7TH GRADE MATH-MIDTERM REVIEW SHEET`( Your Guide to Success)

Inverse Property of Addition (Additive Inverse)

(-a) + a = 0

Associative Property of Multiplication

(a x b) x c = a x (b x c)

Associative Property of Addition

(a+b) + c = a + (b + c)

Factor tables

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finding the number of elements in a factor set

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set notation

A Set is a collection of things (usually numbers). Example: {5, 7, 11} is a set. But we can also "build" a set by describing what is in it. Here is a simple example of set-builder notation: It says "the set of all x's, such that x is greater than 0".

Divisibility rule for 12

A number is divisible by 12 if it is divisible by both 3 and 4. The reason this is true is because 12 = 3 × 4. ... This is the case when the last two digits of the number are divisible by four.

Divisibility rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3. ex.: 342: 3 + 4 + 2 = 9, 9/3 = 3

Variable

A quantity or pronumeral that can take a set of values

Set Builder Notation

A shorthand used to write sets, often sets with an infinite number of elements. Note: The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." It is read aloud exactly the same way when the colon : is replaced by the vertical line.

Constant

A term with no pronumeral part

Algebraic Expression

An algebraic expression is an expression involving constants, variables, and arithmetic operations. The variables represent numbers although specific values are not always given.

Divisibility rule for 2

Any whole number that ends in 0, 2, 4, 6, or 8 will be divisible by 2.

Divisibility rule for 8

If the last three digits of a whole number are divisible by 8, then the entire number is divisible by 8.

null/empty set

In mathematical sets, the null set, also called the empty set, is the set that does not contain anything. It is symbolized or { }. There is only one null set. This is because there is logically only one way that a set can contain nothing.

set partition

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

Rational numbers

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number. ... The decimal expansion of an irrational number continues without repeating.

Power Set

In mathematics, the power set (or powerset) of any set S is the set of all subsets of S, including the empty set and S itself.

Prime Factorization

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The prime factorization of a positive integer is a list of the integer's prime factors, together with their multiplicities; the process of determining these factors is called integer factorization.

infinite sets

In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. Some examples are: the set of all integers, {..., -1, 0, 1, 2, ...}, is a countably infinite set; and. the set of all real numbers is an uncountably infinite set. Infinite set - Wikipedia

Expression

Is formed when terms are added or subtracted

Divisibility rule for 10

Numbers that are divisible by 10 need to be even and divisible by 5, because the prime factors of 10 are 5 and 2. Basically, this means that for a number to be divisible by 10, the last digit must be a 0. Take a look at the last digit: 23,890. The last digit is a 0.

proper subset

Proper subset definition. A proper subset of a set A is a subset of A that is not equal to A . In other words, if B is a proper subset of A , then all elements of B are in A but A contains at least one element that is not in B . Proper subset definition - Math Insight

Divisibility rule for 11

Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number. So, for instance, 2728 has alternating sum of digits 2-7+2-8 = -11.

Divisibility rule for 5

The # must end in 5 or 0.

Pemdas

The Order of Operations. ... A common technique for remembering the order of operations is the abbreviation "PEMDAS", which is turned into the phrase "Please Excuse My Dear Aunt Sally". It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction"

Complements

The complement is the amount you must add to something to make it "whole". For example, in geometry, two angles are said to be complementary when they add up to 90°. One angle is said to be the complement of the other. In the figure below, angles PQR and RQS are complementary. RQS is the complement of PQR.

Intersection

The elements shared by two or more sets.

Lowest Common Multiple(LCM)

The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

Coefficient

The number factor in a term

finite sets

The number of elements of a finite set is a natural number (a non-negative integer) and is called the cardinality of the set. A set that is not finite is called infinite. For example, the set of all positive integers is infinite: { 1 , 2 , 3 , ... } .

Divisibility rule for 9

The prime factors of 9 are 3 and 3. So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9.

Real Numbers

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...).

Combining Like Terms

To combine you just add terms together and make sure that they are all on the same side of the equation.

Divisibility rule for 7

To find out if a number is divisible by seven, take the last digit, double it, and subtract it from the rest of the number. If you get an answer divisible by 7 (including zero), then the original number is divisible by seven. If you don't know the new number's divisibility, you can apply the rule again. Divisibility Rules

Rules of Exponents

When you multiply terms with like bases you add the exponents together. The base stays the same. When you divide terms with like bases you subtract the exponent of the denominator from the exponent of the numerator. This is called getting the power of a power.

Identity Property of Addition

a + 0 = 0 + a = a

Commutative Property of Addition

a + b = b + a

Venn diagrams

a diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.

Roster Notation

a list of elements, separated by commas, enclosed in curly braces.

Whole numbers

a number without fractions; an integer.

subset

a set of which all the elements are contained in another set.

Integers

a whole number; a number that is not a fraction.

Zero Property of Multiplication

a x 0 = 0 x a = 0

Identity Property of Multiplication

a x 1 = 1 x a = a

Inverse Property of Multiplication

a x 1/a = 1

Distributive Property of Addition

a(b + c) = ab + ac

Distributive Property of Multiplication

a(b + c) = ab + bc

Commutative Property of Multiplication

a*b=b*a

Divisibility rule for 4

f the last two digits of a whole number are divisible by 4, then the entire number is divisible by 4.

Divisibility rule for 6

he prime factors of 6 are 2 and 3. So for a number to be divisible by 6, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3.

Union

he union of two sets is everything in both sets. For example if you have the set {3,4,5} and the set {5,6,7}, then the union of these two sets is {3,4,5,6,7}. The symbol for union is a capital U.

Addition Property of Equality

if a = b then a+c = b+c

Multiplicative Property of Equality

if a = b then ac = bc

Factor sets

refers to a set of two numbers, which when multiplied result in a definite number.

Greatest Common Factor(GCF)

the greatest factor that divides two numbers. To find the GCF of two numbers: ... Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Absolute Value

the magnitude of a real number without regard to its sign. 2.

Natural numbers

the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.

Perfect Squares

the product of a rational number multiplied by itself.

Factorials

the product of an integer and all the integers below it; e.g., factorial four ( 4! ) is equal to 24.

Perfect Cubes

the result of multiplying a number three times by itself. We can also say that perfect cubes are the numbers that have exact cube roots. 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, 1,331, 1,728, 2,197, 2,744, 3,375...

equality

when the value in the two sides of the equal symbol are equal in value.