Addition, subtraction, multiplication, and division of integers all come down to how you handle the signs.
On the number line, adding a positive moves right and adding a negative moves left, while subtracting means adding the opposite.
For products and quotients, like signs give a positive and unlike signs a negative, so an even number of negatives stays positive and an odd number turns it negative.
Slide the two numbers here and watch where the arrows point and how the sign of the result changes.
Addition & Subtraction
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Addition on the number line — blue (a), red (b), gold (result)
3
-5
👀 Addition via the Number Line
①Adding a positive moves right
②Adding a negative moves left
③Subtraction = adding the opposite sign: a - b = a + (-b)
Sign Rules — Addition
Same Sign Addition
Same signs → add magnitudes, keep sign
(+3) + (+5) = +8, (-3) + (-5) = -8
Different Sign Addition
Different signs → subtract magnitudes, take sign of larger
(+3) + (-5) = -2, (-3) + (+5) = +2
💡 Converting Subtraction
①Any subtraction can be turned into addition
②a - b = a + (-b)
③Flip the sign and add
④Ex: 3 - (-5) = 3 + 5 = 8
Sign Rules — Multiplication & Division
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Multiplication sign rules — blue (positive), red (negative)
-3
-4
Sign Rules for × and ÷
(+)×(+)=+, (-)×(-)=+, (+)×(-)=-
Same signs → positive; different signs → negative (same for ÷)
Work It Out
Example 1
Compute (−7) + (+3) − (−5).
1
Turn subtraction into addition: −(−5) = +5.
(−7) + (+3) + (+5)
2
Add in order.
= −4 + 5 = 1
▸ 1
Subtraction becomes addition by flipping the sign.
Example 2
Compute (−2)³ × (−3).
1
(−2)³ = −8 (an odd power of a negative is negative).
(−2)³ = −8
2
(negative) × (negative) = (positive).
(−8) × (−3) = 24
▸ 24
Do powers first; a product of two negatives is positive.