Integer Operations

Grade 6 · Math · Study Guide

Master adding, subtracting, multiplying, and dividing positive and negative integers.

Integers are whole numbers and their opposites: ..., -3, -2, -1, 0, 1, 2, 3, ... The number line is your best friend here. Positive numbers are to the right of zero, negative numbers are to the left.

When adding integers, think of it as walking on a number line. Start at the first number and move right for positive, left for negative. Adding two positives gives a positive. Adding two negatives gives a negative (and you add the absolute values). Adding a positive and a negative? Subtract the smaller absolute value from the larger, and keep the sign of the bigger absolute value.

Subtracting an integer is the same as adding its opposite. So 5 - (-3) = 5 + 3 = 8. The 'keep, change, change' trick: KEEP the first number, CHANGE subtraction to addition, CHANGE the sign of the second number.

For multiplication and division, the rules are clean and simple: same signs give a positive result, different signs give a negative result. So (-4) × (-3) = +12, and (-15) ÷ 3 = -5. These rules apply to division exactly the same way as multiplication.

Integer Multiplication/Division Sign Rules
First Sign	Second Sign	Result Sign	Example
+	+	+	4 × 3 = 12
+	−	−	4 × (−3) = −12
−	+	−	(−4) × 3 = −12
−	−	+	(−4) × (−3) = 12

Key terms

Integer: Any whole number, its opposite, or zero — includes ...-2, -1, 0, 1, 2...
Absolute Value: The distance of a number from zero on the number line — always positive
Opposite: Two numbers the same distance from zero but on different sides — like 5 and -5
Additive Inverse: The opposite of a number; any number plus its additive inverse equals zero

Flashcards

Adding integers: same signs: Add absolute values, keep the common sign — e.g. (-4)+(-3) = -7
Adding integers: different signs: Subtract absolute values, keep sign of the larger — e.g. (-7)+3 = -4
Subtracting integers (KCC): Keep the first number, Change to addition, Change the second sign — e.g. 5-(-3) = 5+3 = 8
Multiplying/dividing: same signs: Result is POSITIVE — e.g. (-3)×(-4) = 12
Multiplying/dividing: different signs: Result is NEGATIVE — e.g. (-3)×4 = -12
Absolute value: Distance from zero — always positive. |−8| = 8, |5| = 5

Practice questions

What is (-8) + 3?
1. -5
2. 5
3. -11
4. 11
Show answer
Answer: -5
Different signs: subtract |8|-|3|=5, keep sign of the larger absolute value (negative). Answer: -5.
What is 4 - (-6)?
1. 10
2. -2
3. 2
4. -10
Show answer
Answer: 10
KCC: Keep 4, Change to +, Change -6 to +6. So 4 + 6 = 10.
The product of two negative integers is always negative.
Show answer
Answer: False
Two negative integers multiplied give a POSITIVE result. (-3)×(-4)=+12.
(-7) × (-5) = ___
Show answer
Answer: 35
Same signs (both negative) → positive result. 7×5=35, so (-7)×(-5)=+35.
What is (-36) ÷ 4?
1. -9
2. 9
3. -32
4. 40
Show answer
Answer: -9
Different signs (negative ÷ positive) → negative result. 36÷4=9, so the answer is -9.

Fun facts

Negative numbers weren't fully accepted by European mathematicians until the 1700s — they were called 'absurd' numbers!
Temperature below zero, debt, and below-sea-level elevation are all real-world uses of negative integers.

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