Addition of Improper Fractions worksheet for Grade 6 students.

Let's solve each of these addition of mixed numbers (improper fractions) problems step by step.

We will follow this process for each:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator.
3. Add the fractions.
4. Simplify and convert back to a mixed number if needed.

---

i. $ 4\frac{5}{6} + 2\frac{5}{9} $

Step 1: Convert to improper fractions:
- $ 4\frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6} $
- $ 2\frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{18 + 5}{9} = \frac{23}{9} $

Step 2: Find LCM of 6 and 9 → LCM is 18.

Convert:
- $ \frac{29}{6} = \frac{29 \times 3}{18} = \frac{87}{18} $
- $ \frac{23}{9} = \frac{23 \times 2}{18} = \frac{46}{18} $

Step 3: Add:
- $ \frac{87}{18} + \frac{46}{18} = \frac{133}{18} $

Step 4: Convert to mixed number:
- $ \frac{133}{18} = 7\frac{7}{18} $ (since $ 18 \times 7 = 126 $, remainder 7)

✔ Answer: $ 7\frac{7}{18} $

---

ii. $ 4\frac{3}{6} + 2\frac{5}{9} $

First simplify $ \frac{3}{6} = \frac{1}{2} $, so $ 4\frac{3}{6} = 4\frac{1}{2} $

Now:
- $ 4\frac{1}{2} = \frac{9}{2} $
- $ 2\frac{5}{9} = \frac{23}{9} $

LCM of 2 and 9 is 18.

- $ \frac{9}{2} = \frac{81}{18} $
- $ \frac{23}{9} = \frac{46}{18} $

Add: $ \frac{81 + 46}{18} = \frac{127}{18} $

Convert: $ 127 \div 18 = 7 $ remainder $ 1 $ → $ 7\frac{1}{18} $

✔ Answer: $ 7\frac{1}{18} $

---

iii. $ 4\frac{1}{6} + 3\frac{1}{8} $

Convert:
- $ 4\frac{1}{6} = \frac{25}{6} $
- $ 3\frac{1}{8} = \frac{25}{8} $

LCM of 6 and 8 is 24.

- $ \frac{25}{6} = \frac{100}{24} $
- $ \frac{25}{8} = \frac{75}{24} $

Add: $ \frac{100 + 75}{24} = \frac{175}{24} $

Convert: $ 175 \div 24 = 7 $ remainder $ 7 $ → $ 7\frac{7}{24} $

✔ Answer: $ 7\frac{7}{24} $

---

iv. $ 3\frac{3}{7} + 2\frac{4}{9} $

Convert:
- $ 3\frac{3}{7} = \frac{24}{7} $
- $ 2\frac{4}{9} = \frac{22}{9} $

LCM of 7 and 9 is 63.

- $ \frac{24}{7} = \frac{24 \times 9}{63} = \frac{216}{63} $
- $ \frac{22}{9} = \frac{22 \times 7}{63} = \frac{154}{63} $

Add: $ \frac{216 + 154}{63} = \frac{370}{63} $

Convert: $ 370 \div 63 = 5 $ remainder $ 55 $ → $ 5\frac{55}{63} $

Can we simplify $ \frac{55}{63} $? GCD of 55 and 63 is 1 → already simplified.

✔ Answer: $ 5\frac{55}{63} $

---

v. $ 2\frac{2}{7} + 3\frac{1}{8} $

Convert:
- $ 2\frac{2}{7} = \frac{16}{7} $
- $ 3\frac{1}{8} = \frac{25}{8} $

LCM of 7 and 8 is 56.

- $ \frac{16}{7} = \frac{128}{56} $
- $ \frac{25}{8} = \frac{175}{56} $

Add: $ \frac{128 + 175}{56} = \frac{303}{56} $

Convert: $ 303 \div 56 = 5 $ remainder $ 23 $ → $ 5\frac{23}{56} $

✔ Answer: $ 5\frac{23}{56} $

---

vi. $ 3\frac{1}{6} + 2\frac{3}{8} $

Convert:
- $ 3\frac{1}{6} = \frac{19}{6} $
- $ 2\frac{3}{8} = \frac{19}{8} $

LCM of 6 and 8 is 24.

- $ \frac{19}{6} = \frac{76}{24} $
- $ \frac{19}{8} = \frac{57}{24} $

Add: $ \frac{76 + 57}{24} = \frac{133}{24} $

Convert: $ 133 \div 24 = 5 $ remainder $ 13 $ → $ 5\frac{13}{24} $

✔ Answer: $ 5\frac{13}{24} $

---

vii. $ 3\frac{5}{6} + 2\frac{3}{8} $

Convert:
- $ 3\frac{5}{6} = \frac{23}{6} $
- $ 2\frac{3}{8} = \frac{19}{8} $

LCM of 6 and 8 is 24.

- $ \frac{23}{6} = \frac{92}{24} $
- $ \frac{19}{8} = \frac{57}{24} $

Add: $ \frac{92 + 57}{24} = \frac{149}{24} $

Convert: $ 149 \div 24 = 6 $ remainder $ 5 $ → $ 6\frac{5}{24} $

✔ Answer: $ 6\frac{5}{24} $

---

viii. $ 3\frac{5}{6} + 2\frac{2}{9} $

Convert:
- $ 3\frac{5}{6} = \frac{23}{6} $
- $ 2\frac{2}{9} = \frac{20}{9} $

LCM of 6 and 9 is 18.

- $ \frac{23}{6} = \frac{69}{18} $
- $ \frac{20}{9} = \frac{40}{18} $

Add: $ \frac{69 + 40}{18} = \frac{109}{18} $

Convert: $ 109 \div 18 = 6 $ remainder $ 1 $ → $ 6\frac{1}{18} $

✔ Answer: $ 6\frac{1}{18} $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| i. | $ 7\frac{7}{18} $ |
| ii. | $ 7\frac{1}{18} $ |
| iii. | $ 7\frac{7}{24} $ |
| iv. | $ 5\frac{55}{63} $ |
| v. | $ 5\frac{23}{56} $ |
| vi. | $ 5\frac{13}{24} $ |
| vii. | $ 6\frac{5}{24} $ |
| viii. | $ 6\frac{1}{18} $ |

---

🔍 Summary Tips:

- Always convert mixed numbers to improper fractions first.
- Find the least common denominator (LCD).
- Add numerators after converting.
- Simplify and convert back to mixed number.

Let me know if you'd like a visual explanation or printable version!