Download Reference Page Math Symbols- + add

Reference Page
Math Symbols+ add
- subtract
x multiply
divide = equal
% percent
$ dollar
 cent # number/pound
@ at
 degree
. decimal point
pi
Roman Numerals
Conversion
I=1
C = 100
V=5
D = 500
X = 10
M = 1000
L = 50
 Roman Numerals Conversion Rules: The letters should be arranged from the
one with the largest value to the one with the smallest.
 Each letter's value is added to the previous ones.
 Only powers of ten (I, X, C, M) can be repeated.
 Do not repeat any letter more than three times in a row.
 Because of the preceding rule, certain numbers must be written using
subtraction. In this case, a letter with a smaller value precedes one with a larger
value and the value of the smaller is subtracted from the larger. The result is then
added to the rest of the letters.
 The following rules apply to subtraction: Only powers of ten (I, X, C, M) can be
subtracted.
 The smaller letter must be 1/5th (one-fifth) or 1/10th (one-tenth) the larger one.
 The smaller letter must be either the first letter or preceded by a letter at least ten
times greater than it.
 If another letter follows the larger one, it must be smaller than the number
preceding the larger one.
Measurements-
Measurement Abbreviations-
Time:
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
52 weeks = 1 year
365 days = 1 year
12 months = 1 year
sec - seconds
min - minutes
hr - hours
wk - week
yr - year
mo- months
Weight: (how heavy an object is)
1 pound = 16 ounces
1 ton = 2000 pounds
lb or # - pound
oz - ounces
1 oz is similar to the weight of an envelope
1 pound is similar to a box of powdered sugar
Length:
1 foot = 12 inches
1 yard= 3 feet=36 inches
1 mile = 5280 feet
ft- foot
in-inches
yd- yard
1 inch is similar to the width of two fingers
1 foot is similar to the length of your foot
1 yard is similar to the length of your stride (a giant step)
Volume: (how much an object holds)
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints = 4 cups
1 gallon = 4 quarts
c – cup
pt – pint
qt – quart
gal – gallon
1 fluid ounce is similar to the amount the tablespoon holds
1 cup is similar to a carton of yogurt
1 gallon is similar to a large plastic jug of milk
mi - mile
Key Words in Math
Addition












sum
all
together
total
in all
all together
increased by
more than
combined together
total of
added to
plus
Subtraction














Division
difference
left
less than
How many more?
fewer than
greater than
more than
How many less?
reduced by
decreased by
difference of
remainder
less than
minus
quotient
per
average
each
divide equally
out of
ratio of
percent
goes into
Multiplication
product
in all
times
all
of
total
multiplied by
twice
addend + addend = sum
sum – addend = addend
factor X factor = product
product factor = factor
quotient
divisor dividend
Properties of Numbers
Commutative- when you add or multiply you can do it
in any order or swap the numbers around and get the
same answer.
4 + 2 = 6 just like
2+4=6
5 X 3 = 15 just like 3 X 5 = 15
Identity- a number added to “0” is that number; a
number multiplied by “1” is that number
3+0=3
1X5=5
Order of Operations
Please – Parenthesis ( ) or Brackets [ ]
Excuse – Exponents 32
My Dear – Multiplication & Division left to right
Aunt Sally – Addition & Subtraction left to right
Associative Property- The order in which numbers are
grouped does not affect the sum or product.
(5 + 2) + 3 = 10
(2 X 3) X 4 = 24
just like
just like
5 + (2 + 3) =10
2 X (3 X 4) = 24
MULTIPLICATIONAny number multiplied by “0” = “0” 5 X 0 = 0
Any number multiplied by “1” = that number 2 X 1 = 2
When multiplying an even number by 6, the ones column
equals that number and the tens column equals ½ the number
in the ones column. 6 X 2 = 12, 6 X 4 = 24
When multiplying by 9: (the finger trick)
1. Hold out your hands Each finger is a number. Starting with the pinky on the left hand as one.
2. Decide on the problem, for example 9 x 3 =.
3. Holding up your hands, bend down the "3" finger.
4. The fingers to the left of the "3" are the tens. How many tens are still straight- "2". That's right, 2 tens or
20.
5. The fingers to the right of the "3" finger are the "ones", include both hands.
There are 2 fingers raised on the left hand and 5 on the right, making a total of 7 fingers.
6. Put them together, 2 tens and 7 ones or 27! That's the answer.
9 x 3 = 27
DIVISION- Divide & Conquer
Dragon (Divide)
Mouthwash (Multiply)
Sweetens (Subtract)
Charboiled (Check)
Breath (Bring Down)
How many times will 3 go into 4?
1 5 r2
3 47
1 X 3 =3
4–3=1
Is 1 equal to or larger than 3? No.
Bring down the 7.
- 3__
1 7
-1 5
2
Repeat steps for each number “in the house”.
Division HintsDivide by:
2
5
10
If:
the last digit is even
the last digit is a 5 or a 0
the number ends in 0
Decimals
Addition- When you add decimals be sure to line up the decimal points and keep the columns
straight.
Subtraction- When you subtract decimals, be sure to line up the decimal points and keep the
columns straight.
Multiplication- When you multiply decimals, the number of decimal places in the product
should equal the total number of decimal places in the factors .
Division- When you divide decimals, move the divisor’s decimals point to the right to make it a
whole number. Move the dividend’s decimal point the same number of places to the right.
Write the quotient decimal point directly above the dividend’s decimal point.
Fraction TerminologyFraction- part of a whole
part
_____
whole
numerator
line represents division
denominator
proper fraction- numerator is smaller than denominator
improper fraction- numerator is larger than denominator
mixed number- whole number and fraction
reduce/simplify/lowest terms- all fractions should be reduced
determine if there is a (same) number that will go into the numerator and
denominator both evenly
improper fraction to a mixed number- divide your denominator into your numerator
if there is a remainder make it into fraction form using the remainder as your
numerator and keep the same denominator
mixed number to an improper fraction- multiply the denominator times the whole
number, then add the product and numerator, that sum becomes the numerator and
the denominator stays the same
Any time there is a whole number by itself, put it over the whole number 1 to make it into
fraction form.
fraction to a decimal- divide your numerator by your denominator
Keep the 1st Flip 2nd Change sign to multiplication
%
Percents
What
What
%
What
)
__(1)___% of __(2)___ is __(3)___
X
=
Percent
number
(1) & (2) X
(2) & (3) ÷ *
(1) & (3) ÷
(1) or (2) ) (3)
% to decimal
Move decimal to the left 2 places
Ex.
20% = .20
3% = .03
175% = 1.75 15 ½% =15.50% = .155
decimal to %
Move decimal to the right 2 places
Ex. .50 = 50% .110= 11.0% or 11%
125.5= 12,550%
2.25=225%
Always change % to a decimal before performing
the operation.
* change decimal answer to % for final answer
Ratio & ProportionRatio- comparison of two numbers
-can be written with the word to, a colon (:), or as a fraction
-always write the numbers in the same order as the problem compares them
-the number listed first is the numerator
-reduce
Proportion- two ratios written as equal ratios (4 terms)
-in a proportion problem one of the four terms is missing use an “x” to represent
the missing number
-to find the missing number cross multiply
1. multiply the first numerator by the second denominator
put the sum on the left of the equals sign
2. multiply the first denominator by the second numerator
put the sum on the right of the equals sign
3. divide the number with the “x” by the sum
4. the quotient represents the missing “x”
Integers/Signed Numbers/Positive & Negative Numbers



Positive Numbers – greater than zero (doesn’t have a sign)
Negative Numbers – are less than zero (always written with a negative sign - )
Zero has no sign and is always written as 0
Adding Integers
Same signs-1. Add the numbers
2. Keep the sign
o (+) + (+) = (+)
o (-) + (-) = (-)
Different/Opposite signs – 1. Subtract the numbers
2. Take the sign of your larger number
o (+ larger number) + (- smaller number) = (+) ex. 5 + -2 = 3
o (+ smaller number) + (-larger number) = (-) ex. 2 + -5 = -3
Subtracting Integers
1. Change the sign of the second number
(if it’s negative it becomes positive, if it’s positive it becomes negative)
2. Change subtraction sign to addition
3. Follow adding integer rules
o -9 – 3 = -9 - -3= -9 + -3= -12
Follow subtracting integer rules when larger number is on the right
3 - 9 = 3 - -9 = 3 + -9 = -6
Multiplying/Dividing Integers
Same sign – answer is positive
multiply/divide numbers and make a positive
o (+) X/ : (+) = (+)
o (-) X/ : (-) = (+)
Different sign – answer is negative
Multiply/divide numbers and make a negative
o (+) X/ : (-) = (-)
o (-) X/ : (+) = (-)
 Multiplying more than two signed numbers
o If there is an even number of negative signs, give the product a positive sign.
o If there are an odd number of negative signs, give the product a negative sign.
0 x or : by any number = 0
0 + or – any number = that number
0 is NOT positive or negative
Lines and More
Point- an exact location in space
Line- extends indefinitely in both directions
Line Segment- a portion of a line that has two endpoints
Ray- begins at a fixed point and extends indefinitely in one
direction
Angle- two rays that share an endpoint
Parallel Lines- two lines that will NEVER intersect
Perpendicular Lines- tow lines that cross to form four right angles
Intersecting Lines- lines that have exactly one point in common
Angles
Acute angle measure less than 90O (skinny angle)
Right angle measure 90O (the “perfect” angle; corner of a paper)
Obtuse angle measures between 90O and 180O (the obese/fat angle)
Straight angle measures 180O
Complementary angles have measurements with a sum of 90O
Supplementary angels have measurements with a sum of 180O
Reflex angle measures more than 180O but less than 360O
Straight line = 180O
Circle = 360O
Triangle = 180O
Triangles
A triangle is a polygon with three sides. Triangles can be classified
by the length of their sides or by the measure of their angles.
Equilateral triangles have three equal sides.
Equiangular triangles have three equal angles.
Isosceles triangles have two equal sides. Acute
triangles have three acute angles
Scalene triangles have no equal sides. Right
triangles have one right angle.
Obtuse triangles have one obtuse angle.
dr
d-diameter (distance across the circle)
r-radius (middle of the circle to the outside edge)