Adding Integers Practice Problems & Conceptual Mastery
Adding integers involves combining directed numbers. Whether representing temperature changes, elevation shifts, or financial credits and debits, integer addition follows two clean rules based on sign agreement.
📝 Worked Step-by-Step Example
1. Identify Signs: Opposite signs (-14 and +9). 2. Subtract Absolute Values: |-14| - |9| = 14 - 9 = 5. 3. Assign Sign: |-14| > |9|, so the result is negative: -5 ✅.
🧠 Core Problem-Solving Strategies
1. Same Signs: Add and Keep
When both integers share the same sign, add their absolute values and attach the common sign.
2. Different Signs: Subtract and Take Greater Magnitude
Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger.
3. Number Line Movement
Start at the first number. Move right for positives and left for negatives.
📖 Key Mathematical Terms & Vocabulary
Absolute Value
The distance of a number from zero on the number line, always non-negative: |-x| = x.
Additive Inverse
A number that when added to a given number yields zero (e.g., -5 is the additive inverse of 5).
❓ Frequently Asked Questions
What is the rule for adding two negative integers?
Add their absolute values together and attach a negative sign: (-6) + (-8) = -14.
How do you add integers with different signs?
Subtract the smaller absolute value from the larger, then keep the sign of the larger absolute value.
What is an additive inverse?
Two numbers whose sum is zero, such as 7 and -7.
🗺️ Pedagogical Learning Roadmap
Adding Decimals→
Master core Adding Decimals concepts to build computational fluency.
PrerequisiteDividing Integers→
Master core Dividing Integers concepts to build computational fluency.
Next StepMultiplying Integers→
Advance to Multiplying Integers practice drills and timed challenges.
Next StepSigned Integers→
Advance to Signed Integers practice drills and timed challenges.
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