Algebra Tutorials!
Friday 12th of July
Calculations with Negative Numbers
Solving Linear Equations
Systems of Linear Equations
Solving Linear Equations Graphically
Algebra Expressions
Evaluating Expressions and Solving Equations
Fraction rules
Factoring Quadratic Trinomials
Multiplying and Dividing Fractions
Dividing Decimals by Whole Numbers
Adding and Subtracting Radicals
Subtracting Fractions
Factoring Polynomials by Grouping
Slopes of Perpendicular Lines
Linear Equations
Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
Writing Linear Equations Using Slope and Point
Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
Solving Equations 3
Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
Rounding Numbers
Factoring by Grouping
Polar Form of a Complex Number
Solving Quadratic Equations
Simplifying Complex Fractions
Common Logs
Operations on Signed Numbers
Multiplying Fractions in General
Dividing Polynomials
Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
Solving Linear Equations
The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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Rational Numbers

A rational number is a number that can be expressed in the form , where a and b are integers and b is not equal to 0.




If the graph of a is to the left of the graph of b on a number line, then a < b.

For any two numbers a and b, exactly one of these is true:

a < b, a = b, a > b

You can use cross products to compare two fractions.

For rational numbers and , with b >0 and d > 0,

  1. if , then ad < bc, and
  2. if ad < bc, then .


Use a calculator to write the fractions as decimals. Then order the fractions from least to greatest.


The decimals from least to greatest are So the fractions should be ordered .

Adding and Subtracting Rational Numbers

To add or subtract rational numbers, use the same rules you used to add integers. When you are adding three or more rational numbers, you can use the commutative and associative properties to rearrange the addends.


Find .


The LCD is 8.

The sum is negative.

Subtract absolute values.


Multiplying Rational Numbers

The product of two numbers having the same sign is positive. The product of two numbers having different signs is negative. It is also useful to note that multiplying a number or expression by -1 results in the opposite of the number or expression. This is called the multiplicative property of -1.



Replace x with
Divide out common factors.
Multiply. The signs are different, so the product is negative.


Dividing Rational Numbers

You can use the same rules of signs when dividing rational numbers that you used for multiplying.

Dividing Two Rational Numbers The quotient of two numbers having the same sign is positive.

The quotient of two numbers having different signs is negative.

If a fraction has one or more fractions in the numerator or denominator, it is a complex fraction. To simplify a complex fraction, rewrite it as a division expression.




Rewrite the complex fraction as

Multiply by the reciprocal of -8.
The signs are different, so the product is negative.
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