Math: Flashcards
Rational number
Math: Flashcards
Any number that can be written as a ratio of two integers:
Any number that can be written with an integer
numerator and integer denominator greater than zero.
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Prime number
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 A number that can only be divided by itself and the
number 1.
 0 and 1 are not prime numbers.
 2 is the only even number that is prime.
 No number that ends in 5 or 0 is prime, except for the
number 5.
 If the sum of a number’s digits is divisible by 3, the
number is not a prime number.
Math: Flashcards
Whole number
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Zero and the counting numbers: 1,2,3,4, and so on.
(If a number has a negative sign, a decimal point, or a
fraction, it is not a whole number.)
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Irrational number
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A number than cannot be represented by a ratio of two
integers.
Irrational numbers can be represented by decimals that
do not end and are not repeating.
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The symbol for Pi, an irrational number equal to
approximately 22
7
or 3.1415926535…..
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Real number
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A number that represents a quantity on a number line.
Real numbers include negative numbers, whole numbers,
fractions, and irrational numbers.
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Integer
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A number with no fractions.
Integers include the whole numbers and the opposite of
the counting numbers.
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Absolute value
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The distance of a number from zero on the number line.
Absolute value is always positive and is represented by
two vertical lines.
Example: |−2| = 2
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Numerator
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The number or expression written above the line in a
fraction.
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Denominator
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The quantity below the line in a fraction. The
denominator tells the number of equal parts into which a
whole is divided.
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Scientific notation
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A number that is expressed as the product of a decimal
greater than or equal to 1 but less than 10 and an
exponent with the base of 10.
Example: 18,000,000 = 1.8 x 10⁷
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Associative Property of Addition
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The sum stays the same when the grouping of the
numbers in an addition problem is changed.
Example: (a + b) + c = a + (b + c)
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Commutative Property of Addition
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The sum stays the same when the order of the numbers
in an addition problem changes.
Example: (a + b) + c = a + (b + c)
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Product
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The result of multiplication.
multiplicand x multiplier = product
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Sum
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The result of addition.
addend + addend = sum
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Distributive Property
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With the operations of multiplication and addition or and
subtraction, multiply each term inside the parentheses
with the term outside of the parentheses.
Examples:
a (b + c) = ab + ac
a (b – c) = ab - ac
Math: Flashcards
Reciprocal term
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Two numbers that have a product of 1.
Example:
and
are reciprocals because
x
=1
Math: Flashcards
Additive Inverse Property
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What you add to a number to have a sum of zero.
Example:
2 + -2 = 0, -2 is the additive inverse
-5 + 5 = 0, 5 is the additive inverse
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Transitive Property
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For equalities, if a = b and b = c, then a = c
For inequalities, if a < b and b < c, then a < c
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Fraction
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Part of a whole. The denominator says how many parts
the whole is divided into and the numerator says how
many parts of the whole are present.
Example:
Numerator
=
Denominator
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Divisor
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The quantity by which another quantity is to be divided.
dividend ÷ divisor = quotient
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Dividend
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A quantity to be divided.
dividend ÷ divisor = quotient
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Quotient
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The result of the division of one quantity by another.
dividend ÷ divisor = quotient
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Remainder
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In a whole-number division problem, the amount left over
after division, when decimals are not used.
Example: 18 ÷ 5 = 3, with a remainder of 3
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Percent
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A ratio that compares a number to 100,
using the symbol %.
Example: 25 out of 100 = 25%
Math: Flashcards
Simplify
Math: Flashcards
Make an equation easier to solve.
Some ways to simplify an equation:
 Multiply out the constants and variables.
 Combine like terms.
 Eliminate fractions by multiplying.
 Factor.
Math: Flashcards
Least common denominator
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The smallest common multiple of the denominator of two
or more fractions.
Example: The lease common denominator of
and
is 12.
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Factorizing
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To “split” an expression into multiplication of simpler
expressions.
Example: 2a + 4 = 2(a + 2)
(Use the highest common factor including variables.)
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Dividing fractions:
“KFC”
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Keep the first fraction.
Flip the divisor (take the reciprocal).
Change the division sign to a multiplication sign.
Example:
÷
=
x
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Difference
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The amount that remains after one quantity is subtracted
from another.
minuend – subtrahend = difference
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Coefficient
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A number used to multiply a variable.
Example: In the expression 6a, 6 is the coefficient.
Sometimes a letter stands for the coefficient.
Example: In the expression ay⁴ + by² + 8, “y” is a variable,
and “a” and “b” are coefficients.
Math: Flashcards
Exponential form:
Exponent and Base
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The number that tells how many factors there are is the
exponent.
The number used as the factor is the base.
Example:
4 x 4 x 4 x 4 x 4 = 4⁵
In 4⁵, the base is 4 and the exponent is 5.
Math: Flashcards
Order of operation:
PEMDAS
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Parantheses
Exponents
Multiplication
Division
Addition
Subtraction
PEMDAS
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Variable
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A quantity that can change. In algebraic notation, use a
letter to stand for the variable quantity.
Example: In the expression, 6y + 2, “y” is a variable.
Math: Flashcards
Coordinate grid
Math: Flashcards
A graph with a horizontal x-axis and a vertical y-axis,
in which the coordinates of a point are its distances from
the two intersection axes.
In a coordinate pair, the x value is written first and the y
value is written second. (x,y)
Math: Flashcards
Linear equation
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An equation whose graph on a coordinate grid is a
straight line.
Example of a linear equation: y = mx + b
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Linear equations:
Slope intercept formula
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y = mx + b
“m” is the slope (how steep the line is),
“b” is the y-intercept (where the line crosses the y-axis)
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Inequalities
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A comparison of two or more unequal expressions that
uses the symbols
a < b (a is less than b)
a > b (a is greater than b)
a ≤ b (a is less than or equal to b)
a ≥ b (a is greater than or equal to b)
a ≠ b (a is not equal to b)
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Polynomial equation
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A sum of monomials (called terms) that is set equal to 0.
Example: x² + 4x + 4 = 0
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Pythagorean Theorem
c
a
b
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+
=
In a right triangle, the square of the hypotenuse (c) is
equal to the sum of the squares of the other two sides (a)
and (b).
The hypotenuse is the side of the triangle that is opposite
from the right angle. The hypotenuse is always the
longest side of a triangle.
Math: Flashcards
Monomial
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A number, variable, or product of numbers and variables,
where all exponents are whole numbers.
Examples:
4, 4x, x², xy
Note: Fractions, negative exponents, and exponents that
are variables are not monomials.
Math: Flashcards
Quadratic equation
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An equation in which the highest exponent of a variable is
a square.
A quadratic equation usually takes the form of:
ax² + bx + c = 0
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Factoring formula for difference of perfect squares:
Math: Flashcards
-
= (a + b) (a – b)
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Factoring formula for sum of perfect cubes:
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+
= (a + b) (
– ab +
)
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Factoring formula for difference of perfect cubes:
Math: Flashcards
-
= (a - b) (
+ ab +
)
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Multiplying polynomials:
FOIL
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FOIL = (First Outside Inside Last)
(a + b) (c + d) = ac + ad + bc + bd
Math: Flashcards
Area of a circle:
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Area =
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Circumference of a circle:
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The boundary or perimeter of a circle:
C=2 r
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Area of a rectangle:
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Area = length x width
Math: Flashcards
Area of a triangle:
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Area = (base x height)
height
base
Math: Flashcards
Associative Property of Multiplication
Math: Flashcards
The product stays the same when the grouping of factors
changes.
Example: (a • b) • c = a • (b • c)
Math: Flashcards
Commutative Property of Multiplication
Math: Flashcards
The product stays the same when the order of the factors
changes.
Example: (a • b) • c = a • (b • c)
Math: Flashcards
Examples for simplifying exponents:
(“a” is base, and “m” and “n” are exponents)
Math: Flashcards
(
÷
=
) =
=
=
Example: (2²) (2⁴) = 2⁶
=
Example: 2⁶ ÷ 2⁴ = 2²
Example: (2²)⁴ = 2⁸
Example: 2
Example: 4 =
=
=
=
=8
Math: Flashcards
Ordered pair
Math: Flashcards
A pair of numbers that gives the coordinates of a point on
a coordinate grid. The ordered pair is written with the
horizontal (x) coordinate first and the vertical (y)
coordinate second.
(x,y)
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Prime factorization
Math: Flashcards
The expression of a number as the
product of prime factors.
Example: The prime factorization for 20 is 2 x 2 x 5
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Probability
Math: Flashcards
The chance of an event occurring.
Probability of event = number of favorable outcomes
number of possible outcomes
Math: Flashcards
Ratio
Math: Flashcards
A comparison of two quantities.
A ratio may be expressed as fraction, a decimal, or with a
colon (:) or with “to”.
Example: What is the ratio of oranges to apples if there
are 2 oranges and 5 apples?
, 0.4, 2:5, 2 to 5.
Math: Flashcards
Proportion
Math: Flashcards
An equation showing that two ratios are equal.
Proportions may be written with “to”, a colon, as a
fraction, or in decimal form.
a:b = c:d
a to b = c to d
=
Math: Flashcards
Direct proportion
Math: Flashcards
When two quantities are directly proportional, a change
in one quantity causes a direct change in the other
quantity. Both quantities increase by the same factor, or
both quantities decrease by the same factor.
Math: Flashcards
Inverse Proportion
Math: Flashcards
In an inverse proportion,
when one quantity increases by a certain factor,
the other quantity decreases by the same factor.