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  Wednesday 19th of September      
 
   
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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
Equations
   
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Adding and Subtracting Fractions

Now we can apply these concepts to working with fractions.

To add or subtract fractions with the same denominator (bottom), simply add or subtract the numerators (top).

Example:

Example:

To add or subtract fractions with different denominators (bottom), we must change the fractions so the denominators match. You can use any matching denominator, but finding the denominator with the least common multiple gives you the simplest arithmetic.

 

Example:

Step 1:

First we must change the fractions so they have the same denominator.

We start by finding the least common multiple of the numbers 6 and 9:

Multiples of 9 are 9, 18, 27, 36 ....

Multiples of 6 are 6, 12, 18, 24, 30 ....

The least common multiple is therefore 18.

Step 2:

Change the fractions by multiplying the numerator and denominator by the factor which will make the denominator l8:

For the first fraction

For the second fraction

Step 3:

Now we can add the two fractions:

Step 4:

We always reduce our fractions, and notice both 21 and 18 are divisible by 3. (The greatest common factor is three.)

The answer to the above example, 7/6, is called an improper fraction, because the numerator is larger then the denominator. We convert this into a mixed number, which is a number that contains a whole number. Do this by dividing 7 by 6 and showing the remainder as a fraction.

 

Example:

is the same as 7 divided by 6.

6 goes into 7 once with remainder 1.

The mixed number is , which is written as

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