Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets - Free Printable

To solve the problems involving the addition of mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Simplify the result, converting back to a mixed number if necessary.

Let's solve each problem step by step.

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Problem 1: \( 2 \frac{1}{4} + 3 \frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- \( 3 \frac{1}{3} = 3 + \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3} \)

#### Step 2: Find a common denominator
The denominators are 4 and 3. The least common denominator (LCD) is 12.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \)
- \( \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \)

#### Step 4: Add the fractions
\[ \frac{27}{12} + \frac{40}{12} = \frac{27 + 40}{12} = \frac{67}{12} \]

#### Step 5: Convert back to a mixed number
\[ \frac{67}{12} = 5 \frac{7}{12} \]

Answer: \( 5 \frac{7}{12} \)

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Problem 2: \( 5 \frac{1}{3} + 1 \frac{2}{5} \)

#### Step 1: Convert to improper fractions
- \( 5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \)
- \( 1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5} \)

#### Step 2: Find a common denominator
The denominators are 3 and 5. The LCD is 15.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{16}{3} = \frac{16 \times 5}{3 \times 5} = \frac{80}{15} \)
- \( \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \)

#### Step 4: Add the fractions
\[ \frac{80}{15} + \frac{21}{15} = \frac{80 + 21}{15} = \frac{101}{15} \]

#### Step 5: Convert back to a mixed number
\[ \frac{101}{15} = 6 \frac{11}{15} \]

Answer: \( 6 \frac{11}{15} \)

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Problem 3: \( 4 \frac{1}{2} + 2 \frac{1}{5} \)

#### Step 1: Convert to improper fractions
- \( 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \)
- \( 2 \frac{1}{5} = 2 + \frac{1}{5} = \frac{10}{5} + \frac{1}{5} = \frac{11}{5} \)

#### Step 2: Find a common denominator
The denominators are 2 and 5. The LCD is 10.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{9}{2} = \frac{9 \times 5}{2 \times 5} = \frac{45}{10} \)
- \( \frac{11}{5} = \frac{11 \times 2}{5 \times 2} = \frac{22}{10} \)

#### Step 4: Add the fractions
\[ \frac{45}{10} + \frac{22}{10} = \frac{45 + 22}{10} = \frac{67}{10} \]

#### Step 5: Convert back to a mixed number
\[ \frac{67}{10} = 6 \frac{7}{10} \]

Answer: \( 6 \frac{7}{10} \)

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Problem 4: \( 6 \frac{1}{3} + 3 \frac{1}{6} \)

#### Step 1: Convert to improper fractions
- \( 6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3} \)
- \( 3 \frac{1}{6} = 3 + \frac{1}{6} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6} \)

#### Step 2: Find a common denominator
The denominators are 3 and 6. The LCD is 6.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \)
- \( \frac{19}{6} = \frac{19}{6} \) (already has the denominator 6)

#### Step 4: Add the fractions
\[ \frac{38}{6} + \frac{19}{6} = \frac{38 + 19}{6} = \frac{57}{6} \]

#### Step 5: Simplify and convert back to a mixed number
\[ \frac{57}{6} = 9 \frac{3}{6} = 9 \frac{1}{2} \] (simplify \( \frac{3}{6} \) to \( \frac{1}{2} \))

Answer: \( 9 \frac{1}{2} \)

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Problem 5: \( 2 \frac{1}{7} + 2 \frac{3}{4} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{1}{7} = 2 + \frac{1}{7} = \frac{14}{7} + \frac{1}{7} = \frac{15}{7} \)
- \( 2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \)

#### Step 2: Find a common denominator
The denominators are 7 and 4. The LCD is 28.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{15}{7} = \frac{15 \times 4}{7 \times 4} = \frac{60}{28} \)
- \( \frac{11}{4} = \frac{11 \times 7}{4 \times 7} = \frac{77}{28} \)

#### Step 4: Add the fractions
\[ \frac{60}{28} + \frac{77}{28} = \frac{60 + 77}{28} = \frac{137}{28} \]

#### Step 5: Convert back to a mixed number
\[ \frac{137}{28} = 4 \frac{25}{28} \]

Answer: \( 4 \frac{25}{28} \)

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Problem 6: \( 7 \frac{1}{7} + 4 \frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 7 \frac{1}{7} = 7 + \frac{1}{7} = \frac{49}{7} + \frac{1}{7} = \frac{50}{7} \)
- \( 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{17}{4} \)

#### Step 2: Find a common denominator
The denominators are 7 and 4. The LCD is 28.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{50}{7} = \frac{50 \times 4}{7 \times 4} = \frac{200}{28} \)
- \( \frac{17}{4} = \frac{17 \times 7}{4 \times 7} = \frac{119}{28} \)

#### Step 4: Add the fractions
\[ \frac{200}{28} + \frac{119}{28} = \frac{200 + 119}{28} = \frac{319}{28} \]

#### Step 5: Convert back to a mixed number
\[ \frac{319}{28} = 11 \frac{11}{28} \]

Answer: \( 11 \frac{11}{28} \)

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Problem 7: \( 3 \frac{4}{5} + 6 \frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{4}{5} = 3 + \frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5} \)
- \( 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \)

#### Step 2: Find a common denominator
The denominators are 5 and 2. The LCD is 10.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{19}{5} = \frac{19 \times 2}{5 \times 2} = \frac{38}{10} \)
- \( \frac{13}{2} = \frac{13 \times 5}{2 \times 5} = \frac{65}{10} \)

#### Step 4: Add the fractions
\[ \frac{38}{10} + \frac{65}{10} = \frac{38 + 65}{10} = \frac{103}{10} \]

#### Step 5: Convert back to a mixed number
\[ \frac{103}{10} = 10 \frac{3}{10} \]

Answer: \( 10 \frac{3}{10} \)

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Problem 8: \( 2 \frac{3}{8} + 8 \frac{2}{6} \)

#### Step 1: Convert to improper fractions
- \( 2 \frac{3}{8} = 2 + \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8} \)
- \( 8 \frac{2}{6} = 8 + \frac{2}{6} = \frac{48}{6} + \frac{2}{6} = \frac{50}{6} \)

#### Step 2: Simplify \( \frac{50}{6} \)
\[ \frac{50}{6} = \frac{25}{3} \]

#### Step 3: Find a common denominator
The denominators are 8 and 3. The LCD is 24.

#### Step 4: Rewrite fractions with the common denominator
- \( \frac{19}{8} = \frac{19 \times 3}{8 \times 3} = \frac{57}{24} \)
- \( \frac{25}{3} = \frac{25 \times 8}{3 \times 8} = \frac{200}{24} \)

#### Step 5: Add the fractions
\[ \frac{57}{24} + \frac{200}{24} = \frac{57 + 200}{24} = \frac{257}{24} \]

#### Step 6: Convert back to a mixed number
\[ \frac{257}{24} = 10 \frac{17}{24} \]

Answer: \( 10 \frac{17}{24} \)

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Problem 9: \( 6 \frac{1}{8} + 5 \frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 6 \frac{1}{8} = 6 + \frac{1}{8} = \frac{48}{8} + \frac{1}{8} = \frac{49}{8} \)
- \( 5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3} \)

#### Step 2: Find a common denominator
The denominators are 8 and 3. The LCD is 24.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24} \)
- \( \frac{16}{3} = \frac{16 \times 8}{3 \times 8} = \frac{128}{24} \)

#### Step 4: Add the fractions
\[ \frac{147}{24} + \frac{128}{24} = \frac{147 + 128}{24} = \frac{275}{24} \]

#### Step 5: Convert back to a mixed number
\[ \frac{275}{24} = 11 \frac{11}{24} \]

Answer: \( 11 \frac{11}{24} \)

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Problem 10: \( 3 \frac{2}{5} + 4 \frac{1}{9} \)

#### Step 1: Convert to improper fractions
- \( 3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5} \)
- \( 4 \frac{1}{9} = 4 + \frac{1}{9} = \frac{36}{9} + \frac{1}{9} = \frac{37}{9} \)

#### Step 2: Find a common denominator
The denominators are 5 and 9. The LCD is 45.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{17}{5} = \frac{17 \times 9}{5 \times 9} = \frac{153}{45} \)
- \( \frac{37}{9} = \frac{37 \times 5}{9 \times 5} = \frac{185}{45} \)

#### Step 4: Add the fractions
\[ \frac{153}{45} + \frac{185}{45} = \frac{153 + 185}{45} = \frac{338}{45} \]

#### Step 5: Convert back to a mixed number
\[ \frac{338}{45} = 7 \frac{13}{45} \]

Answer: \( 7 \frac{13}{45} \)

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Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 5 \frac{7}{12} \\
2. & 6 \frac{11}{15} \\
3. & 6 \frac{7}{10} \\
4. & 9 \frac{1}{2} \\
5. & 4 \frac{25}{28} \\
6. & 11 \frac{11}{28} \\
7. & 10 \frac{3}{10} \\
8. & 10 \frac{17}{24} \\
9. & 11 \frac{11}{24} \\
10. & 7 \frac{13}{45} \\
\end{array}
}
\]