Did you know? Yes—subtracting a negative number makes a value larger. For example, 6 − (−3) = 9 because subtracting −3 is equivalent to adding its opposite, +3.
The shortcut “subtraction makes numbers smaller” works only when a positive amount is subtracted. The dependable rule is a − b = a + (−b). If b is negative, its opposite is positive, so the movement is to the right on a number line.
Try this now: predict the direction before calculating −4 − (−7). Removing a negative seven is the same as adding seven: −4 + 7 = 3. The result is greater than −4.
Choose the task you need
1. Rewrite subtraction as addition
Subtraction is addition of the opposite. This single structure handles positive numbers, negative numbers and zero without a list of disconnected sign slogans.
| Expression | Add the opposite | Result | Direction from start |
|---|---|---|---|
| 6 − 3 | 6 + (−3) | 3 | left |
| 6 − (−3) | 6 + 3 | 9 | right |
| −6 − 3 | −6 + (−3) | −9 | left |
| −6 − (−3) | −6 + 3 | −3 | right |
The phrase “two negatives make a positive” is too broad. Two negative numbers added together remain negative. The positive change appears here because the second negative sign belongs to the number being subtracted.
2. See the movement on a number line
A number line makes the direction visible. Subtracting a positive moves left. Subtracting a negative reverses that direction and moves right.
| Start | Operation | Movement | Finish |
|---|---|---|---|
| 2 | subtract 5 | 5 units left | −3 |
| 2 | subtract −5 | 5 units right | 7 |
| −4 | subtract 2 | 2 units left | −6 |
| −4 | subtract −2 | 2 units right | −2 |
OpenStax states the subtraction property as a − b = a + (−b) and gives the special case a − (−b) = a + b. A student should still check the final location rather than recite the rule without direction.
3. Use brackets and signs accurately
Brackets protect the sign of the number being subtracted. Without them, a row of symbols can be misread or copied inaccurately.
Original teaching illustration: read every sign’s job
| Written form | First sign | Second sign | Clear reading |
|---|---|---|---|
| 7 − (−2) | operation: subtract | number sign: negative | seven subtract negative two |
| −7 − 2 | number sign: negative | operation: subtract | negative seven subtract two |
| −7 + (−2) | number sign: negative | operation then number sign | negative seven plus negative two |
| 7 + 2 | operation: add | positive sign omitted | seven plus two |
A useful written habit is to rewrite one line only: 7 − (−2) = 7 + 2. Avoid jumping straight from the original expression to 9 if the learner is still confusing the two signs.
4. Apply the idea without misleading stories
Temperature, elevation and money contexts can help, but the language must match the operation. “Removing a debt” is not identical to every subtraction problem, and a story should not replace the mathematical structure.
| Context | Change represented | Calculation |
|---|---|---|
| Temperature rises 6°C from −4°C | add +6 | −4 + 6 = 2 |
| A downward change of −3 is removed from 5 | subtract −3 | 5 − (−3) = 8 |
| A debt of $7 is cancelled from a balance of −$2 | subtract −7 | −2 − (−7) = 5 |
| A lift descends 4 floors from level 2 | add −4 | 2 + (−4) = −2 |
At Primary level, negative-number work may be limited or informal. At secondary level, directed numbers support algebra, graphs, temperature, elevation and later subject applications. Use examples matched to the learner’s actual programme.
5. Diagnose the error and transfer the rule
A wrong answer can come from a sign-reading problem, a number-line direction problem or an unstable inverse-operation rule. These need different repairs.
| Observed response | Likely unstable point | Repair prompt |
|---|---|---|
| 6 − (−3) = 3 | treats −3 as +3 to subtract | What is the opposite of −3? |
| −4 − (−7) = −11 | moves left for every subtraction | Does subtracting −7 become adding what? |
| Says all two-minus-sign expressions are positive | overgeneralised slogan | What is −4 + (−7)? |
| Gets the rule right but drops brackets | notation is unstable | Which sign belongs to the number? |
A useful exit check mixes four expressions: 5 − 2, 5 − (−2), −5 − 2 and −5 − (−2). Ask for the movement and result. Transfer is visible when the learner explains all four consistently.
When tuition can help
Tuition may help when the learner memorises “change the sign” but cannot say which sign changes, predict the number-line direction or carry the rule into algebra. A tutor can compare brackets, opposites, movement and inverse operations to locate the missing link.
A useful review starts with one fresh Maths task, the learner’s explanation and the exact point where the reasoning changes. eduKateSG’s verified 3-pax format is designed for close observation and precise feedback; it is not a promise of a particular grade.
Sources and scope
- OpenStax Prealgebra 2e: subtract integers
- OpenStax Prealgebra 2e: Chapter 3 key concepts
- MOE: secondary school experience under Full Subject-Based Banding
- SEAB: Secondary Education Certificate (SEC)
The worked examples and teaching checks on this page are original educational illustrations. They explain the stated concept; they do not reproduce a live examination question or promise a grade outcome.
For secondary planning, PG1, PG2 and PG3 are Posting Groups used for admission, while G1, G2 and G3 are subject levels where those levels are offered. The SEC begins in 2027. Check the learner’s actual subject, level, examination year and candidate type; not every subject is offered at every G level.