Terms  Definitions 

Natural or Counting Numbers 
1, 2, 3, 4,...

Whole Numbers 
0, 1, 2, 3,...

Odd Numbers 
Whole numbers not divisible by 2.
1, 3, 5, 7,... 
Even Numbers 
Whole numbers divisible by 2.
0, 2, 4, 6,... 
Integers 
...–2, –1, 0, 1, 2,...

Negative Integers 
...–3, –2, –1

Positive Integers 
The natural numbers.

Rational Numbers 
Can be written as a fraction.
Fractions, such as 2/4 or 5/6. All integers are rational. 7 may be 7/1. Terminating decimals are rational. Repeating decimals are rational. 
Irrational Numbers 
Cannot be written as fraction.
Pi and square roots, for example. 
Commutative Property of Addition 
ORDER does not make a difference.
1 + 3 = 3 + 1 a + b = b + a 
Associative Property of Addition 
GROUPING does not matter.
(3 + 1) + 3 = 3 + (1 + 3) (a + b) + c = a + (b + c) 
Identity Element of Addition 
7 + 0 = 7
a + 0 = a 
Additive Inverse 
The opposite of any number.
a + (–a) = 0 
Commutative Property of Multiplication 
ORDER does not matter.
4 x 5 = 5 x 4 a x b = b x a 
Associative Property of Multiplication 
GROUPING does not matter
(3 x 4) x 2 = 3 x (4 x 2) (a x b) x c = a (b x c) 
Identity Element of Multiplication 
7 x 1 = 7
a x 1 = a 
Multiplicative Inverse 
Reciprocal of the number.
Any number x reciprocal equals 1. 3 x 1/3 = 1 a x 1/a = 1 
Distributive Property 
2(4 + 3) = 2(4) + 2(3)

Order of Operations for Grouping Symbols 
DO parenthesis, then brackets, then braces: ( ) then [ ] then { }.

Order of Operations 
PEMDAS
Please Excuse My Dear Aunt Sally Parenthesis then Exponents then Multiplication/Division then Addition/Subtraction. WORK from left to right on mult and div THEN work left to right on add and subtraction. 
Expanded Notation 
674 = 600 + 70 + 4

Rounding 
5 or higher, round up

Divisibility Rule for 2 
Ends in even number, including 0.

Divisibility Rule of 3 
Sum of digits is divisible by 3.

Divisibility Rule of 4 
Number formed by last two digits is divisible by 4.

Divisibility Rule of 5 
Ends in 0 or 5.

Divisibility Rule of 6 
Divisible by 2 and 3 (use both rules)

Divisibility Rule of 7 
No simple rule.

Divisibility Rule of 8 
Number formed by last three digits is divisible by 8.

Divisibility Rule of 9 
Sum of digits is divisible by 9.

Factors 
Numbers multiplied together to get a product.

Prime Number 
Only divided by itself and 1.

Composite Number 
Divisible by MORE than just itself and 1.

Numerator 
In a fraction, the number on top
2/5 2 is the numerator 
Denominator 
In a fraction, the number on bottom.
3/7 7 is the denominator. 
Proper Fraction 
Numerator is SMALLER than denominator
5/8 
Improper Fraction 
Numerator is LARGER than the denominator
9/4 
Mixed Number 
Contains whole number and fraction.
5 1/3 
Factors 
Whole numbers that when multiplied together yield the number.

Common Factors 
Factors that are the same for two or more numbers.
Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12 Common Factors of 8 and 12: 1, 2, 4 
Greatest Common Factor (GCF) 
Largest common factor of two or more numbers

Multiples 
Multiples of a number are found by multiplying that number by 1, of 2, or 3, etc.
Multiples of 3: 3, 6, 9, 12... 
Least Common Multiple (LCM) 
Smallest common multiple that is common to two or more numbers.

Adding and Subtracting Fractions 
Change denominators to lowest common denominator (LCD).
Add or subtract numerators and keep denominators the same. 
Dividing Fractions 
Invert (turn upside down) the second fraction and multiply the two fractions together.

Minus Preceding a Parenthesis 
When a minus sign is before a parenthesis, it applies to everything withing the parenthesis.
7  (4 + 3  2) = 7  4 3 + 2 = 
Absolute Value 
Numerical value.
Distance in units from zero on number line. 4 = 4 
Exponent 5^3 
A number places above and to the right of a number. It is the power that it is to be raised.
5^3 = 5 x 5 x 5 = 125 
Exponent Rules 
x^1 = x
x^0 = 1 x^3 = 1/x^3 
Squared 
A number multiplied by itself.
3^2 = 3 x 3 = 9 
Perfect Square 
The square of a whole number.

Cubed 
A number multiplied times itself twice.
2^3 = 2 x 2 x 2 = 8 
Square Root of a Number 
A number when multiplied by itself gives you the original number.
Square root of 16 is 4 because 4 x 4 = 16. x^2 is x squared. x^1/2 is the square root of x. The square root of zero is zero. 4^1/2 is 2. 
Powers of Ten 
10^3 = 10 x 10 x 10 = 1,000
10^3 = 1/10 x 1/10 x 1/10 = 1/1000 
Scientific Notation 
A number between 1 and 10 multiplied by a power of 10.
3.56 x 10^7 = 35,600,000 
Multiply in Scientific Notation 
(3 x 10^3)(4 x 10^2) = 1.2 x 10^6
Multiply whole #s and add exponents. 
English Measurements 
5,280 feet = 1 mile
16 ounces (oz) = 1 pound (lb) 2,000 pounds  1 ton (T) 2 cups = 1 pint (pt) 2 pints = 1 quart (qt) 4 quarts = 1 gallon (gal) 
Metric Measurements 
kilo = thousand
hecto = hundred deka = ten deci = tenth centi  hundredth milli = thousandth 
Precision 
Exactness of measurement.
The smaller the unit of measurement, the more PRECISE the measurement. 
Perimeter of a Square 
P = 4s
P is perimeter and s is side. 
Perimeter of a Parallelogram 
P = 2l + 2w OR 2(l +w)
P is perimeter, l is length, w is width. 
Area of Triangle 
A = 1/2bh
A is area, b is base, h is height. 
Perimeter 
P stands for perimeter.
The total distance all the way around the outside of a polygon. 
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