Concept 8 of 8Foundation

📌 Formula Sheet — Integers

The rules of this chapter, with the reasoning behind each.

Sign rules for × and ÷

Means: (+)·(+)=+, (+)·(−)=−, (−)·(+)=−, (−)·(−)=+Use when: multiplying or dividing integers

Why: Multiplication is repeated addition. 3 × 2 = 2+2+2. 3 × (−2) = add −2 three times = −6. (−3) × (−2): taking away 2 three times is like gaining 6. Two negatives 'cancel' direction.

⚠ Trap: Count minus signs in a product. EVEN count → +, ODD → −. (−2)(−3)(−4) has 3 minuses → negative.

Subtraction rule: a − b = a + (−b)

Means: subtracting equals adding the oppositeUse when: any subtraction, especially with negatives

Why: Going 5 steps LEFT is the same as going −5 steps to the right. Subtraction is just 'adding the opposite direction.'

⚠ Trap: 5 − (−3) = 5 + 3 = 8 (not 2!). Two minuses next to each other become plus.

Opposite (additive inverse): a + (−a) = 0

Means: every integer has an opposite that cancels itUse when: simplifying, solving equations

Why: On the number line, a and −a are the same distance from 0 but in opposite directions. Together they bring you back to 0.

⚠ Trap: Opposite of 0 is 0 itself. Opposite of −7 is +7 (not −7).

Absolute value: |a| = distance from 0

Means: |5| = 5, |−5| = 5, |0| = 0Use when: distance on number line, 'how far' questions

Why: Distance is always positive regardless of direction. |a| just strips the sign.

⚠ Trap: |−3| ≠ 3 is WRONG. It IS 3. But −|3| = −3.

Zero rules: a + 0 = a, a × 0 = 0, a × 1 = a

Means: 0 is additive identity, 1 is multiplicative identityUse when: any calculation involving 0 or 1

Why: Adding nothing doesn't change a value. Multiplying by 0 takes away everything. Multiplying by 1 means 'one copy of'.

⚠ Trap: Division by 0 is NOT defined. a ÷ 0 has no meaning.

💡 Tip:Sign mistakes sink more marks than anything. Write the signs clearly; double-check with a number-line mental picture.

▶Prefer a video? Open YouTube search for “integers revision formulas class 6”↗