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Adding and subtracting negative numbers

 Frequently, in maths language the minus sign (—) does not mean "less", it means "the opposite". Look at this example:

Pushing a button in a lift you can go up or down:
If you are on the ground floor and you push the 2 button, you go up 2 floors...
    0 + 2 = 2
..., so you will be on the 2nd floor.

 If you push the —2 button, you go down two floors...
    0 — 2 = —2
... so you will be on the 2nd basement, 2 floors under ground level.
PROBLEM: If you are on the 4th floor and you go down 7 floors, which floor will you be on?

OPERATION: 4 — 7 = —3
SOLUTION: You will be on the 3rd basement, 3 floors under ground level.

How do you calculate this?
    If you have to go down 7 floors and you are on the 4th floor, first you have to go down 4 floors to the ground level:

      4 — 4 = 0

    How many more floors do you have to go down now?

      7 — 4 = 3

    So, you go down another 3 floors from the ground level:

      0 — 3 = —3


The same happens when you add a positive number to a negative one:

PROBLEM: If you are in the 2nd basement and you go up 5 floors, where will you be?

OPERATIONS: —2 + 5 = 3
SOLUTION: You will be on the 3rd floor.


Now, can you calculate the solution to these problems? You can also make a drawing to help you.
  1. It is winter and the temperature at midday is 7ēC, but at night it drops (= goes down) by 12 degrees. What is the temperature in the thermometer?

  2. James Bond's car is flying at 35 meters above the ground when a helicopter attacks him. When it reaches the sea, James Bond dives (= goes down) 75 meters and his flying car dives into the sea and turns into a submarine. How deep into the sea does it go?

  3. On a bus there are 53 passengers and only 5 free seats. 7 passengers get off at the first stop, and 9 more get on. Then 15 passengers get off and 21 get on on the second stop. How many free seats are there now? What does the result mean?

Button icon source: https://openclipart.org/detail/190422/circle-buttons-steel. Thank you!

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JJCC