	Algebra Tutorials!

Thursday 21st of November



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	Calculations with Negative Numbers
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	Evaluating Expressions and Solving Equations
	Fraction rules
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	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
	Percents
	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
	Algebra
	Common Logs
	Operations on Signed Numbers
	Multiplying Fractions in General
	Dividing Polynomials
	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
	fractions
	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
	Quadratics
	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
	Decimals
	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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Adding and Subtracting Fractions

Adding and Subtracting Fractions with the Same Denominator

PROCEDURE: To add fractions with the same denominator, add the numerators and put the sum over the original denominator. To subtract fractions with the same denominator, subtract the numerators and put the difference over the original denominator.

SAMPLE PROBLEM A:

Add the numerators, and put the sum over the original denominator:

SAMPLE PROBLEM B:

Subtract the numerators and put the difference over the original denominator:

Adding and Subtracting Fractions with Different Denominators

Sometimes you have to add or subtract fractions that have different denominators. To do this, you first need to rewrite your fractions so that they DO have the same denominator. Figuring out the least common denominator (LCD) of your fractions is the first step.

PROCEDURE: To find the least common denominator of two fractions, find the least common multiple of the denominators. In other words, look at the multiples of the numbers, and find out which they have in common. The common multiple with the lowest value is your LCD.

SAMPLE PROBLEM:

What is the LCD of ?

Step 1: List the multiples of 4.

(4 Ã— 1) Ã— 4, (4 Ã— 2) Ã— 8, (4 Ã— 3) Ã— 12, (4 Ã— 4) Ã— 16, etc.

Step 2: List the multiples of 3.

(3 Ã— 1) Ã— 3, (3 Ã— 2) Ã— 6, (3 Ã— 3) Ã— 9, (3 Ã— 4) Ã— 12, etc.

The least common denominator of is 12.

Putting the LCD to Work

Now that you know how to find the LCD, you are all set to add and subtract fractions with different denominators. Follow the steps below to see how to use the LCD to add and subtract fractions with different denominators.

PROCEDURE: To add or subtract fractions with different denominators, first find the LCD of the two fractions. Then determine the factor that each denominator is of that LCD. Multiply both the numerator and the denominator by those factors so that the fractions have the same denominator. Then add or subtract the numerators.

SAMPLE PROBLEM:

Step 1: Find the LCD.

(2 Ã— 1) Ã— 2, (2 Ã— 2) Ã— 4, (2 Ã— 3) Ã— 6, (2 Ã— 4) Ã— 8, (2 Ã— 5) Ã— 10, etc.

(5 Ã— 1) Ã— 5, (5 Ã— 2) Ã— 10, etc.

The LCD is 10 .

Step 2: Determine the factor that each denominator is of the LCD.

Because 2 Ã— 5 Ã— 10, 5 is the factor of 2 .

Because 5 Ã— 2 Ã— 10, 2 is the factor of 5 .

Step 3: Multiply the factors of the LCD by the fractions.

Step 4: Add the fractions.