Home
Fields Medal Prize Winners (1998)




TUTORIALS:


Solving Quadratic Equations by Using the Quadratic Formula
Addition with Negative Numbers
Solving Linear Systems of Equations by Elimination
Rational Exponents
Solving Quadratic Inequalities
Systems of Equations That Have No Solution or Infinitely Many Solutions
Dividing Polynomials by Monomials and Binomials
Polar Representation of Complex Numbers
Solving Equations with Fractions
Quadratic Expressions Completing Squares
Graphing Linear Inequalities
Square Roots of Negative Complex Numbers
Simplifying Square Roots
The Equation of a Circle
Fractional Exponents
Finding the Least Common Denominator
Simplifying Square Roots That Contain Whole Numbers
Solving Quadratic Equations by Completing the Square
Graphing Exponential Functions
Decimals and Fractions
Adding and Subtracting Fractions
Adding and Subtracting Rational Expressions with Unlike Denominators
Quadratic Equations with Imaginary Solutions
Graphing Solutions of Inequalities
FOIL Multiplying Polynomials
Multiplying and Dividing Monomials
Order and Inequalities
Exponents and Polynomials
Fractions
Variables and Expressions
Multiplying by 14443
Dividing Rational Expressions
Division Property of Radicals
Equations of a Line - Point-Slope Form
Rationalizing the Denominator
Imaginary Solutions to Equations
Multiplying Polynomials
Multiplying Monomials
Adding Fractions
Rationalizing the Denominator
Rational Expressions
Ratios and Proportions
Rationalizing the Denominator
Like Radical Terms
Adding and Subtracting Rational Expressions With Different Denominators
Percents and Fractions
Reducing Fractions to Lowest Terms
Subtracting Mixed Numbers with Renaming
Simplifying Square Roots That Contain Variables
Factors and Prime Numbers
Rules for Integral Exponents
Multiplying Monomials
Graphing an Inverse Function
Factoring Quadratic Expressions
Solving Quadratic Inequalities
Factoring Polynomials
Multiplying Radicals
Simplifying Fractions 1
Graphing Compound Inequalities
Rationalizing the Denominator
Simplifying Products and Quotients Involving Square Roots
Standard Form of a Line
Multiplication by 572
Adding and Subtracting Fractions
Multiplying Polynomials
Factoring Trinomials
Solving Exponential Equations
Solving Equations with Fractions
Roots
Simplifying Complex Fractions
Multiplying and Dividing Fractions
Mathematical Terms
Solving Quadratic Equations by Factoring
Factoring General Polynomials
Adding Rational Expressions with the Same Denominator
The Trigonometric Functions
Solving Nonlinear Equations by Factoring
Solving Systems of Equations
Midpoint of a Line Segment
Complex Numbers
Graphing Systems of Equations
Reducing Rational Expressions
Powers
Rewriting Algebraic Fractions
Exponents
Rationalizing the Denominator
Adding, Subtracting and Multiplying Polynomials
Radical Notation
Solving Radical Equations
Positive Integral Divisors
Solving Rational Equations
Rational Exponents
Mathematical Terms
Rationalizing the Denominator
Subtracting Rational Expressions with the Same Denominator
Axis of Symmetry and Vertex of a Parabola
Simple Partial Fractions
Simplifying Radicals
Powers of Complex Numbers
Fields Medal Prize Winners (1998)

Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Adding and Subtracting Fractions

Examples with solutions:

Example 1:

Perform the addition , and express your final answer in simplest form.

solution:

The prime factorizations of the two denominators are

10 = 2 1 × 5 1

15 = 3 1 × 5 1

So, the prime factors 2, 3, and 5 occur, each to at most the first power. Thus

LCD = 2 × 3 × 5 = 30

(Notice that this is smaller than the product, 10 × 15 = 150, of the original denominators. The factor 5 occurs in both of the original denominators, but need appear only once in the LCD.)

Now, to convert 3 / 10 to an equivalent fraction with a denominator of 30, we need to multiply top and bottom by 30 / 10 = 3. To convert 7 / 15 to an equivalent fraction with denominator of 30, we need to multiply top and bottom by 30 / 15 = 2. So

Since 23 is a prime number, no simplification of this result is possible, and so our final answer is

 

Example 2:

Perform the addition and express your final answer in simplest form. {\b

solution:

First we write the two denominators as products of prime factors:

48 = 2 4 × 3 1

18 = 2 1 × 3 2

Thus,

LCD = 2 x · 3 y

since the prime factorizations of 48 and 18 contain only 2 and 3 as factors.

Then  
  x = 4, because the highest power of 2 is 4, occurring in the factorization of 48,
and  
  y = 2, because the highest power of 3 is 2, occurring in the factorization of 18.

So,

LCD = 2 4 · 3 2 = 144.

Now, to convert 25 / 48 to an equivalent fraction with a denominator of 144, we must multiply top and bottom by 144 / 48 = 3. To convert 7 / 18 to an equivalent fraction with a denominator of 144, we must multiply top and bottom by 144 / 18 = 8. So, our problem becomes

To check for the possibility of simplification, we need to express the numerator and denominator of this result as a product of prime factors. We already know that

144 = 2 4 · 3 2

It takes just a minute to verify that 131 is not divisible by either 2, 3, 5, 7, or 11, and so 131 must be a prime number already. Therefore no further simplification is possible and our final answer is

(In case you’re wondering why we had to check only that none of 2, 3, 5, 7, and 11 divided evening into 131 to conclude that 131 is a prime number – the reason is this. We don’t have to check any divisors which are not prime numbers themselves, or which are larger than the square root of the number being factored. Since the square root of 131 is less than 12, we only have to check potential prime divisors which are less than 12, and this is the list 2, 3, 5, 7, and 11.)