Next, we will learn subtraction（subtraction）. Subtracting negative numbers may seem confusing at first, but if you remember the rule “change subtraction into addition by changing the sign,” you can calculate using addition alone.
Rule for Subtraction
Subtracting a number is the same asadding the number with the opposite sign.
a − b ＝ a + (−b) （subtraction → change the sign and add）
- (+5)−(+3) ＝ (+5)+(−3) ＝ +2
- (+5)−(−3) ＝ (+5)+(+3) ＝ +8
- (−5)−(+3) ＝ (−5)+(−3) ＝ −8
- (−5)−(−3) ＝ (−5)+(+3) ＝ −2
Calculate the following.
(1) (+4)−(−7) (2) (−6)−(−2) (3) (−9)−(+5)
Answer：
(1) (+4)+(+7) ＝ +11
(2) (−6)+(+2) ＝ −(6−2) ＝ −4
(3) (−9)+(−5) ＝ −(9+5) ＝ −14
Mixed Addition and Subtraction（Expressions Made Only of Terms）
For an expression containing both addition and subtraction, rewrite it as anexpression using addition onlybefore calculating. An addition expression can also be written as a form consisting only of terms.
Example：(+3)−(−5)+(−7)−(+2)
＝ (+3)+(+5)+(−7)+(−2) ← Rewrite as addition
＝ 3 + 5 − 7 − 2 ← Expression listing terms（the first + and the + signs may be omitted）
＝ (3+5) − (7+2) ＝ 8 − 9 ＝ −1
In this way, it is efficient to firstgroup the positive terms and the negative terms separately.
Calculate the following：8 − 12 − (−5) + (−3)
Answer：Rewriting it using addition only gives 8 + (−12) + (+5) + (−3) ＝ 8 − 12 + 5 − 3。
Positive terms：8+5=13。Negative terms：12+3=15。Therefore, 13 − 15 ＝ −2。
- Subtraction → change the sign of the number being subtracted and convert it to addition（a−b = a+(−b)）
- Expression listing terms：the initial positive sign and + signs may be omitted
- For mixed addition and subtraction, separate the expression into the sum of positive terms and the sum of negative terms
- Subtracting from 0：0−a = −a。Subtracting 0 from a：a−0 = a
Practice Problems
- Calculate (+3)−(+8).
- Calculate −7−(−4)+(−6).
- Calculate 5 − 9 + 4 − 11 + 2.
Answers and Explanations
- Answer：−5
Explanation：Convert it to (+3)+(−8). This is addition with different signs; the difference of the absolute values is 8−3=5, and the number with the greater absolute value is −8, so the sign is negative → −5。 - Answer：−9
Explanation：Convert subtraction into addition：−7+(+4)+(−6) ＝ −7+4−6。Positive terms：4。Negative terms：7+6=13。4−13=−9。 - Answer：−9
Explanation：Sum of positive terms：5+4+2=11。Sum of negative terms：9+11=20。11−20=−9。