Signed numbers: the sign rule in 5 lines

Addition and subtraction

Same sign: add the absolute values, keep the common sign.

• $(+3) + (+5) = +8$
• $(-3) + (-5) = -8$

Different signs: subtract the smaller absolute value from the larger, keep the sign of the larger.

• $(+7) + (-3) = +4$ (7 > 3, keep +)
• $(-7) + (+3) = -4$ (7 > 3, keep −)

Subtracting = adding the opposite: $(a) - (b) = (a) + (-b)$

• $5 - (-3) = 5 + 3 = 8$
• $-5 - 3 = -5 + (-3) = -8$

Multiplication and division: the sign rule

$\begin{array}{c|c|c} & + & - \\ \hline + & + & - \\ - & - & + \end{array}$

• Same sign ⇒ positive
• Different signs ⇒ negative

Examples:

• $(+3) \times (+4) = +12$
• $(-3) \times (-4) = +12$
• $(-3) \times (+4) = -12$
• $(-12) \div (-3) = +4$

Count the minuses (product of several)

For a product of several numbers:

• Even number of ”−” ⇒ result positive
• Odd number of ”−” ⇒ result negative

Example: $(-2) \times 3 \times (-4) \times (-1) = -24$ (3 minus signs, odd).

Careful: power of a negative

$(-2)^2 = (-2) \times (-2) = +4$ (parentheses, whole thing is squared)

$-2^2 = -(2 \times 2) = -4$ (no parentheses, only 2 is squared, − stays)

⚠️ Important difference!

Common mistakes

1. $5 - (-3) = 2$ instead of $8$ (double negation).
2. Adding as if all positive.
3. $(-3)^2 = -9$ (wrong, it’s $+9$).
4. Forgetting the even/odd rule in a product of many factors.

?À toi de jouer

(−4) × (−3) × (+2) × (−1) = ?

A.−24B.+24C.−10D.+10

Valider