Using Number Lines to Represent Integers

A number line is one of the most useful tools for understanding integers, from middle school math to tests such as the GED Mathematical Reasoning test. By placing numbers on a line, you can instantly compare their values, find opposites, and visualize addition and subtraction. This lesson shows you exactly how to read, label, and use a number line with integers.

To plot an integer on a number line, start at 0, move right for a positive integer or left for a negative integer, and count one tick per unit. On a number line, the number farther to the right is always greater, so −2 > −7 and 3 > −4. Opposites, such as 5 and −5, are the same distance from 0 on opposite sides.

What Is a Number Line?

A number line is a straight horizontal line with a center point at \(\color{blue}{0}\). Positive integers are plotted to the right of zero, and negative integers are plotted to the left. Each tick mark represents one unit. The arrows at both ends indicate that the number line continues in both directions without end.

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How to Represent Integers on a Number Line

1. Locate zero

Zero is always the reference point (the origin) in the center of the number line. It is neither positive nor negative.

2. Positive integers go right

Count the same number of tick marks to the right of zero as the integer’s value. For example, \(\color{blue}{4}\) is four marks to the right of zero.

3. Negative integers go left

Count the same number of tick marks to the left of zero as the integer’s absolute value. For example, \(\color{blue}{-4}\) is four marks to the left of zero.

4. Comparing integers on the number line

A number farther to the right is always greater. So \(\color{blue}{-1 > -5}\) because \(\color{blue}{-1}\) sits to the right of \(\color{blue}{-5}\) on the number line.

Step-by-Step Summary

1. Draw a horizontal line and mark \(\color{blue}{0}\) in the center.
2. Mark equally spaced tick marks going right (\(\color{blue}{1, 2, 3, \ldots}\)) and left (\(\color{blue}{-1, -2, -3, \ldots}\)).
3. To plot an integer, count from zero: right for positive, left for negative.
4. To compare two integers, the one further right is greater.
5. To find the distance between two integers, count the number of units between them.

Watch: Integers on a Number Line (Video Lesson)

Khan Academy walks through representing integers on a number line and explains why position determines value:

Using Number Lines to Represent Integers – Worked Examples

Example 1: Plot \(\color{blue}{-4}\), \(\color{blue}{0}\), \(\color{blue}{3}\), and \(\color{blue}{5}\) on a number line and list them in order from least to greatest.

Starting from \(\color{blue}{0}\): \(\color{blue}{-4}\) is 4 units to the left; \(\color{blue}{3}\) is 3 units right; \(\color{blue}{5}\) is 5 units right.
Order (left to right on the number line): \(\color{blue}{-4, 0, 3, 5}\).

Example 2: Which is greater, \(\color{blue}{-2}\) or \(\color{blue}{-5}\)?

On a number line, \(\color{blue}{-2}\) sits to the right of \(\color{blue}{-5}\), so \(\color{blue}{-2 > -5}\).

Example 3: What integer is 6 units to the left of \(\color{blue}{2}\) on the number line?

Move 6 units left from \(\color{blue}{2}\): \(\color{blue}{2 – 6 = -4}\). The integer is \(\color{blue}{-4}\).

Example 4: What is the distance between \(\color{blue}{-3}\) and \(\color{blue}{4}\) on the number line?

Count from \(\color{blue}{-3}\) to \(\color{blue}{4}\): that is \(\color{blue}{3 + 4 = 7}\) units. (Or subtract: \(\color{blue}{4 – (-3) = 7}\).)

More Practice: Using a Number Line for Integers (Video)

Math with Mr. J demonstrates using number lines to add integers with clear step-by-step examples:

Exercises for Using Number Lines to Represent Integers

1. Plot \(\color{blue}{-6}\), \(\color{blue}{-1}\), \(\color{blue}{0}\), \(\color{blue}{4}\) on a number line and write them in order from least to greatest.
2. Which is greater: \(\color{blue}{-8}\) or \(\color{blue}{-3}\)?
3. What integer is 5 units to the right of \(\color{blue}{-2}\)?
4. What is the distance between \(\color{blue}{-5}\) and \(\color{blue}{3}\) on the number line?
5. Name the opposite of \(\color{blue}{-6}\) and plot both on a number line.
6. Is \(\color{blue}{-10}\) to the left or right of \(\color{blue}{-4}\)? Which is greater?

Answers

1. \(\color{blue}{-6, -1, 0, 4}\)
2. \(\color{blue}{-3}\) (it is to the right of \(\color{blue}{-8}\))
3. \(\color{blue}{3}\) (\(\color{blue}{-2 + 5 = 3}\))
4. \(\color{blue}{8}\) units (\(\color{blue}{3 – (-5) = 8}\))
5. Opposite of \(\color{blue}{-6}\) is \(\color{blue}{6}\); both are 6 units from zero, on opposite sides.
6. \(\color{blue}{-10}\) is to the left; \(\color{blue}{-4 > -10}\).

Frequently Asked Questions

How do you represent integers on a number line?

Draw a straight line with evenly spaced tick marks and label the middle mark 0. Positive integers go to the right, one unit per tick, and negative integers go to the left. To plot −6, count six ticks left of zero and draw a dot. Arrows on both ends show the line keeps going forever in each direction.

How do you use number lines to add integers?

Start at the first integer, then move right for a positive number or left for a negative number. For −3 + 7, start at −3 and jump 7 units right to land on 4. For 2 + (−5), start at 2 and jump 5 units left to land on −3. Counting the jumps helps you see why adding a negative makes a number smaller.

How do you use number lines to subtract integers?

Start at the first number and move left to subtract a positive integer. Subtracting a negative means moving right, because subtracting −4 is the same as adding 4. So for 1 − 6, move 6 left from 1 to reach −5, and for −2 − (−4), move 4 right from −2 to reach 2. The distance between two points also equals their difference.

How do you use number lines to multiply integers?

Think of multiplication as repeated jumps of equal size starting from zero. For 3 × (−2), make 3 jumps of 2 units to the left and land on −6. For 4 × 3, make 4 jumps of 3 units to the right and land on 12. This shows why a positive times a negative gives a negative product.

How do you use number lines for division?

Division asks how many equal jumps fit into a distance. For 15 ÷ 5, count how many jumps of 5 it takes to go from 0 to 15; it takes 3. For −12 ÷ 4, jumps of 4 units to the left reach −12 after 3 jumps, and since you moved in the negative direction the answer is −3.

Related Topics

• Opposite Integers
• Using Vertical and Horizontal Number Lines to Represent Integers
• Adding and Subtracting Integers
• Integers and Absolute Value
• Using a Venn Diagram to Classify Rational Numbers