Add the Opposite
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 23 of 60.
Every subtraction can be turned into an addition: subtracting a number is adding its opposite. So 4 - 9 is 4 + (-9). You already know how to add numbers with different signs: 9 - 4 is 5, and -9 is further from zero, so the answer is -5.
On the number line, start at 4 and take 9 steps left. Four steps reach zero, and the other five go below it, ending at -5. Whenever you take away more than you have, you cross zero, so a smaller number minus a bigger one is always negative.
Why does this work? Taking away 9 dollars and adding a debt of 9 dollars change your total in exactly the same way. Reading every subtraction as adding the opposite means one set of rules covers both operations.
Challenge
Work out 3 - 11.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Numbers & Operations
1Working on the Board
Your First AnswerType the Next LineOne Line at a TimeDots and BarsFriendly ProductsRecap: Board Work4Adding Integers
Adding Two NegativesDifferent SignsZero PairsAdding Several IntegersRecap: Adding Integers2Order of Operations
Multiply Before AddingLeft to RightParentheses FirstBrackets Inside BracketsThe Fraction Bar GroupsRecap: Order of Operations5Subtracting Integers
Add the OppositeSubtracting a NegativePlus and Minus in a RowDistance Between NumbersRecap: Subtracting Integers