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, if necessary, and convert back to a mixed number if needed.

Let's solve each problem step by step.

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 7 \frac{1}{5} = 7 + \frac{1}{5} = \frac{35}{5} + \frac{1}{5} = \frac{36}{5} \)
- \( 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \)

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

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{36}{5} = \frac{36 \times 3}{5 \times 3} = \frac{108}{15} \)
- \( \frac{11}{3} = \frac{11 \times 5}{3 \times 5} = \frac{55}{15} \)

#### Step 4: Add the fractions
\[ \frac{108}{15} + \frac{55}{15} = \frac{108 + 55}{15} = \frac{163}{15} \]

#### Step 5: Convert back to a mixed number
\[ \frac{163}{15} = 10 \frac{13}{15} \]

Answer: \( 10 \frac{13}{15} \)

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Problem 2: \( 2 \frac{1}{4} + 8 \frac{2}{3} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \)
- \( 8 \frac{2}{3} = 8 + \frac{2}{3} = \frac{24}{3} + \frac{2}{3} = \frac{26}{3} \)

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

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \)
- \( \frac{26}{3} = \frac{26 \times 4}{3 \times 4} = \frac{104}{12} \)

#### Step 4: Add the fractions
\[ \frac{27}{12} + \frac{104}{12} = \frac{27 + 104}{12} = \frac{131}{12} \]

#### Step 5: Convert back to a mixed number
\[ \frac{131}{12} = 10 \frac{11}{12} \]

Answer: \( 10 \frac{11}{12} \)

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Problem 3: \( 9 \frac{1}{7} + 3 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{1}{7} = 9 + \frac{1}{7} = \frac{63}{7} + \frac{1}{7} = \frac{64}{7} \)
- \( 3 \frac{1}{2} = 3 + \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2} \)

#### Step 2: Find a common denominator
The denominators are 7 and 2. The LCD is 14.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{64}{7} = \frac{64 \times 2}{7 \times 2} = \frac{128}{14} \)
- \( \frac{7}{2} = \frac{7 \times 7}{2 \times 7} = \frac{49}{14} \)

#### Step 4: Add the fractions
\[ \frac{128}{14} + \frac{49}{14} = \frac{128 + 49}{14} = \frac{177}{14} \]

#### Step 5: Convert back to a mixed number
\[ \frac{177}{14} = 12 \frac{9}{14} \]

Answer: \( 12 \frac{9}{14} \)

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Problem 4: \( 6 \frac{3}{8} + 4 \frac{4}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 6 \frac{3}{8} = 6 + \frac{3}{8} = \frac{48}{8} + \frac{3}{8} = \frac{51}{8} \)
- \( 4 \frac{4}{5} = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5} \)

#### Step 2: Find a common denominator
The denominators are 8 and 5. The LCD is 40.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{51}{8} = \frac{51 \times 5}{8 \times 5} = \frac{255}{40} \)
- \( \frac{24}{5} = \frac{24 \times 8}{5 \times 8} = \frac{192}{40} \)

#### Step 4: Add the fractions
\[ \frac{255}{40} + \frac{192}{40} = \frac{255 + 192}{40} = \frac{447}{40} \]

#### Step 5: Convert back to a mixed number
\[ \frac{447}{40} = 11 \frac{7}{40} \]

Answer: \( 11 \frac{7}{40} \)

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Problem 5: \( 4 \frac{2}{9} + 10 \frac{4}{7} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 4 \frac{2}{9} = 4 + \frac{2}{9} = \frac{36}{9} + \frac{2}{9} = \frac{38}{9} \)
- \( 10 \frac{4}{7} = 10 + \frac{4}{7} = \frac{70}{7} + \frac{4}{7} = \frac{74}{7} \)

#### Step 2: Find a common denominator
The denominators are 9 and 7. The LCD is 63.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{38}{9} = \frac{38 \times 7}{9 \times 7} = \frac{266}{63} \)
- \( \frac{74}{7} = \frac{74 \times 9}{7 \times 9} = \frac{666}{63} \)

#### Step 4: Add the fractions
\[ \frac{266}{63} + \frac{666}{63} = \frac{266 + 666}{63} = \frac{932}{63} \]

#### Step 5: Convert back to a mixed number
\[ \frac{932}{63} = 14 \frac{50}{63} \]

Answer: \( 14 \frac{50}{63} \)

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Problem 6: \( 5 \frac{4}{11} + 7 \frac{1}{8} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{4}{11} = 5 + \frac{4}{11} = \frac{55}{11} + \frac{4}{11} = \frac{59}{11} \)
- \( 7 \frac{1}{8} = 7 + \frac{1}{8} = \frac{56}{8} + \frac{1}{8} = \frac{57}{8} \)

#### Step 2: Find a common denominator
The denominators are 11 and 8. The LCD is 88.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{59}{11} = \frac{59 \times 8}{11 \times 8} = \frac{472}{88} \)
- \( \frac{57}{8} = \frac{57 \times 11}{8 \times 11} = \frac{627}{88} \)

#### Step 4: Add the fractions
\[ \frac{472}{88} + \frac{627}{88} = \frac{472 + 627}{88} = \frac{1099}{88} \]

#### Step 5: Convert back to a mixed number
\[ \frac{1099}{88} = 12 \frac{43}{88} \]

Answer: \( 12 \frac{43}{88} \)

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Problem 7: \( 11 \frac{8}{9} + 5 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 11 \frac{8}{9} = 11 + \frac{8}{9} = \frac{99}{9} + \frac{8}{9} = \frac{107}{9} \)
- \( 5 \frac{1}{4} = 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \)

#### Step 2: Find a common denominator
The denominators are 9 and 4. The LCD is 36.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{107}{9} = \frac{107 \times 4}{9 \times 4} = \frac{428}{36} \)
- \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)

#### Step 4: Add the fractions
\[ \frac{428}{36} + \frac{189}{36} = \frac{428 + 189}{36} = \frac{617}{36} \]

#### Step 5: Convert back to a mixed number
\[ \frac{617}{36} = 17 \frac{5}{36} \]

Answer: \( 17 \frac{5}{36} \)

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Problem 8: \( 9 \frac{3}{10} + 4 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{3}{10} = 9 + \frac{3}{10} = \frac{90}{10} + \frac{3}{10} = \frac{93}{10} \)
- \( 4 \frac{1}{5} = 4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5} \)

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

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{93}{10} = \frac{93}{10} \)
- \( \frac{21}{5} = \frac{21 \times 2}{5 \times 2} = \frac{42}{10} \)

#### Step 4: Add the fractions
\[ \frac{93}{10} + \frac{42}{10} = \frac{93 + 42}{10} = \frac{135}{10} \]

#### Step 5: Simplify and convert back to a mixed number
\[ \frac{135}{10} = 13 \frac{5}{10} = 13 \frac{1}{2} \]

Answer: \( 13 \frac{1}{2} \)

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Problem 9: \( 7 \frac{5}{12} + 5 \frac{7}{8} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 7 \frac{5}{12} = 7 + \frac{5}{12} = \frac{84}{12} + \frac{5}{12} = \frac{89}{12} \)
- \( 5 \frac{7}{8} = 5 + \frac{7}{8} = \frac{40}{8} + \frac{7}{8} = \frac{47}{8} \)

#### Step 2: Find a common denominator
The denominators are 12 and 8. The LCD is 24.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{89}{12} = \frac{89 \times 2}{12 \times 2} = \frac{178}{24} \)
- \( \frac{47}{8} = \frac{47 \times 3}{8 \times 3} = \frac{141}{24} \)

#### Step 4: Add the fractions
\[ \frac{178}{24} + \frac{141}{24} = \frac{178 + 141}{24} = \frac{319}{24} \]

#### Step 5: Convert back to a mixed number
\[ \frac{319}{24} = 13 \frac{7}{24} \]

Answer: \( 13 \frac{7}{24} \)

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Problem 10: \( 8 \frac{7}{12} + 9 \frac{1}{6} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 8 \frac{7}{12} = 8 + \frac{7}{12} = \frac{96}{12} + \frac{7}{12} = \frac{103}{12} \)
- \( 9 \frac{1}{6} = 9 + \frac{1}{6} = \frac{54}{6} + \frac{1}{6} = \frac{55}{6} \)

#### Step 2: Find a common denominator
The denominators are 12 and 6. The LCD is 12.

#### Step 3: Rewrite the fractions with the common denominator
- \( \frac{103}{12} = \frac{103}{12} \)
- \( \frac{55}{6} = \frac{55 \times 2}{6 \times 2} = \frac{110}{12} \)

#### Step 4: Add the fractions
\[ \frac{103}{12} + \frac{110}{12} = \frac{103 + 110}{12} = \frac{213}{12} \]

#### Step 5: Simplify and convert back to a mixed number
\[ \frac{213}{12} = 17 \frac{9}{12} = 17 \frac{3}{4} \]

Answer: \( 17 \frac{3}{4} \)

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Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 10 \frac{13}{15} \\
2. & 10 \frac{11}{12} \\
3. & 12 \frac{9}{14} \\
4. & 11 \frac{7}{40} \\
5. & 14 \frac{50}{63} \\
6. & 12 \frac{43}{88} \\
7. & 17 \frac{5}{36} \\
8. & 13 \frac{1}{2} \\
9. & 13 \frac{7}{24} \\
10. & 17 \frac{3}{4} \\
\end{array}
}
\]