Mixed Numbers
Convert, add, and subtract mixed numbers.
Mixed Numbers
Mixed Numbers
What you'll learn
- To read, write, and convert between improper fractions and mixed numbers.
- To add and subtract mixed numbers with and without regrouping.
- To apply mixed numbers in measurement (2½ metres of cloth) and time (1¾ hours).
- To master NCERT Math-Magic 5, Chapter 4 problems involving wholes and parts together.
Key concepts
Level 1 — Conversion
Verbal: A mixed number has a whole part and a proper fraction: 2¾ means 2 + 3/4.
Symbolic: Improper → mixed: 11/4 = 2 remainder 3 → 2¾; Mixed → improper: 2¾ = (2×4 + 3)/4 = 11/4.
| Form | Example | Conversion |
|---|---|---|
| Mixed | 3⅕ | (3×5 + 1)/5 = 16/5 |
| Improper | 17/6 | 17 ÷ 6 = 2 R 5 → 2⅚ |
| Whole + fraction | 1 + 2/3 | 5/3 improper |
Level 2 — Add and subtract mixed numbers
Verbal: Add wholes to wholes and fractions to fractions; regroup if fraction sum ≥ 1.
Symbolic: 2⅓ + 1⅔ = (2+1) + (⅓+⅔) = 3 + 1 = 4
Real-life: Tailor uses 1¾ m + 2½ m of ribbon → convert to improper or add parts separately.
| Operation | Strategy |
|---|---|
| Like fractional parts | Add/subtract parts; adjust whole |
| Unlike parts | Convert to improper, find LCD, then convert back |
| Regrouping | Borrow 1 whole = denominator/denominator as fraction |
Worked example
Convert 23/5 to a mixed number.
Step 1 — 23 ÷ 5 = 4 remainder 3
Step 2 — 23/5 = 4⅗
Answer: 4⅗
Evaluate 3⅔ − 1¾
Step 1 — Convert: 3⅔ = 11/3; 1¾ = 7/4
Step 2 — LCD = 12: 44/12 − 21/12 = 23/12
Step 3 — 23/12 = 1 11/12
Answer: 1 11/12
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| 2⅓ + 1⅔ = 3⅔ | Adding fractions but not carrying whole | ⅓+⅔ = 1 → answer is 4 |
| 3¾ − 1½ = 2¼ without regrouping | Subtracting ½ from ¾ directly when needed | Regroup: 3¾ = 3 6/8 = 2 14/8... or use improper |
| Mixed number as 2/3/4 | Writing three numbers | 2¾ — one whole, one fraction |
| Forgetting to simplify fractional part | 2 4/8 left as final | Simplify to 2½ |
Quick check
- Write 17/4 as a mixed number.
- Evaluate: 2⅕ + 1⅖.
- 5 − 2⅓ = ? (hint: regroup 5 as 4 + 3/3 + …)
- Stretch: A recipe needs 2¾ cups flour; you used 1⅛ cups. How much more? (1⅝ cups)
Revision tip: Draw wholes as complete rectangles and fractions as shaded parts — seeing 1⅓ as one whole plus one-third prevents conversion errors.
Open the Practice tab for graded questions on Mixed Numbers.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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