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.

What are the rules for addition/subtraction of integers?

If signs are the same: Keep same sign and add digits.

If signs are different: Keep the sign of the larger number and subtract digits

What are the rules for multiplication/division of integers?

Remove brackets first by multiplying them out, Then multiply/divide the numbers given

What is the definition of the square of an integer?

The product of the integer with itself.

What is the definition of the square root?

The number that multiplies by itself to get the original number.

What is the definition of the cube of an integer?

The product obtained by multiplying an integer by itself twice.

What is the definition of the cube root?

The number that multiplies by itself twice to get the original number.