Visual representations are always useful to help you understand concepts more easily. What about numbers? What can we use to represent numbers to help us understand how they relate to other numbers? A very simple tool that we can use is a number line.
In this article, we will define what a number line is, and its characteristics, and we will explain how to create one. We will also show you how to use the number line to do basic mathematical operations and represent inequalities.
Let's start by defining what we mean by number line.
What is a number line?
A number line is a visual representation of numbers, using a horizontal line, which includes equally spaced divisions representing each number.
Characteristics of a number line
A typical number line will look like the one shown below.
Number line example - StudySmarter Originals
Looking at the number line above, we can identify the following characteristics:
Characteristics of a number line - StudySmarter Originals
How to create a number line?
The steps to create a number line are as follows:
1. Draw a horizontal line with arrowheads at each end, long enough to represent the range of numbers that you require. You can use a ruler to help you draw it, if you are doing it manually.
2. Include equally spaced tick marks along the horizontal line. If using a ruler, you can draw a tick mark on each centimetre as a guide. However, the number line is not the same as a ruler, so the space between tick marks does not have to be exactly 1 cm, but try to be consistent.
3. Label each tick mark below the line with an integer number, starting with zero below the tick mark in the middle of the line.
4. Label the tick marks to the right of zero with positive numbers starting from 1, and add one each time to label the following tick mark moving towards the right.
5. Label the tick marks to the left of zero with negative numbers starting from –1, and subtract one each time to label the following tick mark moving towards the left.
And there you have it, a number line that you can customise depending on what number or range of numbers you need to represent on it!
Examples of a number line
To represent or plot a specific number on the number line, you can draw a circle on the tick mark corresponding to that number.
The labels on a number line normally correspond to integer numbers, but you can actually represent any number on the number line, including fractions and decimals.
If you need to represent bigger numbers on the number line, then you can choose a different scale. For example, if you need to represent the number 40, then you can choose a scale of 5, 10 or 20.
Integers on the number line
First of all, let's see a few examples representing integers on the number line.
a) Represent the number 3 on the number line.
b) Represent the number –1 on the number line.
c) Represent the number 15 on the number line.
Notice that in this case, we have used a scale of 5.
Representing integers on the number line - StudySmarter Originals 
Decimals on the number line
When representing decimal numbers on the number line, you need to think about it as zooming into it, or looking at it closer. To allow you to represent the decimal part of this type of numbers more accurately, we need to create more tick marks or divisions as required.
To represent a decimal number on the number line, you can follow these steps:
Let's see some examples to help you understand the process more clearly.
a) Represent the number 2.5 on the number line.
The decimal number 2.5 is between 2 and 3, so let's label them on the number line.
The decimal part of 2.5 is 5 tenths, so let's draw 9 equally spaced tick marks between 2 and 3.
Each tick mark represents an increment of 0.1.
Now starting from 2, we move towards the right 5 tick marks to find 2.5.
b) Represent the number –3.7 on the number line.
The decimal number –3.7 is between –3 and –4, so we need to label them on the number line.
The decimal part of –3.7 is 7 tenths, so let's draw 9 equally spaced tick marks between –3 and –4.
Starting from –3, we move towards the left 7 tick marks to find –3.7.
Suppose you need to represent decimal numbers with more than one decimal. In that case, you can follow a similar process as before, but labelling the two decimal numbers that the given decimal number is in between.
c) Represent 0.75 on the number line.
The decimal number is between 0.7 and 0.8, so let's label them on the number line.
The decimal part of 0.75 is 75 hundredths, so let's draw 9 equally spaced tick marks between 0.7 and 0.8. In this case, each tick mark represents an increment of 0.01.
Starting from 0.7, we move towards the right 5 tick marks to find 0.75.
Representing decimals on the number line - StudySmarter Originals 
Fractions on the number line
The easiest way to represent fractions on the number line is to convert the fraction into a decimal number by dividing the numerator by the denominator, and then following the same steps as before. Please read Convert between Fractions and Decimals, if you need to refresh the basics.
a) Represent the fraction on the number line.
The fraction is equal to the decimal number 0.5. Now we can follow the same steps as before to represent 0.5 on the number line.
The decimal number 0.5 is between 0 and 1. So let's label them on the number line.
The decimal part of 0.5 is 5 tenths. Let's divide the number line between 0 and 1 into 10 equal intervals.
Starting from 0, we move towards the right 5 tick marks to find 0.5.
Representing fractions on the number line - StudySmarter Originals 
Number line Maths
You can perform mathematical operations like addition, subtraction and multiplication with the help of the number line. Let's see what methods you need to use in each case.
Number line methods
Addition on the number line
To add numbers on the number line you can follow these steps:
Use the number line to solve
Addition on the number line - StudySmarter Originals 
Subtraction on the number line
To subtract numbers on the number line you can follow these steps:
Use the number line to solve
Subtraction on the number line - StudySmarter Originals 
Multiplication on the number line
To multiply numbers on the number line you need to remember that multiplication is the same as repeated addition. Keeping that in mind, we can use the skip count method following these steps:
If either of the factors in the multiplication is negative, but not both, then you need to move towards the left of zero (negative numbers) to represent the solution of the multiplication.
Use the number line to solve
Starting from zero, we move towards the right 3 times in intervals of 2.
Multiplication on the number line - StudySmarter Originals 
Number line inequalities
Let's recall the definition of inequalities.
Inequalities are algebraic expressions that, instead of representing how both sides of an equation are equal, represent how one term is less than (<), less than or equal (≤), greater than (>), or greater than or equal (≥) to the other.
Inequalities can also be represented on the number line. The rules that you need to keep in mind when representing inequalities on the number line are as follows:
Represent the inequalities below on the number line:
| Inequality | Inequality on the number line |
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Inequalities on the number line - StudySmarter Originals 
Please read Solving Inequalities to learn more about this topic.
Number Line - Key takeaways
- A number line is a visual representation of numbers, using a horizontal line, which includes equally spaced divisions representing each number.
- The numbers on the right-hand side of zero are the positive numbers. The numbers on the left-hand side of zero are the negative numbers.
- If you move towards the right on the number line you will find bigger numbers. If you move towards the left on the number line you will find smaller numbers.
- To represent or plot a specific number on the number line, you can draw a circle on the tick mark corresponding to that number.
- You can represent any number on the number line, including fractions and decimals.
- You can perform mathematical operations like addition, subtraction and multiplication with the help of the number line.
- Inequalities can also be represented on the number line. An empty circle is used to represent that the value of x is not part of the solution, and a closed circle is used if the value of x is part of the solution.
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