Number Line: Definition, Diagram, Operations and Examples

Number Line: The number line can be stretched in any direction indefinitely and is shown horizontally. When comparing numbers, a number line might be employed. Each number on a number line is plotted in relation to the origin (zero), and the position of a number on a number line defines its value. This means that every number to the right of zero is a positive number, and any number to the left of zero is a negative number. Let’s look at the number line, digit representation, and how to conduct arithmetic operations on it.

What is Number Line?

A number line is a straight line with numbers placed on it at equal intervals along its length. However, the number line can be extended infinitely in any direction and is represented horizontally.
Numbers will be marked on the number line as given below:

The positive numbers are placed on the right side of zero on the number line, and negative numbers are placed on the left.
The farther we move on the right side of the zero, the value of the numbers increases and the more distant the numbers move to the left side on the number line from zero, the value decreases.
When we compare any two numbers on a number line, the number on the right side of the zero will be more significant.

Operations on the Number Line

The four fundamental operations of mathematics are addition, subtraction, multiplication and division. There are various methods to perform these operations.
A number line is one of the easiest methods to represent arithmetic operations.
The arithmetic operations of numbers can be explained easily on the number line. For example, you can locate the number zero as the middle point of a number line, and all the positive numbers placed on the right side of zero, whereas all the negative numbers are placed on the left side of zero, just as shown below:

Addition of Numbers on Number Line

Positive numbers: When you add any two positive numbers, the result will always be positive. So, while adding positive numbers, the direction of the movement will always be to the right side.
Example: Addition of \(4\) and \(4 (4 + 4 = 8)\)
So, you can see the first number is \(4\), and the second number is also \(4\); both are positive numbers.
Now, find the number \(4\) on a number line, then move \(4\) steps to the right side to reach \(8\).

Negative numbers: When you add two negative numbers, the result you get is always negative. So, when you add any negative numbers, the direction of the move will always be on the left side.
Example: The addition of the negative numbers \(-3\) and \(-5\)

The first number is \(-3\), and the second number is \(-5\); both are negative. Now, locate the number \(-3\) on a number line, then move \(5\) steps to the left side to reach \(-8\).

Addition of fractions on the Number line

You can see the addition of fractions on the number line below in the given an example.
Example: Addition of \(\frac{2}{8} + \frac{3}{8}\)
\(\frac{2}{8}\) means \(2\) parts out of \(8\) parts.
\(\frac{3}{8}\) means \(3\) parts out of \(8\) parts.
Adding the fractions \(\frac{3}{8}\) to \(\frac{2}{8}\) means you have to jump three steps forward from \(\frac{2}{8}\).

You can see by adding \(\frac{2}{8} + \frac{3}{8}\) we got \(\frac{5}{8}.\)

Subtraction of Numbers on Number Line

Positive numbers: When you want to subtract any two positive numbers, move on to the left as far as the value of the second number.
Example: Subtract \(5\) from \(4\)
Here, you can see the first number is \(4\), and the second number is \(5\); both are positive numbers. So, pin the number \(4\) on a number line. Then, move \(5\) steps to the left will give \(-1\).

Negative numbers: When you want to subtract the two negative numbers, then move towards the right side as far as the value of the second number.
Example: Subtract \(-4\) from \(-2\)

Now, mark \(-2\) on the number line. Later, move \(4\) steps to the right to reach \(2\).

Subtraction of fractions on the Number line

You can see the subtraction of fractions on the number line below in the given example.
Example: Subtraction of \(\frac{5}{6} – \frac{2}{6}\)
\(\frac{5}{6}\) means \(5\) parts out of \(6\) parts.
\(\frac{2}{6}\) means \(2\) parts out of \(6\) parts.
Subtracting the fractions \(\frac{2}{6}\) from \(\frac{5}{6}\) means you have to jump two steps backwards from \(\frac{5}{6}.\)

You can that we got \(\frac{5}{6} – \frac{2}{6} = \frac{3}{6}.\)

Multiplication of Numbers of Number Line

You know that multiplication is also known as the repeated addition. To perform multiplication on the number line, you must move towards the right side of the number line for the given number of times.
Example: Multiply: \(4 \times 3\) on a number line.
Now, you will move towards the right side of the number line.
You will get four groups of \(3\) at equal intervals on the number line. So, starting from \(0\), you will move \(4\) times, combining \(3\) intervals at a time.
So, you will reach the number \(12\) by forming \(4\) individual groups. You can see the number line below that shows \(4 \times 3 = 12.\)

Division of Numbers of Number Line

When you divide the integers on the number line, you move towards the number line’s left side and split the given number into equal groups.
You can see that the numbers decrease as you move towards the left side.
Example: To solve \(8 ÷ 4\), you count how many jumps of \(4\) it takes from \(0\) to reach \(8-\)these groups or jumps of \(4\) mean \(8 ÷ 4 = 2\). The number line shows that it takes \(2\) groups of \(4\) to reach \(8\).

Representation of Decimals on the Number Line

Here the decimals are represented on the number line. Say, let us represent \(0.6\) on the number line.
Now, you know that \(0.6\) is more than zero but less than the number one. There are \(6\) tenths in it. Now, divide the unit length between the numbers \(0\) and \(1\) into \(10\) equal parts and take \(6\) parts as shown below:

Uses of Number Line

A number line can be used to carry out addition, subtraction, multiplication etc. You always have to move right to add the numbers, move the left side to subtract the numbers and skip count to multiply the numbers.

Types of Number Line

There are three types of the number line, and they are given below:

1. Real number line: The real number line, or simply call the number line, allows you to visually represent the real numbers by associating them with the unique points on the line.
2. Imaginary number line: In mathematics, a line of imaginary numbers exists like the real number line. The two lines sit at right angles to each other, like the \(x\) and \(y-\) axis of the graph. These two intersect at the zero points of each line. These number lines help you imagine how real and imaginary numbers work.
3. Circular number line: The union of the real number line and the imaginary line is known as the circular number line.

Solved Examples – The Number Line

Q.1. Which numbers lie between \(-8\) and \(-2\)? Write the greatest number and smallest number among them?

Q.2. One button is kept at \(-3\). Write the direction and how many steps you have to move to reach at \(-9\)?
Ans: You have to move six steps to the left side of the number \(-3\).

Q.3. Which number will you reach if you move \(4\) steps to the right of \(-6\)?

Q.4. Which number will you reach if you move \(3\) steps to the right of \(-4\)?
Ans: You reach \(-1\) when you move \(3\) steps to the right side of \(-4\).

Q.5. Which number will you reach if you move \(5\) steps to the left of \(6\)?
Ans: You reach \(1\) when you move \(5\) steps to the left side of \(6\).

Summary

In the given article, we have discussed the definition of the number line. Also, we covered how to add, subtract, multiply, and divide numbers on the number line, followed by addition and subtraction of fractions on the number line and representation of decimals on the number line. Finally, we glanced at the uses of number lines followed by types of the number line. Then you can see a few of the solved examples along with a few FAQs.

Frequently Asked Questions (FAQs) – The Number Line

Q.1. What is a number line?
Ans: A number line is a straight line with numbers marked on it at equal intervals along its length. However, the number line can be extended infinitely in any direction and represented horizontally.

Q.2. What is a number line example?
Ans: The example of the number line is given below:
Example: The addition of the negative numbers \(-3\) and \(-5.\)

The first number is \(-3\), and the second number is \(-5\); both are negative. Now, mark the number \(-3\) on a number line, then move \(5\) steps to the left side to reach \(-8\).

Q.3. How do you explain a number line?
Ans: Positive numbers are placed on the right side of zero on the number line, and negative numbers are placed on the left.
The farther numbers move to the right side from zero on the number line, the value of the numbers increases, and the more distant the numbers move to the left side on the number line from zero, the value decreases.

Q.4. What numbers are used in number lines?
Ans: A number line refers to the pictorial representation of numbers like fractions, integers and whole numbers that are displayed evenly on the straight horizontal line. A number line can be utilised as the tool for comparing and ordering the numbers and also performing operations like addition, subtraction etc.

Q.5. Which is the smallest whole number?
Ans: Zero is the smallest whole number. As the whole number starts, it counts from the number zero, so it is the smallest whole number.

Q.6. What are the types of the number line?
Ans: The types of the number line are given below:
1. Real number line
2. Imaginary number lines and
3. Circular number line

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