🔢 MathGrade 6Lesson 2
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Add and Subtract Integers

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Learning Objectives

  • 1Add two integers using the same-sign and different-sign rules
  • 2Rewrite any integer subtraction as adding the opposite
  • 3Model integer sums and differences on a number line
  • 4Determine the sign of a sum from the magnitudes of its addends
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Mini Lesson

An integer is a whole number, its negative, or zero. You meet integers every day in temperatures below zero, elevations below sea level, and money owed. To add or subtract them well, you only need three rules and a number line you can picture in your head.

Adding Two Integers

  • Same signs: add the magnitudes (the distances from zero) and keep the shared sign — for example, -3 + -4 = -7 and 6 + 5 = 11.
  • Different signs: subtract the smaller magnitude from the larger and keep the sign of the larger magnitude — for example, -8 + 5 = -3 and 7 + -2 = 5.
  • Adding zero never changes a number: -9 + 0 = -9.
  • A number plus its opposite gives zero: -6 + 6 = 0. The opposite is also called the additive inverse.

Subtraction = Add the Opposite

  1. Keep the first number unchanged.
  2. Change the subtraction sign to addition.
  3. Switch the sign of the second number to its opposite.
  4. Apply the addition rules. For example, 4 - 7 becomes 4 + -7 = -3, and -2 - 5 becomes -2 + -5 = -7.

Modeling on a Number Line

  • Start at the first number on the number line.
  • A positive number tells you to move that many units to the right.
  • A negative number tells you to move that many units to the left.
  • For -3 + 5: start at -3, jump 5 to the right, land on 2.
  • For 4 - 7: rewrite as 4 + -7, start at 4, jump 7 to the left, land on -3.
Number Line: -3 + 5 = 2Number Line: -3 + 5 = 2-8-7-6-5-4-3-2-1012345678startend = 2+ 5Move right for positive, left for negative.-3 + 5 = 2
Three rules for adding and subtracting integersInteger Rules1. Same signsAdd magnitudes, keep the shared sign.-3 + -4 = -7 | 5 + 6 = 112. Different signsSubtract magnitudes, keep larger sign.-8 + 5 = -3 | 7 + -2 = 53. Subtract = add the oppositeFlip the second number, then add.4 - 7 = 4 + -7 = -3Magnitude = distance from zero, ignoring the sign.
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Tip: when signs disagree, decide who wins by magnitude — the larger magnitude keeps its sign and you subtract the smaller magnitude from it.

Vocabulary
integer
A whole number, its negative, or zero — like -7, 0, or 12.
sum
The result of adding two or more numbers.
difference
The result of subtracting one number from another.
opposite
The number with the same magnitude but the opposite sign — the opposite of 5 is -5.
additive inverse
A number that adds with another to give zero — the additive inverse of -8 is 8.
magnitude
A number’s distance from zero on a number line, ignoring the sign.
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← Lesson 1: Integers on the Number LineLesson 3: Multiply and Divide Integers →