Course 15 General Math 2

Integer

Any positive or negative whole number, and also zero

Negative Numbers

Whole numbers that are less than zero, such as -7, -23, or -624

Addition

Combining the values of two or more numbers to get their total value. In mathematics, the plus sign (+) is used to show addition.

Sum or Total

The result of addition; in the statement 5 + 3 = 8, the 8 is called the sum or the total.

Addends

The numbers that are being added together; in the equation 5 + 3 = 8, the 5 and the 3 are the addends.

Subtraction

One number is taken away from another to find a difference. To show subtraction, the minus sign (-) is used.

Minuend

The number you're taking away from; for example, in the statement 6 - 4 = 2, 6 is called the minuend.

Subtrahend

The number being subtracted; for example, in the statement 6 - 4 = 2, 4 is called the subtrahend.

Multiplication

Combining two numbers by adding one value to itself a number of times equal to the other number. For example, 6 × 8 is the same as 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6. To show multiplication, the times sign (×), or an asterisk (*), or a dot (⋅) is used.

Multiplier

The number of times you add the multiplicand to itself; in the multiplication statement 3 × 7 = 21, 7 is the multiplier.

Product

The result of multiplication; in the multiplication statement 3 × 7 = 21, 21 is the product.

Multiplicand

The number you are adding to itself; in the multiplication statement 3 × 7 = 21, 3 is the multiplicand.

Division

Separating one number into smaller, equal numbers; to show division, the division sign (÷) or an divisoion bar (/) is used.

Divisor

The number of parts into which you're splitting the dividend; in the division statement 21 ÷ 3 = 7, 3 is the divisor.

Quotient

The result of dividing; in the division statement 21 ÷ 3 = 7, 7 is the quotient.

Remainder

When division is uneven, you're left with a remainder, or a number that is smaller than, and therefore indivisible by, the divisor.

Inverse Operations

The mathematical statements 3 + 4 = 7 and 7 - 4 = 3 are called inverse equations, because each statement is the opposite of the other. For example, since 24 ÷ 8 = 3, we know that 8 × 3 = 24.

Parentheses ( )

Operations inside parentheses should be performed first. If a problem contains more than one set of parentheses, solve the operations from left to right.

Brackets [ ] or Braces { }

Additions to parentheses that mark order of operations; for example, {[(3 + 2) - 4] + 6} = ?; always solve the operations in parentheses first, then the operations in brackets, and finally the operations in braces. You always start at the innermost set and work your way out.

Dividend

The number you're splitting into parts; in the division statement 21 ÷ 3 = 7, 21 is the dividend.

Positive Integers

Whole numbers greater than zero, such as 3, 17, or 461

Factor

Any whole number that can be divided into a given number without leaving a remainder.

Multiple

The product formed by a given number and another number; for example, 24 is a multiple of 2, 4, 6, and 12.

Prime Numbers

Prime numbers are defined as numbers that have only two factors, 1 and the number itself.

Composite Numbers

Composite numbers are numbers that have more than two factors. For example, 8 is a composite number because its factors include 1, 2, 4, and 8.

Prime Factors

All the prime numbers that, when multiplied together, produce that number

Factor Pairs

Two specific numbers that can be multiplied together to produce a given multiple. You can use the rules of divisibility to help you find factor pairs for a given number.

Power of a Number

Indicates how many times to multiply the number by itself (also called an exponent)

Square

Multiply a number by itself once (2 × 2)

Cube

Multiply a number by itself twice (2 × 2 × 2)

Volume

How much space a solid shape takes up. For example, a cube with 3-inch sides has a volume of 27 cubic inches.

Exponent

Indicates how many times to multiply the base by itself (also called a power)

Base

The number that's to be multiplied by itself in an exponential expression

Reciprocal

The reciprocal of a whole number is equal to 1 divided by the number. Whenever you multiply a whole number by its reciprocal, you get 1.

Scientific Notation

Scientific notation is a method of abbreviating large numbers by writing the number as a simple multiplication problem.

Square Root

The square root of a number produces that number when squared.

Radical Sign

The square root of a number is usually written by placing the radical sign (√ ) in front of the number.

Perfect Squares

Perfect squares is when square roots are whole numbers.

Equation

An equation is defined as a mathematical statement that includes the equal sign (=).

True Equation

In a true equation, the numbers to the left of the equal sign are equal to the numbers to the right of the equal sign.

Missing Number

This means you may need to find a missing addend, a missing minuend or subtrahend, a missing multiplicand or multiplier, or a missing dividend or divisor.

Variable

A variable is a missing number that is represented by a letter of the alphabet. Any letter may be used.

Balancing the Equation

When solving an equation, whatever is done to one side of the equals sign must also be done to the other side—this is called balancing the equation.

Positive Number

Any number with a value greater than zero

Negative Number

A number with a value less than zero

Signed Numbers

All negative and positive numbers

Opposite Number

The same number with the opposite sign. For example, 8 is the opposite of −8.

Integers

Positive or negative whole numbers

Origin

Zero, a value that has no opposite

Variable

An unknown number, usually represented by a letter

Monomial

A number, a variable, or a number and a variable multiplied together. For example: 3, abc, 6k, -3xy

Coefficient

The number in front of a variable; it's the number that the variable will be multiplied by. For example, in the monomial 3k, 3 is the coefficient.

Constant

A number by itself without a variable. For example, 5, 9, and 17 are constants.

Polynomial

A combination of two or more monomials. For example, 8x + x - 5 is a polynomial.

Simplifying the Expression

Combining two or more like monomials

Like Terms

Monomials that have the same variable, or group of variables. For example, 5t and −6t (t is the common variable)

Equation

Two or more expressions compared with an equal sign (=). In order to be true, the value of the expressions on each side must be the same. For example, 3 + 5 = 8

Isolate the Variable

Performing operations that get a specific variable on one side of an equation or inequality

Inequality

A mathematical expression comparing two values with a greater than (>) or less than (<) sign.

Integer

Any positive or negative whole number, including zero

Similar

Monomials with the same variable or group of variables (the same as like)

Point

A position in space

Line

A set of points that exist on a straight path.

Segment

The section of a line between two specific points

Ray

A section of a line that begins at one point and continues infinitely in one direction

Angle

The space between two intersected lines, rays, or planes

Plane

A flat surface with length and width.

Vertex

The point where the two sides of an angle meet

Geometry

The branch of mathematics that includes the study of points, lines, surfaces, and solids

Degree

The unit used to measure angles, written as º

Protractor

An instrument used to measure the degrees of an angle

Acute Angle

An angle that measures less than 90°

Right Angle

An angle that measures exactly 90°

Obtuse Angle

An angle with a measurement greater than 90°

Straight Angle

An angle that has a measurement of 180°

Vertical Angles

Where two lines intersect, the angles opposite each other; in a plus sign figure ( + ), the top right and bottom left spaces are vertical angles.

Adjacent Angles

Angles which share a vertex and a common line. For example, in a plus-sign shape ( + ), the spaces in top right and top left make adjacent angles.

Complementary Angles

Two or more angles for which sum of their measures is 90°.

Supplementary Angles

Two angles for which the sum of their measures is 180°

Parallel lines

Two or more lines that extend infinitely the same direction, but never intersect; shown using the symbol ( || )

Perpendicular lines

Two lines that form a 90° angle where they intersect

Polygon

A closed plane figure with three or more sides

Pentagon

A polygon with five sides

Quadrilateral

A polygon with four sides

Triangle

A polygon with three sides.

Octagon

A polygon with eight sides

Nonagon

A polygon with nine sides

Hexagon

A polygon with six sides

Heptagon

A polygon with seven sides

Decagon

A polygon with ten sides

Perimeter

The distance around the outside of a specific area or shape

Regular Polygon

A polygon with sides that are all the same length

Square

A regular quadrilateral with four equal sides and four right angles

Equilateral Triangle

A polygon with three equal-length sides

Circle

A set of points equally distant from a center point

Circumference

The distance around the outside of a circle

Diameter

A straight line going from one point on a circle to another that also includes the center point

Radius

The distance from the center of a circle to any point on the outside edge of the circle

Pi

A number used to find the circumference of any circle, written as π and usually rounded to 3.14 or 22 ⁄ 7

Parallel Lines

Lines that extend in the same direction but never intersect