Grade 8 Number Properties and Algebraic Terms Flashcards
1-Step Equations
identify inverse operation to isolate variable
2-Step Equations
first add/subtract, then multiply/divide to isolate variable
Absolute value
the distance of an integer from 0
Addend
A number which is involved in addition. Numbers being added are considered to be the addends.
adding or subtracting fractions
requires the denominators be the same
Addition with integers
if sign is the SAME – add absolute values and keep the sign
if the sign is DIFFERENT – subtract absolute values and keep the sign of the larger absolute value
Associative property of addition
changing the grouping of addends
changing the grouping of terms will not change the sum
(a + b) + c = a + (b + c);
(5+3) + 1 = 5 + (3 + 1)
Associative property of multiplication
changing the grouping of factors
States that changing grouping of factors does not change the product.
(a*b)c = a(b*c)
(2 * 6) * 7 = 2 * (6 * 7)
Base and Exponent
The exponent is the number that indicates how many times the base is used as a factor: 4 X 4 X 4 = 4 cubed, 4 is the base; 3 is the exponent.
Calculations with exponents
a^n = aaaa…a (n times)
a^0 = 1
a^-n = 1/a^n
a^½ = √a
a^x * a^y = a^x+y
a^x/a^y = a^x-y
(a^x)^y = a^xy
(ab)^x = a^x * b^x
(a/b)^x = a^x/b^x
Coefficient
the number that is multiplied by variable(s)
Commutative property of addition
changing the order of addends
The property which states that two or more addends can be added or that two in any order without changing the sum.
Commutative property of multiplication
changing the order of factors
The property which states that two or more factors can be multiplied in any order without changing the product.
Difference
The amount by which one value is greater or smaller than another.
The result when numbers are subtracted.
Distance formula
Distance = rate times time
Distributive Property
multiplying grouped terms by a factor
a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses,
such as a(b + c) = ab + ac;
ex: 4(3 + 8) = 4(3) + 4(8)
dividing fractions
rewrite the first fraction, write a multiplication sign, write the reciprocal of the second fraction, multiply the fractions
Equation
equivalent expressions
Expanded form of a number
a number that is expressed as the sum of multiples of ten
example 643 = (6x100)+(4x10)+(3x1)
Exponential Notation
a number written as a base and exponent
Expression
a phrase made up of one or more numbers, variables, and operations
Factor
any of the numbers (or symbols) that form a product when multiplied together
Factorial
product of an integer and all smaller positive integers
fraction
relationship of a part to a whole
numerator: represents the part
denominator: represents the whole
Function
relationship between two variables, can have only one x-value correspond to only one y-value
Identity property of 0
adding zero
The sum of a number and zero is always that number.
Identity property of 1
multiplying 1
The property which states that multiplying a number by 1 does not change the number’s value
inequality graphing hints
solid dot means equal to
hollow dot is not equal to
lines to the left mean less than
lines to the right mean greater than
READ CAREFULLY the lines between two dots
Integers
all positive and negative whole numbers
negative integers are to the left of zero, smaller negative integers are further from zero
positive integers are to the right of zero, larger positive integers are further from zero
Interest formula
Interest = principal times rate times time
Like Terms
Expressions that contain the same variables to the same power
Linear Equation
An equation whose solutions form a straight line on a coordinate plane; example: y = 3x - 1
Multiplication and Division with integers
count the number of negative integers
if there are an even number of negative integers, the product or quotient will be positive
if there are an odd number of negative integers, the product of quotient will be negative
multiply or divide mixed numbers
before you multiply or divide mixed numbers, rewrite them as improper fractions
multiplying fractions
multiply the numerators for your new numerator, multiply the denominators for your new denominator, then simplify the product
Opposites
two numbers that have the same absolute value but have different signs
Order of Operations
working left to right repeatedly: Parentheses, Exponents; then Multiplication, Division; then Addition, Subtraction
perfect square
a number that has a whole number for a square root ex: 9, 16, 121
prime number
A whole number that has exactly two factors, 1 and itself.
Product
a quantity obtained by multiplication; the answer to a multiplication problem
proportion
relationship between two equivalent ratios
quadrants
The x- and y-axes divide the coordinate plane into four regions. Each region is called a quadrant.
I (x, y)
II (-x, y)
III (-x, -y)
IV (x, -y)
Quotient
The result after numbers and/or variables are divided
Rate of change
positive and negative
slope of a line: change in y value related to change in x value
ratio that represents amount of something per time unit
ratio
a relationship between two amounts
Rational Number
A number that can be written as a/b where a and b are integers, but b is not equal to 0; an integer or a fraction; examples: 6 can be expressed as 6/1; 0.5 can be expressed as 1/2.
Rational number
a number that can be expressed as a fraction, including integers
Real Number
all rational or irrational numbers; real numbers can be represented on the real number line
Reciprocal
one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; a fraction that has been flipped. The reciprocal of 3/4 is 4/3.
Repeating Decimal
A decimal in which one or more digits repeat infinitely; The repeating portion of the decimal is shown with a short line drawn over the repeating numbers.
Scientific Notation
a standardized way of writing very large or very small numbers
example 35,100,000,000,000 = 3.51 x 10^13
Sequence
An ordered list or numbers; example: 2,4,6,8,10…
special fraction information
fractions with a denominator of 1 are equivalent to the numerator
fractions with a numerator of 1 cannot be simplified
fractions with a numerator of 0 equal 0
fractions with a denominator of 0 are undefined because there is no such thing as “part of nothing”
Square Root
a number that must be multiplied by itself to equal a given number
Subtraction with integers
change the subtraction sign to addition AND the sign of the second number
follow the guidelines for addition
Sum
The result after numbers and/or variables are added
Total Amount formula
Total Amount earned = principal + interest
Variable
a letter that can be replaced with any number from a set
a quantity that varies or changes according to certain circumstances
a placeholder for any value
y = mx+b
m is the slope of the line (change in y over change in x)
b is the y-intercept
