1. Chapter 1 Foundations for Algebra
Variable – a letter or symbol used to represent a value that can change.
Constant – a value that does not change.
Numerical expression - contains only constants and operations.
Algebraic expression – contains variables, constants, and operations.
Coefficient – a number multiplied by a variable: 4x; 3y (4 and 3 are coefficients)

2. Absolute value – the distance from zero to a number on a number line.
Opposites – two numbers with a sum of zero.
Additive inverses – a number and its opposite.
Reciprocals – two numbers whose product is 1.
Multiplicative inverses – a number and its reciprocal.

3. Adding Real Numbers
If two numbers have the same sign, add their absolute values and use the sign of the numbers.
NUMBERS: = 9; = -7
If two numbers have different signs, find the difference of their absolute values and use the sign of the number with the greater absolute value.
NUMBERS: = -1; 8 + (-2) = 6

4. Subtracting Real Numbers
To subtract a number, add its opposite. Then follow the rules for addition of real numbers.
NUMBERS: 3 – 8 = 3 + (-8)
ALGEBRA: a – b = a + (-b)

5. Multiplying and Dividing Real Numbers
If two numbers have the same sign, their product or quotient is positive.
NUMBERS: 4*5 = 20; -15/-5 = 3
If two numbers have different signs, their product or quotient is negative.
NUMBERS: 8(-4) = 32; -24/6 = -4

6. Properties of Zero The product of any number and 0 is 0.
The quotient of 0 and any number is 0.
Division by 0 is undefined.
NUMBERS: 0 * 8 = 0; 0/5 = 0;
12/0 undefined
ALGEBRA: 0 * a = 0; 0/a = 0
a/0 undefined

7. .1
Square root – a number that is multiplied to itself to form a product is called a square root of that product.
Perfect square – a number whose positive square root is a whole number.
Natural numbers (N) – the counting numbers: 1, 2, 3, …
Whole numbers (W) – the natural numbers and zero: 0, 1, 2, 3, …

8. Integers (Z) – whole numbers and their opposites: 0, 1, -1, 2, -2, 3, -3…
Rational numbers – can be expressed in the form a/b, where a and b are both integers and b ‡ 0; ½, 4/1, 13/2
Terminating decimals – have a finite number of digits: 3.5, 2.318, 5.0
Repeating decimals – one or more digits behind the decimal point repeat: …, …, …..
Irrational numbers – cannot be expressed as a/b, they include square roots of non-perfect squares and non-terminating, nonrepeating decimals: …, , etc.

9. REAL NUMBERS Rational numbers (Q) Natural numbers Integers (Z)
Whole numbers (W)
Natural numbers (N)

10. Properties of Addition and Multiplication
COMMUTATIVE PROPERTY: You can add and multiply numbers in any order.
NUMBERS: = 8 + 3; 6 * 7 = 7 * 6
ALGEBRA: a + b = b + a; ab = ba
ASSOCIATIVE PROPERTY: When adding or multiplying, you can group any of the numbers together.
NUMBERS: 6 + (8 + 3) = (6 + 8) + 3; *(4*5) = (3 * 4) * 5
ALGEBRA: a + (b + c) = (a + b) +c; a(bc) = (ab)c

11. Distributive Property
You can multiply a number by a sum or difference; or multiply by each number in the sum or difference and then add. The result is the same.
NUMBERS: 3(4 + 5) = 3(4) + 3(5); (5-3 ) = 8(5) – 8(3)
ALGEBRA: a(b + c) = a(b) + a(c); a(b – c) = a(b) – a(c)

12. Coordinate plane – formed by the intersection of the x and the y axis.
Origin – the point at which the x and the y axis intersect.
Ordered pair – consists of an x-coordinate and a y-coordinate and is written (x,y).
Quadrants – the four sections of the coordinate plane formed by the x and the y axes.
Input – a value that is substituted for the independent variable in a relation or function.
Output – the result of substituting a value for a variable in a function.