Integers
Counting numbers, their opposites, and zero. No decimals or fractions.
(...-4, -3, -2, -1, 0, 1, 2, 3, 4...)
Rational Number
A number that can be expressed as a fraction/ratio and has a decimal value that terminates or repeats.
Irrational Number
A number that has a decimal value that does not repeat or terminate. The square root of a non-perfect square or the cube root of a non-perfect cube.
Terminating Decimal
A decimal that stops or ends
(0.125)
Repeating Decimal
A decimal where a digit or a group of digits repeats forever.
(0.77777777777....)
Equation
A grouping of terms or values that use an equals sign to show an equal relationship. Statement in which two expressions are equal.
2x - 3 =7
Expression
A grouping of terms or values that DOES NOT have an equals sign
6x + 7
Solution
A value we can put in place of the variable that makes the equation true.
2 + x =4
2 + 2 =4
4=4
Variable
A letter or symbol that represents an unknown value
(x)
Coefficient
The number multiplied by a variable in a term. The number with the variable.
12x
Constant
A value or number that never changes in an equation. A term that doesn't have a variable.
12x - 3 = 4
^ ^
Distributive Property
Multiply a number outside parenthesis to both terms inside to get rid of parenthesis.
3(x - 7)
Combining Like Terms
Simplifying the expression to lessen the number of terms
5x + 9 + 2x
5x +2x =7x
9=9
7x + 9
Opposite
Two numbers that are equal distance from zero (positive/negative)
-4 and 4
Inverses
An operation that reveres/ undoes another
(addition and subtraction)
Step to Solving an Equation
1. Distribute
2. Combine Like Terms
3. Eliminate a variable from one side of the equation
4. Undo the Constant
5. Undo the Variable
6. Undo the Power- Square root or cube root
Infinite Solution
An equation that has the same variable coefficient and constant on either side of the equal sign
3x + 4 = 3x + 4
One Solution
An equation that has one or different variable coefficient on each side of the equal sign
-2x + 4 = 6x + 7
No Solution
An equation that has the same variable coefficients but different constants on either side of the equal sign
6x + 7 = 6x + 1
Pythagorean Theorem
In a right triangle, the hypotenuse squared is equal to the sum of the legs squared. Used to find the distance between two points and prove that a triangle is right or not.
a^2 + b^2 = c^2
Hypotenuse
The longest side of a right triangle. Opposite the right triangle
Leg
The two shorter sides of a right triangle. They form the right triangle
Volume
Space occupied within a three- dimensional object
Radius
Th distance from the center of a circle to any point on its edge
Diameter
The distance from one point on a circle through the center to another point on the circle.