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Beginning Algebra
Tutorial 6: Subtracting Real Numbers

Learning Objectives

 After completing this tutorial, you should be able to: Subtract real numbers that have the same sign. Subtract real numbers that have different signs. Simplify an expression that has subtraction in it using the order of operations.

Introduction

 This tutorial reviews subtracting real numbers and intertwines that with some order of operation and evaluation problems. I have the utmost confidence that you are familiar with subtraction, but sometimes the rules for negative numbers (yuck!) get a little mixed up from time to time.  So, it is good to go over them to make sure you have them down. Even in this day and age of calculators, it is very important to know these basic rules of operations on real numbers.  Even if you are using a calculator, you are the one that is putting the information into it, so you need to know things like when you are subtracting versus adding and the order that you need to put it in.  Also, if you are using a calculator you should have a rough idea as to what the answer should be. You never know, you may hit a wrong key and get a wrong answer (it happens to the best of us).  Also, your batteries in your calculator may run out and you may have to do a problem by hand (scary!!!).   You want to be prepared for those Murphy's Law moments.

Tutorial

 Subtracting Real Numbers a - b = a + (-b)    or  a - (-b) = a + b

 In other words, to subtract b, you add the opposite of b.  Now, you do not have to write it out like this if you are already comfortable with it. This just gives you the thought behind it.

 Example 1:   Subtract   -3 - 5.

 -3 - 5 = -3 + (-5) = -8.  Subtracting 5 is the same as adding a -5.  Once it is written as addition, we just follow the rules for addition, as shown in Tutorial 5: Adding Real Numbers, to complete for an answer of -8.

 Example 2:   Subtract  -3 - (-5).

 -3 - (-5) = -3 + 5 = 2.  Subtracting -5 is the same as adding 5.  Once it is written as addition, we just follow the rules for addition, as shown in Tutorial 5: Adding Real Numbers, to complete for an answer of 2.

 Example 3:   Subtract .

 *Rewrite as addition   *Mult. top and bottom of 1st fraction by 2 and 2nd by 3  to get the LCD of 6 *Take the difference of the numerators and write over common denominator 6

 The difference between 14/6 and 3/6 is 11/6 and the sign of 14/6 (the larger absolute value) is -.  That is how we get the answer -11/6

 Example 4:   Simplify .

 Since we have several operations going on in this problem, we will have to use the order of operations to make sure that we get the correct answer.

 *Exponent *Multiply *25 - 8 = 17

 Example 5:   Simplify

 Since we have several operations going on in this problem, we will have to use the order of operations to make sure that we get the correct answer.

 *Eval. inside absolute value   *Exponent *Multiplication *7 + 6 = 13 *13 - 15 = -2

 Example 6:   Evaluate the expression    if  x = -2 and y = 5.

 Plugging -2 for x and 5 for y and simplifying we get:

 *Plug in -2 for x and 5 for y *Rewrite num. as addition of opposite *Add    *Simplify fraction

 Example 7:   Is -1 a solution of -x + 4 = 6 + x?

 Replacing x with -1 we get:

 *Plug in -1 for x *Take the opposite of -1 *Add

 Is -1 a solution? Since we got a TRUE statement (5 does in fact equal 5), then -1 is a solution to this equation.

Practice Problems

 These are practice problems to help bring you to the next level.  It will allow you to check and see if you have an understanding of these types of problems. Math works just like anything else, if you want to get good at it, then you need to practice it.  Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.  In fact there is no such thing as too much practice. To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that  problem.  At the link you will find the answer as well as any steps that went into finding that answer.

Practice Problems 1a - 1b: Subtract.

 1a.    -10 - (-2) (answer/discussion to 1a) 1b.  - 4.1 - 5.3 (answer/discussion to 1b)

Practice Problems 2a - 2b: Simplify.

Practice Problem 3a: Evaluate the expression when x = 2 and y = -2.

Practice Problem 4a: Is -2 a solution to the given equation?

Need Extra Help on these Topics?

The following is a webpage that can assist you in the topics that were covered on this page:

 http://www.mathleague.com/help/integers/integers.htm#subtractingintegers This webpage goes over subtracting real numbers.

Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.

Last revised on July 24, 2011 by Kim Seward.