Maths · Visual explanation
Subtracting a negative: why do you move right?
Separate the starting position from the change on a labelled number line.
The short answer
Subtracting a number means adding its additive inverse. The inverse of −3 is +3 because their sum is zero. So subtracting −3 has the same effect as adding +3.
Conceptual illustration. Colours distinguish parts of the model.
Where the confusion starts
“Two negatives make a positive” is too vague on its own. In −5 − 3, both the starting number and the subtraction involve negatives in different ways, and the answer is −8. Read the operation as well as the sign of each number.
WORK IT THROUGH
Compare −2 − 3 with −2 − (−3).
- Start at −2 in both calculations.
- For −2 − 3, add −3: move three units left to −5.
- For −2 − (−3), add +3: move three units right to +1.
CHECK YOUR UNDERSTANDING
Calculate −4 − (−6). Describe the movement.
Make a prediction or write an answer before opening the explanation.
Reveal the explanation
2. Start at −4 and add the inverse of −6, which is +6. Move six units right, crossing zero.
SEE IT. CHANGE IT. EXPLAIN IT.
Take the next step in the lesson.
Use the visual explanation in the lesson, then choose Practice to test the idea with another question.
Spotted something unclear? Send feedback. These are original teaching explanations, not predictions of future exam questions.