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Adding and Subtracting Mixed Numbers
Lesson: Adding & Subtracting Mixed Numbers
Year 7 — adding and subtracting mixed numbers clearly and visually.
1. What are mixed numbers?
A mixed number has a whole number and a fraction. Example: 3 1/4.
To add or subtract mixed numbers, we usually convert them into improper fractions.
2. Method for adding mixed numbers
- Convert each mixed number to an improper fraction.
- Find a common denominator (if needed).
- Add the numerators.
- Simplify and convert back to a mixed number if needed.
Example: 1 2/5 + 2 3/10
Convert: 1 2/5 = 7/5, 2 3/10 = 23/10
LCM of 5 and 10 = 10
7/5 = 14/10, so add: 14/10 + 23/10 = 37/10
Convert back: 37/10 = 3 7/10
3. Method for subtracting mixed numbers
- Convert mixed numbers into improper fractions.
- Find a common denominator.
- Subtract the numerators.
- Simplify and convert back.
Example: 4 1/6 - 1 3/4
Convert: 4 1/6 = 25/6, 1 3/4 = 7/4
LCM of 6 and 4 = 12
25/6 = 50/12, 7/4 = 21/12
Subtract: 50/12 - 21/12 = 29/12
Convert back: 29/12 = 2 5/12
4. Shortcut: Adding wholes first
Sometimes you can add the whole numbers first, then the fractions separately.
Example: 3 1/8 + 2 5/8
Add wholes: 3 + 2 = 5
Add fractions: 1/8 + 5/8 = 6/8 = 3/4
Total = 5 3/4
5. Common mistakes
- Forgetting to convert to improper fractions before adding/subtracting.
- Not finding a common denominator.
- Leaving answers unsimplified.
6. Practice
2 3/4 + 1 2/35 1/5 - 2 4/53 1/6 + 4 5/126 2/3 - 3 1/91 3/8 + 2 7/16
Answers (teacher)
- LCM 12 →
2 3/4 = 11/4 = 33/12,1 2/3 = 5/3 = 20/12→53/12 = 4 5/12 5 1/5 = 26/5,2 4/5 = 14/5→26/5 - 14/5 = 12/5 = 2 2/5- LCM 12 →
3 1/6 = 19/6 = 38/12,4 5/12 = 53/12→91/12 = 7 7/12 - LCM 9 →
6 2/3 = 20/3 = 60/9,3 1/9 = 28/9→32/9 = 3 5/9 - LCM 16 →
1 3/8 = 11/8 = 22/16,2 7/16 = 39/16→61/16 = 3 13/16