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divisible by 3

if the sum of the digits is divisible by 3

Ex) 456 ---> 4+5+6=15, 15 is divisible by 3

Ex) 456 ---> 4+5+6=15, 15 is divisible by 3

divisible by 4

if the number named by the last 2 digits is divisible by 4

Ex) 3936 is divisible by 4 because 36 is divisible by 4

Ex) 3936 is divisible by 4 because 36 is divisible by 4

divisible by 6

if rules for 2 and 3 check out ---- 1) the number is even & 2) the sum of the digits is divisible by 3

divisible by 8

if the number named by the last three digits is divisible by 8

Ex) 13802120 ---> 120/8 = 15

Ex) 13802120 ---> 120/8 = 15

divisible by 9

if the sum of the digits is divisible by 9

Ex) 3483 ---> 3+4+8+3=18, 18 is divisible by 9

Ex) 3483 ---> 3+4+8+3=18, 18 is divisible by 9

divisible by 11

if the difference between the sum of the even-place digits and the sum of the odd-place digits is a multiple of 11

Ex) 928,193,926 ---> odd sum (9+8+9+9+6=41) even sum (2+1+3+2=8) ---> 41-8=33, 33 is divisible by 11

Ex) 928,193,926 ---> odd sum (9+8+9+9+6=41) even sum (2+1+3+2=8) ---> 41-8=33, 33 is divisible by 11

multiplying decimals

count the number of decimal places and add them

Ex) 45.67 x .987 (5 places) = 45.07629 (5 places)

Ex) 45.67 x .987 (5 places) = 45.07629 (5 places)

dividing decimals

move the decimal point in the divisor and the dividend the same number of places to get whole numbers

Ex) 23.1 / .004 ----> 23.1 x 1000 / .004 x 1000 ----> 23100/4 ---> 5775

Ex) 23.1 / .004 ----> 23.1 x 1000 / .004 x 1000 ----> 23100/4 ---> 5775

1/2

.5 OR 50%

1/4

.25 OR 25%

3/4

.75 OR 75%

1/5

.2 OR 20%

2/5

.4 OR 40%

3/5

.6 OR 60%

4/5

.8 OR 80%

1/6

.16 OR 16 2/3%

1/3

.33 OR 33 1/3%

2/3

.6 OR 66 2/3%

5/6

.83 OR 83 1/3%

1/8

.125 OR 12 1/2%

3/8

.375 OR 37 1/2%

5/8

.625 OR 62 1/2%

7/8

.875 OR 87 1/2%

1/16

.0625 OR 6 1/4%

3/16

.1875 OR 18 3/4%

5/16

.3125 OR 31 1/4%

7/16

.4375 OR 43 3/4%

9/16

.5625 OR 56 1/4%

11/16

.6875 OR 68 3/4%

13/16

.8125 OR 81 1/4%

15/16

93 3/4%

(x²)(x³)

= x²⁺³

(x³) / (x²)

= x³⁻² OR 1 / x²⁻³

(x²)³

= x²⋅³

(xy)³

= (x³)(y³)

(x/y)³

= (x³) / (y³)

x^⁻³

= 1 / x³

1 / x^-m

= x^m

x⁰

= 1 (x ≠ 0)

x^(p/r)

= x^(power/root)

2²

4

2³

8

2⁴

16

2⁵

32

2⁶

64

2⁷

128

2⁸

256

2⁹

512

2¹⁰

1024

3²

9

3³

27

3⁴

81

3⁵

243

3⁶

729

4²

16

4⁴

256

5²

25

5³

125

6²

36

6³

216

7²

49

8²

64

9²

81

10²

100

11²

121

12²

144

13²

169

14²

196

15²

225

16²

256

17²

289

18²

324

19²

361

20²

400

21²

441

22²

484

23²

529

24²

576

25²

625

26²

676

27²

729

28²

784

29²

841

30²

900

31²

961

32²

1024