Operations with "Signed" Numbers

Operations with signed numbers, including fractions and mixed numbers, are often very much misunderstood.  Basically, when you operate with the signs and no (  ) you are adding or subtracting terms.  Two like signs means to add and the answer has the same sign as the numbers.  Two unlike signs means to subtract the “smaller” from the “larger” and take the sign of the “larger” number.

For example:  –3–4= –7 … two like signs add, and –12+5= –7 … two unlike signs subtract.

Sometimes it is helpful to separate the terms so that you will retrain your eyes to look for signs.

For example, look at the difference in the above example and how the same example would look with additional spacing …  … now you can clearly see that the numbers both have the same sign and therefore need to be added!

Also, –12   +5  =  –7 … separation allows the eyes to see that the signs are different and therefore need to be subtracted!

When you are multiplying or dividing, simply count how many negative signs that you have.
Even numbers of negative signs makes the answer positive, while odd numbers of negative signs makes the answer negative.

For example:   odd numbers of negative signs (3 in this case) means that the answer is negative,  while  even numbers of negative signs (2 in this case) means that the answer is positive.

SO, now what would 

First you would have to multiply     … order of operations says to multiply before you add or subtract and the (  ) means to multiply the negative (invisible 1) times the –10 in the  (  ) to get 10.   Then you would have .

For more information on a similar topic see the related page Like Terms.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 09-Jan-2014