What are Positive Numbers?
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.
What are Negative 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.
What are Integers?
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.
Comparison of Integers on the Number line
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.
Solved Examples on Integers
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.
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.