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.