It is often said that a picture can paint a thousand words. In mathematics, a number line is used to visually represent numbers. The number line can be a good guide for kids to learn numbers and also for mathematicians to visualize complex numerical calculations. In this article, we look at the definition, operation, and uses of a number line.
Number line definition
A number line can be considered as a visual representation of numbers on a line. They are divided into a number of parts with a unit distance between them. A set of numbers can be compared and arranged in descending or ascending order. The numbers on a number line are placed with respect to the origin (zero). Thus, we can find the value of a number based on its position.
We know that integers consist of negative integers, zero, and positive integers. So the number line with positive and negative numbers can be called an integer number line.
This shows that any number right to zero is known as positive numbers, and the numbers left to zero are known as negative numbers.
Parts of a number line
Negative integers: A negative number is any number that is less than zero. So if we move left from zero we can encounter negative numbers on a number line.Â
Zero: The whole number between -1 and 1, with the symbol 0. It is not positive and is also not negative.
Positive Numbers: Positive integer is a whole number greater than zero, but not a fraction. The numbers which we generally use like 1,2,3 etc are positive numbers by default.
Linear inequalities: Two real numbers can be compared by using algebraic expressions represented as ‘<’, ‘>’, ‘≤’ or ‘≥’. The symbols ‘<‘ and ‘>’ represent strict inequalities.
Decimals: A decimal is a place between two integers. We can keep up space between any two integers into tenths, thousandths, etc.
Fractions on a number line
We can also use number lines to represent fractions or decimal values. The space between two integers can be divided into tenths or hundredths to accommodate the decimal value. For example, the number 4/5, which is 0.8 can be represented as follows.
Operations using a number line:
We can use a number line for:
- Addition of numbers
- Subtraction of numbers
- Comparing a set of numbers
How to add positive and negative numbers in a number line?
- To add a positive number, move right on the number line.
- To add a negative number, move left on the number line
- Move left to subtract a positive number.
- Move right to subtract a negative number.
For example, 1 + 6,
For example, 5 – 7,
How to compare a set of numbers on a number line?
We can compare numbers using ‘<’, ‘>’ symbols on a number line.
For example, let us compare the numbers 4,5,6,-6,1.
From the number line we can see that -6 > 1 > 4 > 5 > 6
The number can be arranged in ascending order by moving left to right on a number line: -6,1,4,5,6
The number can be arranged in descending order by moving right to left on a number line: 6,5,4,1,-6
Uses of a number line
- Number lines enable to representation of negative numbers and positive numbers in the same line.
- They also enable to show irrational numbers so such as √2, -√2, etc.
- They also help to understand numbers visually.
