Number Lines

Number line is a fundamental tool in mathematics that provides a visual representation of numbers. It serves as a guiding map for understanding the order of numbers, their magnitudes, and the principles of addition and subtraction.

In this article we have covered the basic concepts related to a number line; what is a number line, the different parts of a number line, negative and positive number lines, how to draw a number line, performing operations on a number line, and others in detail.

What is a Number Line?

A number line is a straight line that represents the number pictographically. It helps us see and compare numbers easily. Imagine it like a road where zero is the starting point. In the center of a number line, we have a zero and on the left of zero, we have negative numbers, and on the right, we have positive numbers. So, when we go to the right, the numbers get bigger. It’s like walking along the road and seeing bigger numbers as we go.

For example, on a number line, if we have -3, 0, and 5, we can see that 5 is to the right of 0, so it’s bigger than 0, and -3 is to the left, so it’s smaller than 0.

Number Line

How to Draw a Number Line?

A number line can be drawn very easily, just follow the below given steps:

Step 1: Make a straight line with arrows at both ends. You can also make it go up and down.

Step 2: Decide on a scale depending on your number. Let’s say your number is 8; you might choose a scale of 2. If it’s 75, you could go with a scale of 15 or 25. It depends on the number you have.

Step 3: Put marks at even spaces. If your scale is 2, mark 0, 2, 4, 6, 8, and so forth.

Step 4: Identify and circle the point on the line that represents your number. For example, if your number is 8, find that spot and circle it.

Numbers on a Number Line

Understanding arithmetic on a number line starts with locating numbers. Zero is the midpoint, with positive numbers to the right and negative numbers to the left. Moving left means decreasing value; for instance, 1 is greater than -1. The number line also locates integers, fractions, and decimals. It’s a useful tool to visualize and compare numerical values.

Negative Number Line

The numbers lesser than Zero and placed on the left hand side of the number lines are called Negative Number. They include number such as, -12, -31, -101, etc.

Positive Number Line

The numbers greater than Zero and placed on the right hand side of the number lines are called Positive Number. They include number such as, 2, 12, 56, etc.

The image added below shows, positive and negative numbers on the number line.

Number Line 1 to 100

Number line from 1 to 100 represents integers in sequential order. It serves as a visual tool to understand the relative magnitude and relationships between numbers, aiding in mathematical concepts like addition, subtraction, and ordering.

Parts of a Number Line

A number line has two parts. On the left of zero is the negative part, and on the right is the positive part. The negative part has numbers smaller than zero, and the positive part has numbers larger than zero. The number line keeps going forever in both directions (left and right).

Positive and Negative Number Line

Look at the different sections of the number line to understand these features:

• Numbers on the right side are bigger than the ones on their left.
• Numbers on the left side are smaller than the ones on their right.
• The middle point or starting point of the number line is 0.
• Numbers are always spaced equally on a number line.

Number Line with Decimals

On a number line, we can represent various types of numbers, including whole numbers, fractions, decimals, integers, rational numbers, and irrational numbers. In this section we will se how to place a decimal number. For example take a number 3.7

Identify the Whole Number: Look at the whole number part of the decimal. In 3.7, the whole number part is 3.

Draw the Number Line: Create a number line and mark points for the whole numbers. For 3.7, mark points for 3 and 4, leaving some space between them.

Consider the Decimal Part: Examine the digit after the decimal point, the tenths place. In 3.7, the tenths place digit is 7. Divide the space between 3 and 4 into 10 equal parts and place 3.7 on the seventh part to the right of 3.

Rational Number on Number Line

Rational Numbers are the numbers that are represented in the form of p/q and they can also be easily represented on the number line.

Irrational Number on Number Line

Irrational Numbers are the numbers that are not represented in the form of p/q and they can also be easily represented on the number line.

Addition on Number Line

Addition on a number line involves moving to the right for positive numbers and to the left for negatives. It’s a visual method where combining integers is represented by shifting along the line to reach the sum.

Adding Positive Numbers

On adding two positive numbers on a number line the resultant will always be positive, For example 3 + 2 = 5

Adding Positive Numbers

Adding Negative Numbers

On adding two negative numbers on a number line the resultant will always be negative. For example (-3) + (-2) = (-5)

Adding Negative Numbers

Subtraction on Number Line

Subtraction on a number line involves moving to the left from a given point. The numerical difference between two values is represented by the distance traveled. For instance, subtracting 30 from 50 on a number line implies moving 20 units to the left.

Subtracting Positive Numbers

On subtracting two positive numbers on a number line the result can be a positive number or a negative number, depending on the the greater or the smaller the first number is. For example 2-3= (-1) , here the first number is 2, which is smaller than 3. That’s why the result is negative. But if we do 3-2 than the result will be +1.

2 – 3 = -1

3 – 2 = 1

Subtracting Negative Numbers

Subtraction on a number line is a way to find the difference between two numbers. Here’s how it works:

• Draw the Number Line: Start by drawing a number line. Place the larger number at the starting point and the smaller number to its right.
• Counting Backwards: To subtract, move to the left on the number line. Each step to the left represents subtracting one from the starting number.
• Find the Difference: The point where you land on the number line is the difference between the two numbers.

For example, if you have 8 – 3, you will start at 8 on the number line and move three steps to the left. You land on 5, so the difference is 5.

Subtracting on a number line gives a visual representation of the process, making it easier to understand the concept of finding the difference between two numbers.

Inequalities on a Number Line

In math, inequalities are like sentences that tell us about the relationship between numbers. When we draw them on a number line, we’re showing which part of the numbers we’re talking about.

Graphing Inequalities on a Number Line

Imagine looking at a picture that represents these inequalities: a number x is greater than or equal to 4 (z ≥ 4), greater than 4 (x > 4), less than or equal to 4 (x ≤ 4), and less than 4 (x < 4).

The symbols (≥, >, ≤, <) are like the words in our math language that tell us how the numbers compare. And the number line acts like a map, helping us visually understand which range of numbers our inequality is referring to.

Real Life Use of Number Line

Various uses of the Number Lines are,

• To Show Temperature: A number line helps us understand daily temperatures, with warmer temperatures to the right and colder temperatures to the left.
• To Shows Distance: Using a number line for kilometers or miles helps us measure and compare distances. It’s useful for planning travel routes.
• Managing finances on a number line allows for a visual representation of expenses and income, making it easier to track and compare amounts.

Read More,

• Number System
• Whole Numbers
• Real Numbers
• Rational Numbers

Number Line Examples

Examples 1: Add 8 and 6 using number line.

Solution:

Example 2: From 9 use 3 unit to left.

Solution:

Example 3: Subtract 5 from 7 using number line.

Solution:

Practice Questions on Number Lines

Q1: On a number line, mark the position of the number -2.

Q2: Graph the inequality y > 7 on a number line and indicate the shaded region.

Q3: Choose an appropriate scale and mark the points at equal intervals from 0 to 10 on a number line.

Q4: Given the inequality z ≤ 5, graph it on a number line and highlight the section that satisfies the inequality.

Q5: Place the numbers 1, 4, and 7 on a number line. Indicate which number is greater and which is smaller.

FAQs on Number Lines

1. What is a Number Line in Math?

A number line in math is a straight line that represents numbers in order, with zero in the center. It helps visualize and understand the relative size and position of numbers.

2. What is an Open Number Line?

An open number line is an unmarked or unlabeled number line. It provides a flexible visual tool in mathematics for representing and solving problems without specific numerical values.

3. What is a Double Number Line?

A double number line is a diagram that displays two number lines, often used to represent and compare two related quantities or variables in mathematical relationships.

4. Which is the Smallest Whole Number?

The smallest whole number is 0

5. How Many Numbers Can be Represented in a Number Line?

A number line can represent an infinite set of numbers. It extends infinitely in both directions, allowing the representation of any real number.

6. What are the Uses of a Number Line?

Number lines are used for various mathematical tasks, including addition, subtraction, understanding the order of numbers, and visualizing mathematical relationships and patterns.

7. Are Number Lines Infinite?

Yes, number lines are infinite in both directions that means they continue indefinitely in the positive and negative directions.

8. Who discovered the Number Line?

The concept of the number line has evolved over time without a single attributed inventor. Various mathematicians and cultures, including ancient Indian, Greeks and Chinese scholars, contributed to its development.