Grade 6 Addition and Subtraction of Fractions Worksheets - free ... - Free Printable

Problem: Adding Mixed Numbers

The task is to solve the addition of mixed numbers for each problem listed in the worksheet. Below, I will solve each problem step by step.

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#### 1. \( 3 \frac{3}{4} + 7 \frac{5}{11} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 3 \frac{3}{4} = 3 + \frac{3}{4} = \frac{12}{4} + \frac{3}{4} = \frac{15}{4} \)
- \( 7 \frac{5}{11} = 7 + \frac{5}{11} = \frac{77}{11} + \frac{5}{11} = \frac{82}{11} \)

Step 2: Find a common denominator for \( \frac{15}{4} \) and \( \frac{82}{11} \).
- The least common denominator (LCD) of 4 and 11 is \( 44 \).

Step 3: Rewrite the fractions with the common denominator.
- \( \frac{15}{4} = \frac{15 \times 11}{4 \times 11} = \frac{165}{44} \)
- \( \frac{82}{11} = \frac{82 \times 4}{11 \times 4} = \frac{328}{44} \)

Step 4: Add the fractions.
- \( \frac{165}{44} + \frac{328}{44} = \frac{165 + 328}{44} = \frac{493}{44} \)

Step 5: Convert the improper fraction back to a mixed number.
- \( \frac{493}{44} = 11 \frac{9}{44} \) (since \( 493 \div 44 = 11 \) remainder \( 9 \))

Final Answer:
\[ \boxed{11 \frac{9}{44}} \]

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#### 2. \( 10 \frac{10}{12} + 6 \frac{3}{9} \)

Step 1: Simplify the fractions in the mixed numbers.
- \( \frac{10}{12} = \frac{5}{6} \) (simplify by dividing numerator and denominator by 2)
- \( \frac{3}{9} = \frac{1}{3} \) (simplify by dividing numerator and denominator by 3)

So, the problem becomes:
\[ 10 \frac{5}{6} + 6 \frac{1}{3} \]

Step 2: Convert the mixed numbers to improper fractions.
- \( 10 \frac{5}{6} = 10 + \frac{5}{6} = \frac{60}{6} + \frac{5}{6} = \frac{65}{6} \)
- \( 6 \frac{1}{3} = 6 + \frac{1}{3} = \frac{18}{3} + \frac{1}{3} = \frac{19}{3} \)

Step 3: Find a common denominator for \( \frac{65}{6} \) and \( \frac{19}{3} \).
- The LCD of 6 and 3 is \( 6 \).

Step 4: Rewrite the fractions with the common denominator.
- \( \frac{65}{6} \) remains \( \frac{65}{6} \)
- \( \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \)

Step 5: Add the fractions.
- \( \frac{65}{6} + \frac{38}{6} = \frac{65 + 38}{6} = \frac{103}{6} \)

Step 6: Convert the improper fraction back to a mixed number.
- \( \frac{103}{6} = 17 \frac{1}{6} \) (since \( 103 \div 6 = 17 \) remainder \( 1 \))

Final Answer:
\[ \boxed{17 \frac{1}{6}} \]

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#### 3. \( 17 \frac{3}{8} + 13 \frac{1}{3} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 17 \frac{3}{8} = 17 + \frac{3}{8} = \frac{136}{8} + \frac{3}{8} = \frac{139}{8} \)
- \( 13 \frac{1}{3} = 13 + \frac{1}{3} = \frac{39}{3} + \frac{1}{3} = \frac{40}{3} \)

Step 2: Find a common denominator for \( \frac{139}{8} \) and \( \frac{40}{3} \).
- The LCD of 8 and 3 is \( 24 \).

Step 3: Rewrite the fractions with the common denominator.
- \( \frac{139}{8} = \frac{139 \times 3}{8 \times 3} = \frac{417}{24} \)
- \( \frac{40}{3} = \frac{40 \times 8}{3 \times 8} = \frac{320}{24} \)

Step 4: Add the fractions.
- \( \frac{417}{24} + \frac{320}{24} = \frac{417 + 320}{24} = \frac{737}{24} \)

Step 5: Convert the improper fraction back to a mixed number.
- \( \frac{737}{24} = 30 \frac{17}{24} \) (since \( 737 \div 24 = 30 \) remainder \( 17 \))

Final Answer:
\[ \boxed{30 \frac{17}{24}} \]

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#### 4. \( 15 \frac{2}{3} + 16 \frac{3}{11} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 15 \frac{2}{3} = 15 + \frac{2}{3} = \frac{45}{3} + \frac{2}{3} = \frac{47}{3} \)
- \( 16 \frac{3}{11} = 16 + \frac{3}{11} = \frac{176}{11} + \frac{3}{11} = \frac{179}{11} \)

Step 2: Find a common denominator for \( \frac{47}{3} \) and \( \frac{179}{11} \).
- The LCD of 3 and 11 is \( 33 \).

Step 3: Rewrite the fractions with the common denominator.
- \( \frac{47}{3} = \frac{47 \times 11}{3 \times 11} = \frac{517}{33} \)
- \( \frac{179}{11} = \frac{179 \times 3}{11 \times 3} = \frac{537}{33} \)

Step 4: Add the fractions.
- \( \frac{517}{33} + \frac{537}{33} = \frac{517 + 537}{33} = \frac{1054}{33} \)

Step 5: Convert the improper fraction back to a mixed number.
- \( \frac{1054}{33} = 31 \frac{31}{33} \) (since \( 1054 \div 33 = 31 \) remainder \( 31 \))

Final Answer:
\[ \boxed{31 \frac{31}{33}} \]

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#### 5. \( 20 \frac{5}{6} + 14 \frac{1}{6} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 20 \frac{5}{6} = 20 + \frac{5}{6} = \frac{120}{6} + \frac{5}{6} = \frac{125}{6} \)
- \( 14 \frac{1}{6} = 14 + \frac{1}{6} = \frac{84}{6} + \frac{1}{6} = \frac{85}{6} \)

Step 2: Add the fractions.
- \( \frac{125}{6} + \frac{85}{6} = \frac{125 + 85}{6} = \frac{210}{6} \)

Step 3: Simplify the improper fraction.
- \( \frac{210}{6} = 35 \) (since \( 210 \div 6 = 35 \))

Final Answer:
\[ \boxed{35} \]

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#### 6. \( 18 \frac{2}{5} + 8 \frac{2}{9} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 18 \frac{2}{5} = 18 + \frac{2}{5} = \frac{90}{5} + \frac{2}{5} = \frac{92}{5} \)
- \( 8 \frac{2}{9} = 8 + \frac{2}{9} = \frac{72}{9} + \frac{2}{9} = \frac{74}{9} \)

Step 2: Find a common denominator for \( \frac{92}{5} \) and \( \frac{74}{9} \).
- The LCD of 5 and 9 is \( 45 \).

Step 3: Rewrite the fractions with the common denominator.
- \( \frac{92}{5} = \frac{92 \times 9}{5 \times 9} = \frac{828}{45} \)
- \( \frac{74}{9} = \frac{74 \times 5}{9 \times 5} = \frac{370}{45} \)

Step 4: Add the fractions.
- \( \frac{828}{45} + \frac{370}{45} = \frac{828 + 370}{45} = \frac{1198}{45} \)

Step 5: Convert the improper fraction back to a mixed number.
- \( \frac{1198}{45} = 26 \frac{28}{45} \) (since \( 1198 \div 45 = 26 \) remainder \( 28 \))

Final Answer:
\[ \boxed{26 \frac{28}{45}} \]

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#### 7. \( 3 \frac{3}{10} + 8 \frac{5}{10} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 3 \frac{3}{10} = 3 + \frac{3}{10} = \frac{30}{10} + \frac{3}{10} = \frac{33}{10} \)
- \( 8 \frac{5}{10} = 8 + \frac{5}{10} = \frac{80}{10} + \frac{5}{10} = \frac{85}{10} \)

Step 2: Add the fractions.
- \( \frac{33}{10} + \frac{85}{10} = \frac{33 + 85}{10} = \frac{118}{10} \)

Step 3: Simplify the improper fraction.
- \( \frac{118}{10} = 11 \frac{8}{10} = 11 \frac{4}{5} \) (simplify \( \frac{8}{10} \) to \( \frac{4}{5} \))

Final Answer:
\[ \boxed{11 \frac{4}{5}} \]

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#### 8. \( 12 \frac{5}{6} + 16 \frac{2}{3} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 12 \frac{5}{6} = 12 + \frac{5}{6} = \frac{72}{6} + \frac{5}{6} = \frac{77}{6} \)
- \( 16 \frac{2}{3} = 16 + \frac{2}{3} = \frac{48}{3} + \frac{2}{3} = \frac{50}{3} \)

Step 2: Find a common denominator for \( \frac{77}{6} \) and \( \frac{50}{3} \).
- The LCD of 6 and 3 is \( 6 \).

Step 3: Rewrite the fractions with the common denominator.
- \( \frac{77}{6} \) remains \( \frac{77}{6} \)
- \( \frac{50}{3} = \frac{50 \times 2}{3 \times 2} = \frac{100}{6} \)

Step 4: Add the fractions.
- \( \frac{77}{6} + \frac{100}{6} = \frac{77 + 100}{6} = \frac{177}{6} \)

Step 5: Simplify the improper fraction.
- \( \frac{177}{6} = 29 \frac{3}{6} = 29 \frac{1}{2} \) (simplify \( \frac{3}{6} \) to \( \frac{1}{2} \))

Final Answer:
\[ \boxed{29 \frac{1}{2}} \]

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#### 9. \( 1 \frac{2}{7} + 11 \frac{3}{6} \)

Step 1: Simplify the fractions in the mixed numbers.
- \( \frac{3}{6} = \frac{1}{2} \) (simplify by dividing numerator and denominator by 3)

So, the problem becomes:
\[ 1 \frac{2}{7} + 11 \frac{1}{2} \]

Step 2: Convert the mixed numbers to improper fractions.
- \( 1 \frac{2}{7} = 1 + \frac{2}{7} = \frac{7}{7} + \frac{2}{7} = \frac{9}{7} \)
- \( 11 \frac{1}{2} = 11 + \frac{1}{2} = \frac{22}{2} + \frac{1}{2} = \frac{23}{2} \)

Step 3: Find a common denominator for \( \frac{9}{7} \) and \( \frac{23}{2} \).
- The LCD of 7 and 2 is \( 14 \).

Step 4: Rewrite the fractions with the common denominator.
- \( \frac{9}{7} = \frac{9 \times 2}{7 \times 2} = \frac{18}{14} \)
- \( \frac{23}{2} = \frac{23 \times 7}{2 \times 7} = \frac{161}{14} \)

Step 5: Add the fractions.
- \( \frac{18}{14} + \frac{161}{14} = \frac{18 + 161}{14} = \frac{179}{14} \)

Step 6: Convert the improper fraction back to a mixed number.
- \( \frac{179}{14} = 12 \frac{11}{14} \) (since \( 179 \div 14 = 12 \) remainder \( 11 \))

Final Answer:
\[ \boxed{12 \frac{11}{14}} \]

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#### 10. \( 14 \frac{5}{7} + 17 \frac{2}{7} \)

Step 1: Convert the mixed numbers to improper fractions.
- \( 14 \frac{5}{7} = 14 + \frac{5}{7} = \frac{98}{7} + \frac{5}{7} = \frac{103}{7} \)
- \( 17 \frac{2}{7} = 17 + \frac{2}{7} = \frac{119}{7} + \frac{2}{7} = \frac{121}{7} \)

Step 2: Add the fractions.
- \( \frac{103}{7} + \frac{121}{7} = \frac{103 + 121}{7} = \frac{224}{7} \)

Step 3: Simplify the improper fraction.
- \( \frac{224}{7} = 32 \) (since \( 224 \div 7 = 32 \))

Final Answer:
\[ \boxed{32} \]

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Final Answers:

1. \( \boxed{11 \frac{9}{44}} \)
2. \( \boxed{17 \frac{1}{6}} \)
3. \( \boxed{30 \frac{17}{24}} \)
4. \( \boxed{31 \frac{31}{33}} \)
5. \( \boxed{35} \)
6. \( \boxed{26 \frac{28}{45}} \)
7. \( \boxed{11 \frac{4}{5}} \)
8. \( \boxed{29 \frac{1}{2}} \)
9. \( \boxed{12 \frac{11}{14}} \)
10. \( \boxed{32} \)