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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The ability to work confidently with fractions, both number fractions and algebraic fractions, is an essential skill which underpins all other algebraic processes. In this leaflet we remind you of how number fractions are simplified, added, subtracted, multiplied and divided.

1. Expressing a fraction in its simplest form

In any fraction , say, the number p at the top is called the numerator. The number q at the bottom is called the denominator. The number q must never be zero. A fraction can always be expressed in different, yet equivalent forms. For example, the two fractions and are equivalent. They represent the same value. A fraction is expressed in its simplest form by cancelling any factors which are common to both the numerator and the denominator. You need to remember that factors are numbers which are multiplied together. We note that

and so there is a factor of 2 which is common to both the numerator and the denominator. This common factor can be cancelled to leave the equivalent fraction . Cancelling is equivalent to dividing the top and the bottom by the common factor.


is equivalent to since

2. Addition and subtraction of fractions

To add two fractions we first re-write each fraction so that they both have the same denominator. This denominator is chosen to be the lowest common denominator. The is the smallest number which is a multiple of both denominators. Then, the numerators only are added, and the result is divided by the lowest common denominator.






a) In this case the denominators of each fraction are already the same. The lowest common denominator is 16. We perform the addition by simply adding the numerators and dividing the result by the lowest common denominator. So, . This answer can be expressed in the simpler form by cancelling the common factor 4.

b) To add these fractions we must rewrite them so that they have the same denominator. The lowest common denominator is 16 because this is the smallest number which is a multiple of both denominators. Note that is equivalent to and so we write .




The smallest number which is a multiple of the given denominators is 30. We express each fraction with a denominator of 30.

3. Multiplication and division of fractions

Multiplication of fractions is more straightforward. We simply multiply the numerators to give a new numerator, and multiply the denominators to give a new denominator. For example

Division is performed by inverting the second fraction and then multiplying. So,

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