Grade 7 Number Properties and Algebraic Terms Flashcards
Addend
A number which is involved in addition. Numbers being added are considered to be the addends.
Sum
The result after numbers and/or variables are added
Difference
The amount by which one value is greater or smaller than another.
The result when numbers are subtracted.
Factor
any of the numbers (or symbols) that form a product when multiplied together
Product
a quantity obtained by multiplication; the answer to a multiplication problem
Quotient
The result after numbers and/or variables are divided
Order of Operations
working left to right repeatedly: Parentheses, Exponents; then Multiplication, Division; then Addition, Subtraction
Expression
a phrase made up of one or more numbers, variables, and operations
Equation
equivalent expressions
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
1-Step Equations
identify inverse operation to isolate variable
2-Step Equations
first add/subtract, then multiply/divide to isolate variable
Function
relationship between two variables, can have only one x-value correspond to only one y-value
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
Expanded form of a number
a number that is expressed as the sum of multiples of ten
example 643 = (6x100)+(4x10)+(3x1)
fraction
relationship of a part to a whole
numerator: represents the part
denominator: represents the whole
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”
adding or subtracting fractions
requires the denominators be the same
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
dividing fractions
rewrite the first fraction, write a multiplication sign, write the reciprocal of the second fraction, multiply the fractions
ratio
a relationship between two amounts
proportion
relationship between two equivalent ratios
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
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.
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)
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)
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
Absolute value
the distance of an integer from 0
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
Subtraction with integers
change the subtraction sign to addition AND the sign of the second number
follow the guidelines for addition
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
Rational number
a number that can be expressed as a fraction, including integers
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.
Square Root
a number that must be multiplied by itself to equal a given number
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)
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
Factorial
product of an integer and all smaller positive integers
