Pre-Algebra
Numbers and operations
Adding and subtracting rational numbers
20 practice questions
0 video lessons
Theory + worked examples
Adding and Subtracting Rational Numbers
California Pre-Algebra • Standard 7.NS.1 • Numbers & Operations
Adding and Subtracting Rational Numbers 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 rational numbers, including fractions and decimals.
To add or subtract rational numbers, use a common denominator for fractions and apply the integer sign rules.
Theory
To add or subtract rational numbers:
- Write fractions over a common denominator.
- Add or subtract the numerators (or line up decimals).
- Apply the integer sign rules and simplify.
Subtracting a rational means adding its opposite.
Adding fractions.
Signs work as with integers.
Common denominator:
\[\dfrac{a}{c}\pm\dfrac{b}{c}=\dfrac{a\pm b}{c}\]
Line up decimal points when adding decimals.
How to add or subtract rationals
- Find a common denominator for fractions.
- Rewrite each fraction.
- Combine numerators with the sign rules.
- Simplify the result.
Example 1 — Common denominator
Find \(\dfrac{1}{4}+\dfrac{1}{6}\).
Solution
LCD is \(12\).
| \(\dfrac{3}{12}+\dfrac{2}{12}\) | \(=\) | \(\dfrac{5}{12}\) |
Example 2 — Negative fraction
Find \(-\dfrac{2}{3}+\dfrac{1}{3}\).
Solution
Same denominator; different signs.
| \(-\dfrac{2}{3}+\dfrac{1}{3}\) | \(=\) | \(-\dfrac{1}{3}\) |
Example 3 — Decimals
Find \(2.5+(-1.8)\).
Solution
Different signs: subtract.
| \(2.5-1.8\) | \(=\) | \(0.7\) |
Example 4 — Subtract
Find \(\dfrac{3}{4}-\left(-\dfrac{1}{4}\right)\).
Solution
Add the opposite.
| \(\dfrac{3}{4}+\dfrac{1}{4}\) | \(=\) | \(1\) |
Common pitfalls
Only add numerators — the common denominator stays.
Need a common denominator before adding fractions.
Line up decimal points, don't just append digits.
Frequently asked questions
How do I add fractions?
Use a common denominator, then add the numerators.
Do the sign rules change for fractions?
No, they match the integer rules.
What is \(\dfrac{1}{4}+\dfrac{1}{6}\)?
\(\dfrac{5}{12}\).
How do I subtract a negative fraction?
Add its opposite.
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