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Finding the Greatest Common Factor
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Adding Fractions
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Adding and Subtracting Polynomials
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Factoring
Multiplication Properties of Exponents
Completing the Square
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Combining Like Radical Terms
Elimination Using Multiplication
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Pythagoras' Theorem 1
Finding the Least Common Multiples
Multiplying and Dividing in Scientific Notation
Adding and Subtracting Fractions
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Adding and Subtracting Fractions
Multiplication by 111
Adding Fractions
Multiplying and Dividing Rational Numbers
Multiplication by 50
Solving Linear Inequalities in One Variable
Simplifying Cube Roots That Contain Integers
Graphing Compound Inequalities
Simple Trinomials as Products of Binomials
Writing Linear Equations in Slope-Intercept Form
Solving Linear Equations
Lines and Equations
The Intercepts of a Parabola
Absolute Value Function
Solving Equations
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Complex Numbers
Factoring the Difference of Two Squares
Multiplying and Dividing Rational Expressions
Adding and Subtracting Radicals
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Solving Systems of Equations
Factoring Out the Opposite of the GCF
Multiplying Special Polynomials
Properties of Exponents
Scientific Notation
Multiplying Rational Expressions
Adding and Subtracting Rational Expressions With Unlike Denominators
Multiplication by 25
Decimals to Fractions
Solving Quadratic Equations by Completing the Square
Quotient Rule for Exponents
Simplifying Square Roots
Multiplying and Dividing Rational Expressions
Independent, Inconsistent, and Dependent Systems of Equations
Slopes
Graphing Lines in the Coordinate Plane
Graphing Functions
Powers of Ten
Zero Power Property of Exponents
The Vertex of a Parabola
Rationalizing the Denominator
Test for Factorability for Quadratic Trinomials
Trinomial Squares
Solving Two-Step Equations
Solving Linear Equations Containing Fractions
Multiplying by 125
Exponent Properties
Multiplying Fractions
Adding and Subtracting Rational Expressions With the Same Denominator
Quadratic Expressions - Completing Squares
Adding and Subtracting Mixed Numbers with Different Denominators
Solving a Formula for a Given Variable
Factoring Trinomials
Multiplying and Dividing Fractions
Multiplying and Dividing Complex Numbers in Polar Form
Power Equations and their Graphs
Solving Linear Systems of Equations by Substitution
Solving Polynomial Equations by Factoring
Laws of Exponents
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Systems of Linear Equations
Properties of Rational Exponents
Power of a Product and Power of a Quotient
Factoring Differences of Perfect Squares
Dividing Fractions
Factoring a Polynomial by Finding the GCF
Graphing Linear Equations
Steps in Factoring
Multiplication Property of Exponents
Solving Systems of Linear Equations in Three Variables
Solving Exponential Equations
Finding the GCF of a Set of Monomials
 
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Adding and Substracting Fractions

In this section we look at the addition (and subtraction) of fractions. If fractions are to be added then they must have the same denominators .

Example

Write the following sums of fractions as single fractions.

Solution

a) Taking all the fractions with denominator 24,

(b) This time, taking all the fractions with denominator 12,

The exercise below is designed to give you some practice at addition and subtraction of fractions.

Exercise

Evaluate the following, putting the final answer in its lowest terms.

(a) The lowest common denominator is 24, so

(b) Before proceeding, note that the second fraction is not in its lowest terms. Since 2/4=(1 × 2 )/(2 × 2 )=1/2,

This fraction is called an improper fraction since the numerator is larger than the denominator. It is perfectly acceptable as a fraction but it may also written as .

(c) The least common denominator of the two fractions is 20 so

This is another improper fraction which may be written as

(d) The least common denominator of the two fractions is 12 so

This is another improper fraction which is equal to

(e) The least common denominator of the two fractions is 6 so

where the common factor 2 has been cancelled to obtain the final answer.

(f) The least common denominator of the two fractions is 30 so

where the final answer is obtained after cancellation of the common factor 2.

To finish this section there follows two simple quizzes.

Quiz

Which of the following fractions is the result of evaluating the sum 3 4 - 2 3 + 1 6 ?

(a) 1/4, (b) 1/3, (c) 1/5, (d) 3/8.

Solution

The least common denominator of the three fractions is 12, so

Quiz

From the fraction given below, choose the one which is mid-way between 2/3 and 4/5.

(a) 2/3, (b) 3/5, (c) 10/15 (d) 11/15.

Solution

The least common denominator of the two fractions is 15. Writing both fractions with this denominator gives

The fraction mid-way between 10/15 and 12/15 is 11/15.

 

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