Sign rules: + × − = −, the table to memorize

Multiplication and division

Same signs → +. Different signs → −.

Operation	Result
$(+) \times (+)$	$+$
$(-) \times (-)$	$+$
$(+) \times (-)$	$-$
$(-) \times (+)$	$-$

Same for division.

Examples:

• $(-3) \times (-4) = +12$
• $(-8) \div 2 = -4$
• $5 \times (-6) = -30$

Counting many signs

Count the number of minus signs:

• Even → positive result
• Odd → negative result

$(-1) \times (-2) \times (-3) \times (-4) = +24$ (4 minuses = even = +) $(-1) \times (-2) \times (-3) = -6$ (3 minuses = odd = −)

Addition and subtraction

Step 1: turn every subtraction into an addition of the opposite. $a - b = a + (-b)$

Step 2: two rules by signs:

• Same signs: add absolute values, keep the sign.
• Different signs: subtract smaller absolute value from larger, take the sign of the larger.

Examples:

• $-5 + (-3) = -8$ (same signs → add, keep −)
• $-5 + 2 = -3$ (different → $5 - 2 = 3$, sign of $-5$ so −)
• $7 - 10 = 7 + (-10) = -3$

The double-sign trap

$5 - (-3)$ ⇒ subtracting a negative = adding → $5 + 3 = 8$. $-2 - (-7)$ ⇒ $-2 + 7 = 5$.

Common mistakes

1. Forgetting the sign before parentheses: $-(3 - 5) = -3 + 5 = 2$ (the − distributes).
2. Confusing subtraction and negative sign: $-5 - 3$ means ”$-5$ minus $3$” = $-8$, not $-5 \times 3$.

?À toi de jouer

What is (−4) × (−5) + (−3) × 2?

A.14B.26C.−26D.−14

Valider