Integers

What are natural numbers and provide examples?

Natural numbers are a set of positive integers starting from 1 and increasing without bound. Examples include: 1, 2, 3, 4, ...

What are integers and how are they represented?

Integers are a set of numbers that include all whole numbers and their negative counterparts. They do not include fractions or decimals. The set of integers is represented as Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}.

How can integers be represented on a number line?

Integers can be represented on a number line by placing each integer at equal intervals along the line, with negative numbers extending in the left direction and positive numbers extending in the right direction.

What is the process of ordering integers?

Ordering integers involves arranging them in either ascending (from smallest to largest) or descending (from largest to smallest) order.

Arrange the following integers in ascending order: 3, 1, 9, 0, 8, 18, 2, 7.

Ascending order: 0, 1, 2, 3, 7, 8, 9, 18.

Arrange the following integers in descending order: 3, 1, 9, 0, 8, 18, 2, 7.

Descending order: 18, 9, 8, 7, 3, 2, 1, 0.

How do you compare integers using inequality signs?

Integers can be compared using inequality signs like < (less than) and > (greater than) to denote the relationship between values.

Use an example to demonstrate the use of inequality signs with integers.

For example: 3 < 7 means that 3 is less than 7.

Evaluate the following using a number line: what is -2 + 8?

-2 + 8 = 6, which can be determined by starting at -2 on the number line, moving 8 units to the right.

Evaluate the following using a number line: what is 3 - 3?

3 - 3 = 0, which can be determined by starting at 3 on the number line and moving 3 units to the left.