3. Division of Algebraic Expressions
Our first examples of division of algebraic expressions involve simplifying and canceling.
Dividing by a Fraction
Recall the following when dividing algebraic expressions.
The reciprocal of a number x, is `1/x`.
For example, the reciprocal of 5 is `1/5` and the reciprocal of `1 2/3` is `3/5`.
To divide by a fraction, you multiply by the reciprocal of the fraction.
For example, `3/4 -: 7/x=3/4xxx/7=(3x)/28`
Long Division in Algebra
Before we do an example using algebra, let’s remember how to do long division with numbers first.
Let’s do 23,576 divided by 13.
We can write this as a fraction:
Now, to divide this, (assuming we do not have a calculator) we could proceed as follows.
23 divided by 13 = 1 with remainder 10.
We bring the 5 (the next number after 3) down.
Now we have
105 divided by 13 is 8 with remainder 1
We continue until we get to the last number, 6.
Our result means that the answer is 1,813 with remainder 7, or:
We use a similar technique for long division in algebra.
Example 6 - Algebraic Long Division
You can see how algebraic long division is used in a later section, Remainder and Factor Theorems.
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Short URL for this Page
Save typing! You can use this URL to reach this page:
Algebra Lessons on DVD
Easy to understand algebra lessons on DVD. See samples before you commit.
More info: Algebra videos