## Math 6 Chapter 2 Lesson 7: Subtraction of two integers

## 1. Summary of theory Tóm

### 1.1. Difference of two integers

**Example 1:** We have

A = 2 – 6 = 2 + (-6) = – 4

**From there we have the rule:**

The difference of two integers a and b is the sum of a and the opposite of b:

a – b = a + (-b)

**Comment:** The difference of two integers a and b is an x that, when added to b, gives a. Thus, in Z the subtraction is always performed.

### 1.2. Rule of brackets

**Example 2:** We have

a. A = 5 + (2-9) = 5 + |2 +(-9)|=5+(-7)=-2

B = 5 + 2 – 9 = 7 + (-9) = 2.

Notice: A = B = 1 \( \Rightarrow \) A = 6 (8-3) = 6 – 8 + 3

**From there we have the rule:**

- When removing brackets with “-” in front, we must change the signs of all terms in brackets “+” to “-” and “-” to “+”
- When the brackets with a “+” sign are removed, the signs of the terms in the brackets remain the same.

### 1.3. Transition rule

**Example 3:** We have

x + 2 = 8\( \Rightarrow \)x = 8 – 2 = 6

x – 9 = 5 \( \Rightarrow \) x +(-9) = 5\( \Rightarrow \)x =5 – (-9) = 5 + 9 = 14

**From there we have the rule:**

When transferring a term from one side of an equation to another, we must change the sign of that term: the ‘+’ sign to the ‘-‘ sign and the ‘-‘ sign to the ‘+’ sign.

### 1.4. Algebra sum

We have the definition:

A sequence of operations that adds and subtracts whole numbers is called an algebraic sum.

In an algebraic sum we can:

- Change arbitrarily the positions of terms with their signs.
- Put brackets to group the terms arbitrarily. But it should be noted: if the brackets are preceded by a “-” sign, all terms inside the brackets must be changed.

## 2. Illustrated exercise

**Question 1: **Find x knows:

a. (x – 25) + 18 = 0

b. (-27 – x) – 23 = 0

c. |x- 5| = 4.

**Verse 2: **Calculated by rational (-1215) – (-215 + 115) – (-1115).

**Question 3: **Sum all integers x such that -4 < x < 6.

## 3. Practice

### 3.1. Essay exercises

**Question 1:** Calculation: S = 1 – 2 + 3 – 4 + 5 – ….- 48 + 49 -50.

**Verse 2:** Calculate expression value:

A = (a – b + c) – (-c – b + a)

Knowing a = -5, b = 2, c = -8

**Question 3: **Prove that: a – (b – c) = (a + c) – b

Apply to calculate: A = 157 – (130 -43)

### 3.2. Multiple choice exercises Bài

**Question 1:** Simplifying the expression x + 1982 + 172 + (-1982) – 162 we get the result:

A. x – 10 B. x + 10 C. 10 D. x

**Verse 2: **Sum (-43567 – 123) + 43567 equals:

A. -123 B. -124 C. -125 D. 87011

**Question 3:** The result of the calculation (-98) + 8 + 12 + 98 is:

A. 0 B. 4 C. 10 D. 20

**Question 4:** Select the correct answers:

A. (-7) + 1100 + (-13) + (-1100) = 20 B. (-7) + 1100 + (-13) + (-1100) = -20

C. (-7) + 1100 + (-13) + (-1100) = 30 D. (-7) + 1100 + (-13) + (-1100) = -10

**Question 5: **Simplifying the expression 235 + x – (65 + x) + x we get:

A. x + 170 B. 300 + x C. 300 – x D. 170 + 3x

## 4. Conclusion

Through this lesson Add two integers with different signs, you need to complete some of the objectives given by the lesson such as:

- Difference of two integers
- Mastering the rule of brackets, the rule of transition
- Algebraic sum definition

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