Using Number Lines to Subtract Integers

To subtract an integer on a number line, add its opposite: move right for subtracting a negative, left for subtracting a positive. Turning every subtraction into an addition is what keeps the direction straight.

• To add positive integers, move towards the right on a number line.
• To add negative integers, move towards the left on a number line.
• To subtract integers, add their opposites.

1. Start at the first number (the minuend) and move left for each unit of a positive subtrahend, or right for each unit of a negative subtrahend. For example, if you’re subtracting -3 from 4, start at 4 and move 3 units to the right.
2. Label the endpoint of the distance you traveled with the difference. So in the example above, the difference would be labeled as 7.
3. Write the difference as the solution to the subtraction problem. In this case, the solution would be 4 − (−3) = 7.

Using Number Lines to Subtract Integers, Example 1

Using Number Lines to Subtract Integers, Example 2

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Four Worked Examples, One for Each Case

Here is the first one step by step. Put your finger on 5. You are subtracting a positive 8, so move left 8 units: 4, 3, 2, 1, 0, −1, −2, −3. You land on −3, so 5 − 8 = −3.

Now the trickiest one. For −6 − (−2), put your finger on −6. You are subtracting a negative, so turn around and move right 2 units: −5, −4. You land on −4.

Check with addition

Subtraction and addition undo each other. If 4 − (−3) = 7, then 7 + (−3) should give 4, and it does. Use this check whenever a sign feels confusing.

Adding and subtracting integers is part of the Common Core grade 7 standards (7.NS.A.1), and many 6th grade classes start with it on the number line.

Frequently Asked Questions

How do you subtract numbers on a number line?

Start at the first number. If you subtract a positive number, move left that many units. If you subtract a negative number, move right that many units. The point where you stop is the answer. For example, 2 − 6 = −4, because moving 6 left from 2 lands on −4.

What are the two rules for subtracting integers?

First, keep the first number, change the minus sign to a plus, and change the second number to its opposite. Second, then follow the addition rules: same signs, add and keep the sign; different signs, subtract and keep the sign of the number farther from zero. So 3 − (−5) becomes 3 + 5 = 8.

Why does subtracting a negative number move you to the right?

Subtracting means taking away. Taking away a debt of 3 dollars leaves you 3 dollars better off, so the value goes up. On a number line, going up means moving right. That is why 4 − (−3) equals 4 + 3, which is 7.

How do you subtract a bigger number from a smaller one on a number line?

Start at the smaller number and move left by the bigger one. You will pass zero and land on a negative number. For 3 − 7, start at 3, move 7 units left, and stop at −4. The answer is negative because you took away more than you had.