Symbols Propertiee of Addition & Multiplieationeqtnl

rnt equal

approximatelyeqtnl

greater than

less than

greater than orequalto

less than or equal to

square root

infinity

percent

union

intersection

pi (3.1416)

Sguares and Square floots

1. Commutiative property of additiona + b = b + a

2. Commutative properg of multiplicationab= ba

3. Associative property of additiona + ( b + c ) = ( a + b ) + c

4. Associative property of multiplicationa(tu) = (abl c

5. Distributive property of multiplication over additiona ( b + c ) = a b + a c

6. Distributive properg of multiplication oversubtraction

a (b- c) = ab- ac

Numbers

1

2

3

4

5

6

7

E

9

1

4

I

1 6

25

36

49

u81

1 0

1 1

1 2

1 5

2CI

25

100

112

114

1

1.+14

1.V32

2

2.236

2.&g:

2.&8

2.828

3

100

121

144

225

'400

625

10,000

1t4

1116

3.162

3.317

3.464

3.873

4.472

5

1 0

o.707

112

l ! ? i l t : , I i . . : ; , i i i 1 ,

A whole number with only two factors: itself and 1.EXAMPLE: 2 , 3 , 7 , 11, 13, 17.

l l i l ! : : 1 ! 1 i . l t r i , t . i : t

A number that is a factor of two or more numbers.EXAMPLE: 1,2, and 4 are common factors of 12 and 16.

, ' : . ' l t , l ! r i i ; j

The greatest number that is a factor of two or more numbers.EXAMPLE: 4 is the greatest common factor of 12 and 16.' r : . , 1

, . ' . : : i l t l : , 1 t , , 1 t : : , i :

The smallesl number that is a multiple of two or more numbers.EXAMPLE: 12 is the least common mult iple of 2,3,4, and 6.

Order of OperatlonsL Do all operations within parentheses.

2. Do all powers and roots.

3. Do multiplication and division in order from left to right.

4. Do addition and subtraction in order from left to right.

Multiplication TableFraction Rules

3 - numerator5 - denominator

To dd or subtracf differenttractions, first obtain a@mmon denominator:

To muftiply.

1 - 2 _ 1 Y 2 _ 23 5 3 x 5 1 5

To divide, multiply the firstwith the reciprocal of thesecond fraction:

Fractione & DecimalEqulvelents wlth

Percentages

1 - 1 . 0 = 1 0 0 %

112= 0 .5 = 50 " /o

113 = 0.3 = 33.3%

114 = O.25 = 25%

1/5 = O.2 = 2OV"

116 = 0.16 = 16.6%

118 = 0 .125= 12 .5%

119 = 0.1 = 11.1"/o

1 / 1 0 = 0 . 1 = 1 0 %

1 / 1 2 = 0 . 0 8 3 = 8 . 3 / o

213 = 0.6 = 66.6%

314 = 0.75 = 75o/"

L * L - 5 _ + q = 1 13 5 1 5 1 5 1 5

+.*=f'f=+

x 0 1 2 3 4 5 6 7 I 9 1 0 11 1 2 1 3 1 4

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 2 3 4 5 6 7 I I 1 0 1 1 12 1 3 1 4

2 0 2 4 6 I ' t0 1 2 1 4 16 1 8 20 22 24 26 28

3 0 3 6 I 12 1 5 1 8 21 24 27 30 33 36 39 42

4 0 4 I 12 1 6 20 24 28 32 36 40 4 I 52 56

5 0 5 1 0 1 5 2A 25 30 35 N 45 50 55 60 65 70

6 0 6 1 2 1 8 24 30 36 42 48 54 60 66 72 78 84

7 0 7 1 4 21 28 35 42 49 56 63 70 77 84 91 98

I 0 I 1 6 24 32 40 48 56 &4 72 80 88 96 104 112

I 0 I 1 8 27 36 45 54 63 72 81 90 99 108 117 126

1 0 0 1 0 20 30 40 50 60 70 80 90 'r001 1 0120 130 140

1 1 0 1 1 22 33 M 55 66 77 88 99 1 1 0121 132 143 154

12 0 12 24 36 48 60 72 u 96 108 120 132 1 4 156 168

1 3 0 1 3 26 39 52 65 78 91 104 117 1301#! 156 169 182

1 4 o 1 4 28 42 56 70 u 98 112 126 140 154 168 182 't96

1 5 0 1 5 30 45 60 75 90 105 120 135 1s0165 180 195 210

Greek Alphabet Weights and Measures

A

B

f

A

E

Z

H

oI

K

A

M

N

;

fI

P

T

Y

oX

Y

Ct

c[

p

T6

t

enet

K

i.

trv

\

alpha

beta

gamma

delta

epsilon

zeta

eta

theta

iota

kappa

lambda

mu

o omrcron

np i

p rho

o sigma

x tau

rl upsilon

0 phi

x chi

v psi

o omega

Prefixes

Troy Weiglil24 gnins ='l pennyweight20 pennyweights = 1 ounce12ounces=1 pound

Avoirdupois Weigltt27 11/32 gmins = 1 dram16drams=l ounce16ounces=1 pound100 pounds = 1 short cwt.20 short cwl = 1 short ton

Apothecaries' Weight20gra ins=lscrup le3scrup les=1dramSdrams= louncel2ounces=1 pound

Linear Measure12inches=1footSfeet=1yard5 12 yards = 1 rod40rods=l fur long8 furlongs (5280 feet) =

1 statute mile

Illarinerc' Measurc . ''

6 feet = 1 fathom ,1000 fathoms (approx.) =

1 nautical mile3 nautical miles = 1 leagrc

Apoftecaries'Fhrid ffiro60 minims = | fruid dram8 fluid drams = 1 ffuid ounce16 fluid ounces = 1 pint2pints=l quart4quar ts= lga l lon

I i q r r i i l 1 r i V i t ! r ' r r ' r l f o ! r ' . i s t r r t t s t ; r p p r r r r . !

Square illeasure144 square inches = 1 square foot9 square feet = 1 square yard30 1/4 square yards = 1 square rod160 square rods = 1 acre640 acres = 1 square mib

Gubic llleasurc1728 cubic inches = 1 cubic foot27 cubic feet = 1 cubic yard

Surmyon'illeasurc7.92 inches=1l ink100l inks=lcha in

Liquid Measure4gil ts=lpint2pints=1 quad4quarb=l gallon31 12 gallons = l.barrel2banels=1 hogshead

Dr;ileasure2pin ts= lquar t$quar ts=1peck4pecks=1 bushel

Wood tleasum,16 cubic feet = 1 cotd foot8 cord feet = 1 eord

Angular and Giurlar Measure60seconds=l minute60minutes=ldegreeS degrces = 1 right angle180 degrees = 1 straight angle360degrees=lcircle

Linear lfleasurc10 millimeters = 1 centimeter10 centimeters = 1 decimeter .l0decimeters=l meterl0meters=l dekameter10 del<ameters = t hectometer10 hectometers = 1 kilometer

$quare llleasure1@ sq. millimeters = 1 sq. centimeter100 sq. centimeters = 1 sq. decimeter100 sq. decimeters = 1 sq. meter100 sq. meters = 1 sq. dekameter100 sq. delometers = 1 sq. hectometer100 sq. hectometers = 1 sq. kilometer

Gubic tleasure1000 cu. millimeters = 1 cu. centimeter1@0 cu. centimeters = 1 cu. decimeter1fr)0 cu. decimeters = 1 cu. meter

LSid ileasure10 milliliters = 1 centiliter10 centiliters = 1 deciliterl0deci l i ters=l l i terl0l i ters=l dekal i ter10 dekaliters = t hectoliter10 hectoliters = 1 kiloliter

Iflass Measure10 millignms = 1 centigram10 centigrams = 1 decigraml0dec igrams=1graml0grams=l dekagnams10 dekagrams = t hectogram10 hectograms = 1 kilognam100 kilograms = 1 quintall0qu in ta ls=1ton

= 1 ml = 0.001 liter= 2ml = 0 .002l i ter= S m l= 1 5 m l = 1 5 c c= 30m l= 5 9 m l= 79m l= 1 1 8 m l= 158 ml= 177 ml= 207 ml= 237 ml= 473 ml= 1005 ml = 1 liter= 473 ml= 946 ml= 3785 ml= 1000 ml

nuXi

mono

di

tri

tetra

penta

hexa

hepta

octa

ennea

deca

hendeca

dodeca

1/3 cup112 cup213 cup3/4 cup718 cup1 cup2 cups4 1/4 cups1 pint2 pints4 quarts1 liter

1

2

3

4

5

6

7

8

I

1 0

1 1

1 2

1/4 teaspoon =1/2 teaspoon =1 teaspoon =1 tablespoon =2 tablespoong =1/4 cup =

0.034 fluid ounce0.068 fluid ounce

1/2 fluid ounce1 fluid ounce2 fluid ounces22f3l\uid ounces4 fluid ounces5 1/3 fluid ounces6 fluid ounces7 fluid ounces8 fluid ounces16lluirl ounces34 fluid ounces16 fluirl ounces32 fluid ounces128 fluid ounces1.057 quarts

= l c c= Z c c= 1/3 tablespoon= 3 teaspoons= 1/8 cup= 4 tablespoons= 5 1/3 tablespoons= I tablespoons= l0ASbblespoons= 12 tablespoons= 14 tablespoons= 16 tablespoons= 32 tablespoons

= 2 cups= 1 quart= 1 gallon= 1/4 gallon

i l r y t u W r r t ; f i l M e . l s r t r c s { . r p l } r 0 r i

1 ounce2 ounces3 ounms4 ounces8 ounces12 ounces16 ounces32 ounces1 kilogram

=

== 1/4 pound= 1/2 pound= 3/4 pound= 1 pound= 2 pounds= 2.2 pounds

30 grams (28.35 g)55 grams85 grams125 grams250 grams375 grams454 grams =907 grams =1000 gnms =

a bit less than1l2 kilognma bit less than I kilogram35.2 ounces