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Interpret gains and losses with integers

A gain is represented by a positive integer and a loss by a negative integer, with zero representing no change; the absolute value indicates the amount of the gain or loss, while the sign indicates its direction relative to a chosen reference point. A number line connects these meanings to position and order, supporting later reasoning about integer addition and subtraction; formal rules for more advanced integer operations or generalized signed quantities are not included here.

Detailed Explanation: Interpret gains and losses with integers

Choose a reference point and call it 00. Then use the sign to show direction:

  • A positive integer, such as +5+5, means a gain of 55.
  • A negative integer, such as −5-5, means a loss of 55.
  • 00 means no change.
  • The absolute value, written ∣n∣\vert n \vert, tells the amount of the gain or loss. The sign tells its direction.

On a number line, positive numbers are to the right of 00, and negative numbers are to the left.

Example: In a game, a player’s score changes from the starting score. The record shows a change of −6-6 points. What does this mean?

  1. The reference point is the starting score, represented by 00.
  2. The negative sign means the score went down, so it is a loss.
  3. The amount of the loss is the absolute value:
∣−6∣=6 \vert -6 \vert =6
  1. Therefore, the player lost 66 points.
  2. On a number line, start at 00 and move 66 units left. You land at −6-6.

So, −6-6 represents a loss of 66 points. The number +6+6 would represent a gain of 66 points, while 00 would represent no change.

Learn by doing: Interpret gains and losses with integers

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    Number Line - Negative Integers, Select Dot - Labelled

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