Integers

Integers are like whole numbers, but they also include negative numbers … but still no fractions allowed!

So, integers can be negative {−1, −2,−3, −4, … }, positive {1, 2, 3, 4, … }, or zero {0}

We can put that all together like this:

Integers = { …, −4, −3, −2, −1, 0, 1, 2, 3, 4, … }

Examples: −16, −3, 0, 1 and 198 are all integers.

(But numbers like ½, 1.1 and 3.5 are not integers)

Ordering of Integers 

is stated for the series or a sequence where numbers are arranged in an order. The integers are ordered on a number line based on positive integers and negative integers. The integers that are greater than 0 are positive integers and integers less than 0 are negative integers.

As we know, the arrangement of numbers can be made in two ways:

• Ascending order
• Descending order

In ascending order, the integers are arranged from smallest to largest value, whereas in descending order, the integers are arranged from largest to smallest value.

How do you compare and order integers?

To order integers, you have to compare them. You can use a number line to do so if needed. The numbers decrease as you move to the left and increase as you move to the right on a number line. Negative integers are less than positive integers.

Facts:

• Order of Integers on the left side of the number line is smaller than 0 and the order of integers on the right side of the number line is greater than 0.
• The more the integer is negative, the more its value is smaller.
• The more the integer is positive, the more its value is greater.
• Zero is neither a negative integer nor a positive integer.
• All positive integers are greater than all the negative integers.

Comparing Integers

One integer can be either greater or smaller than another integer. Thus, to compare two integers, we use symbols greater than (>) and less than (<). Also, if two integers are equal to each other then we use the ‘equal to’ (=) symbol. See the examples below:

• 0 > – 8
• 8 > – 5
• 0 < 3
• -1 > -10
• 10 < 12
• -20 < 1
• -100 < -10
• 100 > -200

From the above examples, we can observe that the more an integer is negative, the less its value is.

Examples

• Which integers lie between 0 and -3?

Solution: By the order of integers, we know that,

-3 < -2 < -1 < 0

Therefore, there are two integers between 0 and -3, they are -1 and -2.

• Which is the largest integer and smallest integer among the following?

8, 10, -12, 0, 23, 1, 3, -7, -22

Solution: Given, the integers are:

8, 10, -12, 0, 23, 1, 3, -7, -22

Smallest integer = -22

Largest integer = 23

• Ruby is at -2. In which direction and how many steps should he move to reach at 6?

Solution: Ruby has to move 8 steps to the right of -2 to reach 6.

• Which number will we reach if we move 5 steps to the right of –3?

Solution: If we move 5 steps to the right of -3, we reach 2.