Dividing Mixed Numbers
To divide mixed numbers, follow two steps: convert each mixed number to an improper fraction, then apply the Keep-Change-Flip rule for fraction division.
Step-by-Step
- Convert all mixed numbers to improper fractions.
- Keep the first fraction unchanged.
- Change ÷ to ×.
- Flip the second fraction.
- Multiply and simplify.
Worked Examples
Easy: 3½ ÷ 1¾
3½ = 7/2. 1¾ = 7/4. KCF: 7/2 × 4/7 = 28/14 = 2
Medium: 2⅔ ÷ 1⅓
2⅔ = 8/3. 1⅓ = 4/3. KCF: 8/3 × 3/4 = 24/12 = 2
Advanced: 4¼ ÷ 2⅙
4¼ = 17/4. 2⅙ = 23/9. KCF: 17/4 × 9/23 = 153/92 = 1 61/92
Key Takeaways
- Always convert to improper fractions first.
- Apply KCF (Keep, Change, Flip) exactly as with fraction division.
- Simplify before multiplying where possible to keep numbers small.
- Check: multiply the answer by the divisor — you should recover the dividend.
Practice Questions
- Calculate 2½ ÷ 1¼.
- Calculate 3¾ ÷ 1½.
- Calculate 5⅓ ÷ 2⅔.
- A piece of fabric 4½ m long is cut into pieces of 1½ m each. How many pieces?
- Calculate 6¼ ÷ 2½.