Teach: Positive and Negative Numbers ② Addition

Positive and Negative Numbers ② Addition（Addition）

We will learn the addition（addition）of positive and negative numbers. Since handling signs is important, remember the rules accurately. It is helpful to imagine that “adding a positive number moves right on the number line, while adding a negative number moves left.”

Addition of Numbers with the Same Sign

For adding two numbers with the same sign（both positive or both negative）,
　give the sum of the absolute values the common sign.

  • (+3)+(+5) ＝ +(3+5) ＝ +8
  • (−3)+(−5) ＝ −(3+5) ＝ −8

Addition of Numbers with Different Signs

For adding two numbers with different signs（one positive and the other negative）,
　find the difference between the absolute values and give it the sign of the number with the greater absolute value.

  • (+5)+(−3) ＝ +(5−3) ＝ +2（+5 has the greater absolute value）
  • (−5)+(+3) ＝ −(5−3) ＝ −2（−5 has the greater absolute value）
  • (+4)+(−4) ＝ 0（different signs with equal absolute values give 0）
Example ①
Calculate the following.
(1) (−7)+(−4)　(2) (+9)+(−5)　(3) (−6)+(+8)
Answer：
(1) Same sign（negative）→ sum of absolute values 7+4=11, sign is negative → −11
(2) Different signs → difference of absolute values 9−5=4, +9 has the greater absolute value → +4
(3) Different signs → difference of absolute values 8−6=2, +8 has the greater absolute value → +2

Addition of Three or More Numbers

In addition, thecommutative law（the order may be changed）and theassociative law（calculation may begin anywhere）hold. When adding three or more numbers, it is easier to firstgroup the positive numbers and the negative numbers separately.

Example ②
Calculate (+6)+(−4)+(+3)+(−9).
Answer：Sum of positive numbers：6+3=9. Sum of negative numbers：(−4)+(−9)=−13。
Therefore, (+9)+(−13)=−(13−9)= −4。
Key Points
  • Addition with the same sign：sum of absolute values with the common sign
  • Addition with different signs：difference of absolute values with the sign of the greater absolute value
  • The sum of numbers with different signs and equal absolute values is 0
  • For three or more numbers, group the positive and negative numbers separately before calculating

Practice Problems

  1. Calculate (−8)+(−6).
  2. Calculate (+12)+(−7).
  3. Calculate (−5)+(+9)+(−4)+(+2).

Answers and Explanations

  1. Answer：−14
    Explanation：Addition with the same sign（negative）. Give the sum of the absolute values, 8+6=14, the negative sign.
  2. Answer：+5
    Explanation：Addition with different signs. The difference of the absolute values is 12−7=5. Since +12 has the greater absolute value, the sign is positive. +5.
  3. Answer：+2
    Explanation：Sum of positive numbers：9+2=11. Sum of negative numbers：(−5)+(−4)=−9。(+11)+(−9) = +(11−9) = +2。

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