Free Math Guide
Learn how the operation and the sign of the second integer determine whether to move left or right, then use one-unit jumps to find the answer.
A number line turns integer operations into movement. The first integer tells you where to begin. The operation and the sign of the second integer tell you which direction to move. Its absolute value tells you how many one-unit jumps to make. The number where you land is the answer.
Values increase as you move right and decrease as you move left. Zero separates the positive integers from the negative integers, but it does not interrupt the pattern: every neighboring tick is exactly one unit apart.
Each one-unit jump to the left subtracts one from your current position.
Each one-unit jump to the right adds one to your current position.
In −3 + 5, begin at −3—not at zero and not at 5. The second integer describes the change from that starting position.
Do not look only at the plus or minus sign between the integers. Read the operation together with the sign of the second integer.
| Operation | Direction | Reason | Example |
|---|---|---|---|
| Add a positive integer | Move right | Adding a positive amount increases the value. | −3 + 5 = 2 |
| Add a negative integer | Move left | Adding a negative amount decreases the value. | 4 + (−6) = −2 |
| Subtract a positive integer | Move left | Taking away a positive amount decreases the value. | 3 − 7 = −4 |
| Subtract a negative integer | Move right | Subtracting a negative is equivalent to adding its opposite. | −4 − (−3) = −1 |
The signs determine the direction. The absolute value of the second integer determines the number of jumps. In 2 − (−5), move right because a negative is being subtracted, then make 5 jumps because |−5| = 5.
For addition, the sign of the second integer directly gives the direction. A positive second integer moves right; a negative second integer moves left.
Start at the first integer and make one rightward jump for each unit in the positive addend.
Five jumps right from −3 land on 2.
Start at the first integer and make one leftward jump for each unit in the negative addend.
Six jumps left from 4 land on −2.
Subtraction reverses the direction associated with the second integer. Subtracting a positive moves left, while subtracting a negative moves right.
Taking away a positive amount decreases the starting value.
Seven jumps left from 3 land on −4.
Taking away a negative amount has the same effect as adding its positive opposite.
Three jumps right from −4 land on −1.
The identity a − b = a + (−b) explains both subtraction rules. For example, 5 − 8 becomes 5 + (−8), while 5 − (−8) becomes 5 + 8.
Zero is an ordinary position on the number line. Landing on or passing through zero uses a jump just like moving between any two neighboring integers.
Crossing zero does not create a new problem. Keep moving in the same direction until you have made the required number of jumps.
A negative integer represents movement to the left. Subtraction reverses a change. Reversing a leftward change produces rightward movement, which is why subtracting a negative increases the value.
The opposite of −5 is +5, so the subtraction becomes five jumps right.
The final value, 7, is greater than the starting value, 2, because the movement was to the right.
In 2 − (−5), the first minus sign is the subtraction operation. The second minus sign belongs to the integer −5. They have different jobs, even though they appear next to each other.
Solve 5 + 3.
Solve −4 + 7.
Solve 3 + (−8).
Solve −2 − 5.
Solve 6 − (−4).
Solve −7 − (−9).
The first integer—not zero—is the starting position. In −5 + 3, begin at −5.
A jump is movement from one tick to the next. The starting point is not one of the jumps.
Adding a negative integer moves left because the value decreases.
Subtracting a negative integer moves right because it is equivalent to adding a positive integer.
Zero does not reverse your movement. Continue in the same direction until every required jump is complete.
In 4 − (−6), the operation is subtraction and the second integer is negative six. Both signs matter.
Distance is always nonnegative. Use the absolute value of the second integer to count the jumps.
Solve randomized addition and subtraction problems, choose the direction, make one-unit jumps, cross zero, undo mistakes, and receive immediate feedback across three difficulty levels.
Open the Integer Number Line ToolPractice moving left and right through randomized integer addition and subtraction problems.
Review sign rules, visual models, and strategies for adding integers.
Learn to rewrite subtraction as adding the opposite and solve signed-number differences.
Browse additional guides, worksheets, lessons, and interactive learning tools.
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