Power of a Power Property of Exponents
Adding and Subtracting Rational Numbers
Solving Equations with Radicals and Exponents
Quadratic Equations
Using Intercepts for Graphing Linear Equations
Graphing Linear Equations in Two
Multiplying Fractions
Solving Linear Equations Containing Fractions
Evaluating Polynomials
Multiplication Property of Square and Cube  Roots
Writing a Fraction in Simplest Form
Square Roots
The Pythagorean Theorem
Factoring The Difference of 2 Squares
Solving Polynomial Equations
Roots and Powers
Writing Linear Equations in Standard Form
Solving Nonlinear Equations by Substitution
Straight Lines
The Square of a Binomial
Solving Equations
Adding and Subtracting Like Fractions
Finding the Equation of an Inverse Function
Slope of a Line
Rules for Nonnegative Integral Exponents

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Adding and Subtracting Like Fractions

Let’s first discuss how to add and subtract like fractions. Suppose that we want to add and . A diagram can help us understand what is involved. First we shade one-fifth of the diagram, then another three-fifths.

We see in the diagram that the total shaded area is four-fifths, so . Note that we added the original numerators to get the numerator of the answer but that the denominator stayed the same.

The diagram shows how to subtract like fractions by computing . If we shade four-fifths of the diagram and then remove the shading in one-fifth, three-fifths remain shaded. Therefore . Note that we could have gotten this answer simply by subtracting numerators without changing the denominator.

The following rule summarizes how to add or subtract fractions, provided that they have the same denominator.

To Add (or Subtract) Like Fractions

  • first add (or subtract) the numerators,
  • then use the given denominator, and
  • finally write the answer in simplest form.




Applying the rule, we get


Be careful not to add the denominators when adding like fractions.


Add: .


So the sum of .



Find the difference between .



In the following diagram, how far is it from the college to the library via city hall?


Examining the diagram, we see that

  • the distance from the college to city hall is mile and that
  • the distance from city hall to the library is mile

To find the distance from the college to the library via city hall, we add.

The distance is 1 mile.


According to one study, of the people who exercise regularly live at least to age 70, in contrast to only of the people who do not exercise regularly. What is the difference between these two fractions?


Subtracting, we get . Therefore the difference between these fractions is . We can check our answer by adding to to get .