit divisible by 2
3: sum of digits is divisible by 3
4: last 2 digits are divisible by 4 (i.e. 1748 -> last 2 are 48 which is divisible by 4)
5: last digit is 0 or 5
6: divisible by both 2 and 3
7: difference between last digit2 and rest of the numbers is divisible by 7 (i.e. 287 -> 28-(72)=28-14=14 which is divisible by 7)
8: last 3 digits are divisible by 8
9: sum of digits is divisible by 9
10: last digit is 0
11: sum of odd-placed digits - sum of even-placed digits is divisible by 11 (i.e. 7293 -> (7+9)-(2+3)=16-5=11 which is divisible by 11)

Question 7

Prime numbers between 1 and 100

Answer 7

2 (only even prime), 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 8

Prime numbers between 101 and 200

Answer 8

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

Question 9

Prime factorization

Answer 9

Breaking down a number to its prime factors

i.e. 480 = 4810 = 6825 = 242325 = 2222325 = 2^53*5

Question 10

Multiples of 3

Answer 10

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60

Question 11

Multiples of 4

Answer 11

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80

Question 12

Multiples of 6

Answer 12

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120

Question 13

Multiples of 7

Answer 13

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140

Question 14

Multiples of 8

Answer 14

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160

Question 15

Multiples of 9

Answer 15

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

Question 16

Multiples of 11

Answer 16

11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220

Question 17

Multiples of 12

Answer 17

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240

Question 18

Multiples of 13

Answer 18

13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260

Question 19

Multiples of 14

Answer 19

14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280

Question 20

Multiples of 15

Answer 20

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300

Question 21

Multiples of 16

Answer 21

16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320

Question 22

Multiples of 17

Answer 22

17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 187, 204, 221, 238, 255, 272, 289, 306, 323, 340

Question 23

Multiples of 18

Answer 23

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360

Question 24

Multiples of 19

Answer 24

19, 38, 57, 76, 95, 114, 133, 152, 171, 190, 209, 228, 247, 266, 285, 304, 323, 342, 361, 380