Use integer sign rules first, then use fraction or mixed number procedures.
When signs are different, subtract the absolute values.
When signs are the same, add the absolute values and keep that sign.
For mixed numbers, find a common denominator before combining fraction parts.
💡 Main Idea
Adding signed mixed numbers works just like adding signed integers. First decide whether the signs are the same or different. If the signs are different, subtract the absolute values and keep the sign of the number with the larger absolute value. If the signs are the same, add the absolute values and keep that sign. Then use fraction rules carefully with common denominators.
✏️ Worked Examples – Fraction Models - Positive and Negative Mixed Numbers
Step 4: The negative number has the greater absolute value, so the answer is negative.
Final Answer:
\(\displaystyle \boxed{-2\frac{1}{2}}\)
🧠 Math Vocabulary
Mixed Number: A number made of a whole number and a fraction.
Absolute Value: The distance a number is from zero.
Common Denominator: A shared denominator used to combine fractions.
Unlike Denominators: Fractions with different denominators.
Zero Pair: A positive amount and an equal negative amount that cancel to zero.
📚 What You Should Already Know
Students should already know integer sign rules, how to compare absolute values, and how to find a common denominator when adding or subtracting fractions and mixed numbers.
🚀 What Comes Next
Next, students can apply these same ideas to signed fraction expressions, multi-step rational number problems, and word problems involving gains, losses, temperature, and elevation.
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