Pre-Algebra
Numbers and operations
Adding and subtracting integers
20 practice questions
0 video lessons
Theory + worked examples
Adding and Subtracting Integers
California Pre-Algebra • Standard 7.NS.1 • Numbers & Operations
Adding and Subtracting Integers is a topic in Numbers & Operations in the California Common Core State Standards. It is aligned to Standard 7.NS.1, which requires students to add and subtract integers using the sign rules and by adding the opposite.
To add or subtract integers, combine same signs, subtract different signs, and rewrite subtraction as adding the opposite.
Theory
Rules for adding and subtracting integers:
- Same signs: add the values, keep the sign.
- Different signs: subtract, keep the sign of the larger.
- Subtracting is the same as adding the opposite.
\(a-b=a+(-b)\) turns every subtraction into an addition.
Adding moves along the number line.
The sign rules.
Subtraction as addition:
\[a-b=a+(-b)\]
Two negatives in a row become a plus.
How to add or subtract integers
- Rewrite subtraction as adding the opposite.
- Same signs: add and keep the sign.
- Different signs: subtract and take the larger sign.
- Check on a number line if unsure.
Example 1 — Same signs
Find \(-4+(-5)\).
Solution
Same sign: add and keep the sign.
| \(-4+(-5)\) | \(=\) | \(-9\) |
Example 2 — Different signs
Find \(-8+3\).
Solution
Subtract and keep the sign of the larger absolute value.
| \(-8+3\) | \(=\) | \(-5\) |
Example 3 — Add the opposite
Find \(6-(-2)\).
Solution
Subtracting is adding the opposite.
| \(6-(-2)\) | \(=\) | \(6+2=8\) |
Example 4 — Context
The temperature is \(-3^\circ\) and drops \(5^\circ\). Find the new temp.
Solution
Dropping means subtract.
| \(-3-5\) | \(=\) | \(-8^\circ\) |
Common pitfalls
\(6-(-2)=8\), not \(4\) — two minuses make a plus.
Different signs subtract; don't just add the digits.
Keep the sign of the larger absolute value.
Frequently asked questions
How do I add integers with the same sign?
Add the values and keep the common sign.
How do I subtract an integer?
Add its opposite.
What is \(-4+(-5)\)?
\(-9\).
What is \(6-(-2)\)?
\(8\).
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