## Math 6 Chapter 2 Lesson 3: Order in the set of integers

## 1. Summary of theory Tóm

### 1.1. Compare two integers

When represented on the number line (horizontal), point a is to the left of point b, then integer a is smaller than integer b.

So:

– Every positive number is greater than 0

– Every negative number is less than 0 and every integer less than 0 is negative

Every negative number is less than every positive number

### 1.2. Absolute value of an integer

On the number line, the distance from the point a to the origin O is called the absolute value of a. The absolute value of a is denoted by |a| . (referred to as the absolute value of a). So:

– The absolute value of zero is 0

– The absolute value of a positive integer is itself.

The absolute value of a negative integer is its reciprocal.

– Two opposite numbers have the same absolute value.

– Of two negative integers, the number with the smaller absolute value is the larger number.

## 2. Illustrated exercise

**Question 1:** Compare

a. 2 and 7 b. – 2 and – 7 c. – 4 and 2

__Solution guide__

a. 2 < 7 b. – 2 > – 7 c. – 4 < 2

**Note:** The integer b is said to be consecutive after the integer a if a < b and there is no integer between a and b. Then we also say that the integer a is the predecessor of b.

**Verse 2: **Calculate** ** |13|, |-20|, |-75|, |0|

__Solution guide__

|13| = 13

|-20| = 20

|-75| = 75

|0| = 0

**Question 3: **

a. Arrange the following integers in ascending order: 5, -15, 8, 3, -1, 0

b. Arrange the following integers in descending order: -97, 10, 0, 4, -9, 2000

__Solution guide__

a. Ascending order: -15, -1, 0, 3, 5, 8

b. Descending order: 2000, 10, 4, 0, -9, -97

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Find the absolute value of numbers: 1998, -2001, -9

**Verse 2:** Write the set X of integers x satisfying:

a. -2 < x < 5 b. \( - 6 \le x \le - 1\)

c. \(0 < x \le 7\) d. \( - 1 \le x < 6\)

**Question 3:**

a. Find the next number of numbers: 5, -6, 0, -2

b. Find the previous number of the numbers: -11, 0, 2, -99

c. Is an integer a positive or negative if its successor is a negative number?

### 3.2. Multiple choice exercises Bài

**Question 1: **Choose the false statement?

A. the absolute value of a positive number is what it is

B. Of two negative numbers, the one with the smaller absolute value is the larger number

C. Two opposite numbers have the same absolute value

D. Zero has no absolute value

**Verse 2: **Find the absolute value of the following numbers: -1945; 2000; -2019

A. -1945; 2000; 2019

B. 1945; -2000; 2019

C. 1945; 2000; 2019

D. -1945; -2000; -2019

**Question 3: **Find \(x \in Z\), knowing that -4

A. 0; first; 2; 3; 4

B. -3; -2; -first

C. -3; -2; -first; first; 2; 3

D. -3; -2; -first; 0; first; 2; 3

**Question 4: **Calculate the value of the following expression: |-12|+|-4|-7

A. -23

B. 23

C. 9

D. -9

**Question 5: **Find an integer x knowing that the number following a is a positive integer and the number preceding a is a negative integer

A. -1

B. 0

C. 1

D. -2

## 4. Conclusion

Through the lesson The order in this set of integers, you need to complete some of the objectives given by the lesson such as:

- Know how to compare two integers
- Absolute value of integer
- Apply theory to do some exercises related to the order in the set of integers

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