Distance Between Numbers
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 26 of 60.
How far apart are -2 and 6 on the number line? Count it: 2 steps from -2 up to zero, then 6 more to reach 6, so 8 steps. Subtraction finds it at once: |-2 - 6| is |-8|, which is 8.
Why the absolute value bars? A difference can come out negative, depending on which number you take from which: -2 - 6 is -8, while 6 - (-2) is 8. A distance is never negative, so the bars keep only the size. That also means the order does not matter: |6 - (-2)| is 8 as well.
So the distance between two numbers is the absolute value of their difference. As always with bars, work out what is inside them first, then drop the sign.
Challenge
How far apart are -7 and 8 on the number line? Work out |-7 - 8|, one step per line.
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