Up and Down
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 53 of 60.
Heights are measured from sea level, which plays the part of zero. A cliff top 30 metres above the sea is at 30; a reef 7 metres under the water is at -7. Moving up adds and moving down subtracts, whichever side of the surface you are on.
A seal rests on a rock 4 metres above the water. It dives 10 metres down, then swims 3 metres up. Use h for height: h = 4 - 10 + 3. Left to right, 4 - 10 is -6, so the next line is h = -6 + 3, and then h = -3. The seal is 3 metres below the surface.
The signs do the bookkeeping for you. You never need a separate rule for crossing the surface: the seal passes zero on its way down, and the arithmetic handles it. The sign of the result tells you which side you ended on.
Challenge
A diver is 12 metres below the surface, at -12 metres. She rises 5 metres, then dives 9 metres. Find her depth d as a signed number. Write d equal to the story's calculation, then work it down to one number.
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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