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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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.


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


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.


What is the LCD of ?

Step 1: List the multiples of 4.

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

Step 2: List the multiples of 3.

(3 × 1) × 3, (3 × 2) × 6, (3 × 3) × 9, (3 × 4) × 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.


Step 1: Find the LCD.

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

(5 × 1) × 5, (5 × 2) × 10, etc.

The LCD is 10 .

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

Because 2 × 5 × 10, 5 is the factor of 2 .

Because 5 × 2 × 10, 2 is the factor of 5 .

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

Step 4: Add the fractions.

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