Grade 6 math worksheet for adding mixed numbers, provided by K5 Learning.

Let's solve each problem on the "Adding Mixed Numbers" worksheet step by step. The goal is to add mixed numbers (a whole number and a fraction) by converting them into improper fractions, finding a common denominator, adding, and then simplifying back into a mixed number if needed.

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Problem 1:

$3\frac{1}{5} + 7\frac{5}{11}$

Step 1: Convert to improper fractions
- $3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}$
- $7\frac{5}{11} = \frac{7 \times 11 + 5}{11} = \frac{82}{11}$

Step 2: Find common denominator
LCM of 5 and 11 is 55.

Convert both:
- $\frac{16}{5} = \frac{16 \times 11}{5 \times 11} = \frac{176}{55}$
- $\frac{82}{11} = \frac{82 \times 5}{11 \times 5} = \frac{410}{55}$

Step 3: Add
$\frac{176}{55} + \frac{410}{55} = \frac{586}{55}$

Step 4: Convert to mixed number
$586 \div 55 = 10$ remainder $36$, so $10\frac{36}{55}$

✔ Answer: $10\frac{36}{55}$

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Problem 2:

$4\frac{10}{12} + 6\frac{5}{6}$

Simplify first:
- $4\frac{10}{12} = 4\frac{5}{6}$ (since $\frac{10}{12} = \frac{5}{6}$)

Now:
$4\frac{5}{6} + 6\frac{5}{6} = (4+6) + (\frac{5}{6} + \frac{5}{6}) = 10 + \frac{10}{6}$

$\frac{10}{6} = 1\frac{4}{6} = 1\frac{2}{3}$

So total: $10 + 1\frac{2}{3} = 11\frac{2}{3}$

✔ Answer: $11\frac{2}{3}$

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Problem 3:

$17\frac{1}{2} + 13\frac{1}{3}$

Convert to improper fractions:
- $17\frac{1}{2} = \frac{35}{2}$
- $13\frac{1}{3} = \frac{40}{3}$

Common denominator: LCM of 2 and 3 is 6
- $\frac{35}{2} = \frac{105}{6}$
- $\frac{40}{3} = \frac{80}{6}$

Add: $\frac{105}{6} + \frac{80}{6} = \frac{185}{6}$

Convert: $185 \div 6 = 30$ remainder $5$, so $30\frac{5}{6}$

✔ Answer: $30\frac{5}{6}$

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Problem 4:

$15\frac{6}{12} + 16\frac{3}{4}$

Simplify:
- $15\frac{6}{12} = 15\frac{1}{2}$ (since $\frac{6}{12} = \frac{1}{2}$)
- $16\frac{3}{4}$ stays same

Now: $15\frac{1}{2} + 16\frac{3}{4}$

Convert:
- $15\frac{1}{2} = \frac{31}{2}$
- $16\frac{3}{4} = \frac{67}{4}$

Common denominator: 4
- $\frac{31}{2} = \frac{62}{4}$
- $\frac{67}{4}$ remains

Add: $\frac{62}{4} + \frac{67}{4} = \frac{129}{4}$

Convert: $129 \div 4 = 32$ remainder $1$, so $32\frac{1}{4}$

✔ Answer: $32\frac{1}{4}$

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Problem 5:

$20\frac{1}{4} + 14\frac{1}{8}$

Convert:
- $20\frac{1}{4} = \frac{81}{4}$
- $14\frac{1}{8} = \frac{113}{8}$

Common denominator: 8
- $\frac{81}{4} = \frac{162}{8}$
- $\frac{113}{8}$ stays

Add: $\frac{162}{8} + \frac{113}{8} = \frac{275}{8}$

Convert: $275 \div 8 = 34$ remainder $3$, so $34\frac{3}{8}$

✔ Answer: $34\frac{3}{8}$

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Problem 6:

$18\frac{3}{4} + 8\frac{1}{2}$

Convert:
- $18\frac{3}{4} = \frac{75}{4}$
- $8\frac{1}{2} = \frac{17}{2}$

Common denominator: 4
- $\frac{17}{2} = \frac{34}{4}$

Add: $\frac{75}{4} + \frac{34}{4} = \frac{109}{4}$

Convert: $109 \div 4 = 27$ remainder $1$, so $27\frac{1}{4}$

✔ Answer: $27\frac{1}{4}$

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Problem 7:

$3\frac{1}{10} + 8\frac{8}{10}$

Same denominators!
Add whole parts: $3 + 8 = 11$
Add fractions: $\frac{1}{10} + \frac{8}{10} = \frac{9}{10}$

Total: $11\frac{9}{10}$

✔ Answer: $11\frac{9}{10}$

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Problem 8:

$12\frac{2}{5} + 16\frac{2}{5}$

Same denominator:
Whole parts: $12 + 16 = 28$
Fractions: $\frac{2}{5} + \frac{2}{5} = \frac{4}{5}$

Total: $28\frac{4}{5}$

✔ Answer: $28\frac{4}{5}$

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Problem 9:

$1\frac{1}{3} + 11\frac{2}{3}$

Same denominator:
Whole parts: $1 + 11 = 12$
Fractions: $\frac{1}{3} + \frac{2}{3} = \frac{3}{3} = 1$

Add: $12 + 1 = 13$

✔ Answer: $13$

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Problem 10:

$14\frac{1}{4} + 17\frac{3}{4}$

Same denominator:
Whole parts: $14 + 17 = 31$
Fractions: $\frac{1}{4} + \frac{3}{4} = \frac{4}{4} = 1$

Add: $31 + 1 = 32$

✔ Answer: $32$

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✔ Final Answers:

1. $10\frac{36}{55}$
2. $11\frac{2}{3}$
3. $30\frac{5}{6}$
4. $32\frac{1}{4}$
5. $34\frac{3}{8}$
6. $27\frac{1}{4}$
7. $11\frac{9}{10}$
8. $28\frac{4}{5}$
9. $13$
10. $32$

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