In this lesson we are going to learn which is the easiest way of comparing two natural numbers, how to compare integers and to use mathematical signs of comparison.
In the most commonly used base-10 positional system, the value of a position in a number is always smaller than the value of the positions to its left. Also, the value of a position in a number is always larger than the value of the positions to its right. These statements are true no matter which numerals are in those positions.
How to compare natural numbers?
The easiest way to compare numbers is to draw a number line and mark the numbers you want to compare on it. On the number line, the value of the number is increasing from left to the right.
The conclusion is that if the number $A$ is positioned to the right of the number $B$, then the number $A$ is larger than the number $B$. In the opposite case, if the number $A$ is positioned to the left of the number $B$, then the number $A$ is smaller than the number $B$.
The “rule of number value increasing” from the left to the right on the number line stated above also applies to integers.
You need to determine their “position” on the number line and then see if the number $A$ is positioned to the left or to the right of the number $B$. The value of integers decrease as their absolute value increases and reverse. It is also useful to remember that the value of negative numbers is always smaller than the value the positive numbers (unless we’re talking about comparing their absolute values, which are always positive).
Imagine the previous picture, but with a minus sign before the numbers (integers). The result of the comparison of these numbers will be opposite to the result of the comparison for their positive counterparts.
Signs used for comparing numbers
In mathematics there are six signs that we use when comparing numbers. The most important signs are:
● Larger than (>)
● Smaller than (<)
● Equal to (=)
The easiest way to remember these signs is to remember that the tip of the arrow is always on the side of the smaller number and wide part of arrow is always on the side of the larger number. We can tell that: “the arrow sign always points to the smaller number”.
The other signs are combinations of the signs mentioned above:
● Larger than or equal to (≥)
● Smaller than or equal to (≤)
● Different than (≠)