## What Is a Number Line in Math?

In math, a number line can be defined as a pictorial representation of numbers on a straight line. The numbers on a number line are placed sequentially at equal distances along its length. It can be extended infinitely in any direction and is usually represented horizontally.

The numbers on a number line increase as one moves from left to right and decrease on moving from right to left.

## Different Types of Numbers on a Number Line

A number line can be used to represent any type of numbers, like fractions, decimals, integers, etc.

## Number Lines as Mathematical Tools

**To compare numbers**

Writing numbers on it makes comparing numbers easier. Numbers on the left are smaller than the numbers on the right of it.

**To add/subtract numbers**

A number line can also be used to carry out addition and subtraction. We move right to add, move left to subtract. Let’s have a look.

**Steps to add/subtract on a number line:**

- Locate the first number on the number line.
**To add:**move as many steps as the second number to the right.**To subtract:**move as many steps as the second number to the right.- The number you land on is the answer.

**To multiply/divide numbers**

A number line can also be used to carry out multiplication and division. We skip count on a it to show jumps of equal size. Let’s have a look.

## Fun Facts

- A number line is usually represented horizontally and can be extended infinitely in any direction.
- The first mention of the number line as a tool for adding and subtracting is found in the
*Treatise on Algebra*by John Wallis. In his work, Wallis describes addition and subtraction on it in terms of moving forward and backward, in the context of a person walking. - A blank number line is a visual diagram with no numbers or markers and is essentially used as a tool for solving word problems.

Let us practice number line examples to understand it even better.

## Solved Examples

**Example 1: Compare **$–25$** and **$15$** using a number line.**

**Solution**: Let’s locate –25 and 15 on the number line.

Since, $–25$ is to the left of $15$, $–25 \lt 15$.

**Example 2: Add **$–7 + 7$**.**

**Solution**: Let’s locate –7 on the number line and move 7 steps to the right to find the answer.

So, $–7 + 7 = 0$

**Example 3: Subtract **$6 $–$ 7$**.**

**Solution**: Let’s locate 8 on the number line and move 11 steps to the left to find the answer.

So, $6 $–$ 7 = –1$.

**Example 4. Multiply **$2 \times 8$**.**

**Solution**: Starting from 0, let’s make 2 jumps of 8 to the right on the number line to find the answer.

So, $2 \times 8 = 16$.

## Practice Problems

## Number Line - Definition with Examples

### 1How can we solve $17 $–$ 6$ on the number line?

To subtract on a number line, we locate the first number (17) and move as many steps as the second number (6) to the left.

### 2How can we solve $8 \times 9$ on the number line?

$8 \times 9$ can be interpreted as 8 times 9 or 8 jumps of 9. So, to multiply on a number line, starting from 0, we would make 8 equal jumps of jump size 9.

### 3Solve $–8 + 2$.

To solve $–8 + 2$, we need to take 2 jumps to the right from $–8$. That is, $–8 \Rightarrow –7 \Rightarrow –6$. So, $–8 + 2 = –6$.

### 4Solve: $28 \div 4$

To solve $28 \div 4$, we need to take jumps of 4, starting from 28 till we reach 0. The number of jumps that we take is the answer. Doing so, we get $7$ jumps $(28 \Rightarrow 24 \Rightarrow 20 \Rightarrow 16 \Rightarrow 12 \Rightarrow 8 \Rightarrow 4 \Rightarrow 0)$, so, $28 \div 4 = 7$.

## Conclusion

One can mark positive, negative, whole, and rational numbers with a number line. Numbers appearing on the right side of 0 are positive numbers, and those reflected on the left side of it are negative. Using it, one can compare numbers and carry out arithmetic operations such as: addition, subtraction, multiplication, and division.

## Frequently Asked Questions

**What is a number line?**

A number line is a pictorial representation of numbers on a straight line, usually a horizontal line. The numbers on the it are placed sequentially at equal distances along its length.

**What are the uses of a number line?**

A number line can be used as a tool for various purposes. For example: to teach number sequence, to compare numbers, and to perform arithmetic operations on numbers.

**How many numbers can be represented in a number line?**

Infinitely, many numbers can be represented on a number line as it can be extended indefinitely on both sides.

**How are negative and positive integers placed on a number line?**

The positive integers are placed to the right of 0 and the negative integers are placed to the left of 0.