Basic Math and Pre-Algebra GED ACT SAT Test Prep Review Flashcards

Elementary arithmetic
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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Definition:
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