Home / United States / Math Classes / 6th Grade Math / Integers on the Number Line and their Comparison

Integers are numbers that do not have a fractional component. Integers range from negative numbers to positive numbers and include zero. Here we will learn to represent integers on a number line and use this concept to compare two integers with each other....Read MoreRead Less

Positive numbers are whole numbers greater than 0. These numbers can be written with or without a positive sign or a plus sign, “+”.

+ 1, 96, + 26, 25000 are all examples of positive numbers.

Negative numbers are opposites of whole numbers excluding 0 on the number line. These numbers are written with negative sign or a minus sign, “–”.

-1, -96, -36, and -45634 are written with a minus sign and are negative numbers.

**Example:**

A footballer scored 5 goals in a game. We use a positive number to indicate the situation so the five goals are represented as +5 or 5 goals. Very cold temperatures are represented using negative numbers such as -3 degree Fahrenheit, -10 degrees Fahrenheit, etc.

Integers are the set of numbers such as … -2, -1, 0, 1, 2, … The integers consist of negative numbers, “0” and positive numbers. Integers do not have any fractional or decimal parts.

**Graph of integers and their opposite.**

A number is known as **an opposite** of another number if both the numbers are at the same distance from 0 on the number line. For example, 7 and -7 are both equidistant from 0, and hence are opposite to each other.

On a horizontal number line, numbers to the left of the 0 are less than the numbers on the right. On a vertical line the numbers below the 0 are less than the numbers above.

**For example,** we compare 1 and -5 on a horizontal number line by graphing both these numbers on the number line.

1 is to the right of -5. This only means that 1 is greater than -5.

Again, we can compare -2 and -4 on the vertical number line after adding these numbers at appropriate points on the number line.

-4 is below -2, which only indicates, -4 is smaller or lesser than -2.

**Example 1: **Plot the number 3 and opposite of integer 3 on a number line.

**Solution**:

Draw a horizontal number line. Mark the number 3 on the number line. Now count 3 in the opposite direction of 0, which is to the left. You will reach the point that represents -3. Hence -3 is at the same distance as 3 is from 0, but in the opposite direction. Hence, -3 is the opposite of 3 as shown in the diagram.

**Example 2: **Represents these situations using a positive or negative integer.

**Solution**:

**Example 3: **Compare the given integers -5, 3, 0, -3, 4 and order them from the least to the greatest on a number line.

Graph each integer on a number line.

Write the integers as they appear on the number line from left to right.

So, the order from the least to the greatest integer is -5, -3, 0, 3, 4.

**Example 4: **David was playing with his brother. Both of them have a few marbles and they decide to play a game. In the first round, David loses 3 marbles. In the second round, he won 5 marbles. Write an integer that represents the marbles that were either lost or won by David.

**Solution:**

In the first round, David lost 3 marbles. As this is a reduction in the number of marbles David had, it is represented as -3, a negative integer.

In the second round, he won 5 marbles, this is represented by +5 or 5, a positive integer.

Frequently Asked Questions on Integers

Yes, all negative numbers are less than 0, as they lie to the left of 0 on a number line.

**For example**, let’s compare 0 and -4.

The integer 0 is greater than -4. Because 0 is on the right of -4 on the number line.

Yes, all the positive integers lie to the right of all the negative integers on a number line. Therefore, negative integers are always less than positive integers.

The fact is that “0” is neither a positive nor negative integer. However, the number zero makes it easier to distinguish between positive integers on the right of it, and negative numbers on the left of it.