Grade 5 Fractions worksheet: Adding mixed numbers (like ... - Free Printable

Problem: Adding Mixed Numbers (Like Denominators)

The task involves adding mixed numbers where the denominators are the same. The steps to solve these problems are as follows:

1. Separate the whole numbers and fractions: Add the whole numbers separately and add the fractions separately.
2. Add the fractions: Since the denominators are the same, simply add the numerators and keep the denominator unchanged.
3. Simplify if necessary: If the resulting fraction is improper (numerator ≥ denominator), convert it to a mixed number and add its whole number part to the sum of the whole numbers.
4. Combine the results: Add the sum of the whole numbers and the simplified fraction.

Let's solve each problem step by step.

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

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 3 + 5 = 8 \)
- Fractions: \( \frac{3}{5} + \frac{4}{5} = \frac{3+4}{5} = \frac{7}{5} \)

- Step 2: Simplify the fraction.
- \( \frac{7}{5} \) is an improper fraction, so convert it to a mixed number: \( \frac{7}{5} = 1 \frac{2}{5} \).

- Step 3: Combine the results.
- \( 8 + 1 \frac{2}{5} = 9 \frac{2}{5} \)

Answer: \( 9 \frac{2}{5} \)

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

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 5 + 5 = 10 \)
- Fractions: \( \frac{3}{7} + \frac{6}{7} = \frac{3+6}{7} = \frac{9}{7} \)

- Step 2: Simplify the fraction.
- \( \frac{9}{7} \) is an improper fraction, so convert it to a mixed number: \( \frac{9}{7} = 1 \frac{2}{7} \).

- Step 3: Combine the results.
- \( 10 + 1 \frac{2}{7} = 11 \frac{2}{7} \)

Answer: \( 11 \frac{2}{7} \)

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Problem 3: \( 1 \frac{6}{18} + 9 \frac{8}{18} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 1 + 9 = 10 \)
- Fractions: \( \frac{6}{18} + \frac{8}{18} = \frac{6+8}{18} = \frac{14}{18} \)

- Step 2: Simplify the fraction.
- \( \frac{14}{18} \) can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD), which is 2: \( \frac{14 \div 2}{18 \div 2} = \frac{7}{9} \).

- Step 3: Combine the results.
- \( 10 + \frac{7}{9} = 10 \frac{7}{9} \)

Answer: \( 10 \frac{7}{9} \)

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Problem 4: \( 2 \frac{8}{15} + 6 \frac{2}{15} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 2 + 6 = 8 \)
- Fractions: \( \frac{8}{15} + \frac{2}{15} = \frac{8+2}{15} = \frac{10}{15} \)

- Step 2: Simplify the fraction.
- \( \frac{10}{15} \) can be simplified by dividing both numerator and denominator by their GCD, which is 5: \( \frac{10 \div 5}{15 \div 5} = \frac{2}{3} \).

- Step 3: Combine the results.
- \( 8 + \frac{2}{3} = 8 \frac{2}{3} \)

Answer: \( 8 \frac{2}{3} \)

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Problem 5: \( 3 \frac{10}{12} + 4 \frac{11}{12} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 3 + 4 = 7 \)
- Fractions: \( \frac{10}{12} + \frac{11}{12} = \frac{10+11}{12} = \frac{21}{12} \)

- Step 2: Simplify the fraction.
- \( \frac{21}{12} \) is an improper fraction, so convert it to a mixed number: \( \frac{21}{12} = 1 \frac{9}{12} \).
- Further simplify \( \frac{9}{12} \) by dividing both numerator and denominator by their GCD, which is 3: \( \frac{9 \div 3}{12 \div 3} = \frac{3}{4} \).
- So, \( \frac{21}{12} = 1 \frac{3}{4} \).

- Step 3: Combine the results.
- \( 7 + 1 \frac{3}{4} = 8 \frac{3}{4} \)

Answer: \( 8 \frac{3}{4} \)

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Problem 6: \( 6 \frac{6}{14} + 4 \frac{7}{14} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 6 + 4 = 10 \)
- Fractions: \( \frac{6}{14} + \frac{7}{14} = \frac{6+7}{14} = \frac{13}{14} \)

- Step 2: Simplify the fraction.
- \( \frac{13}{14} \) is already in simplest form.

- Step 3: Combine the results.
- \( 10 + \frac{13}{14} = 10 \frac{13}{14} \)

Answer: \( 10 \frac{13}{14} \)

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Problem 7: \( 2 \frac{12}{20} + 8 \frac{3}{20} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 2 + 8 = 10 \)
- Fractions: \( \frac{12}{20} + \frac{3}{20} = \frac{12+3}{20} = \frac{15}{20} \)

- Step 2: Simplify the fraction.
- \( \frac{15}{20} \) can be simplified by dividing both numerator and denominator by their GCD, which is 5: \( \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \).

- Step 3: Combine the results.
- \( 10 + \frac{3}{4} = 10 \frac{3}{4} \)

Answer: \( 10 \frac{3}{4} \)

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

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 8 + 9 = 17 \)
- Fractions: \( \frac{3}{4} + \frac{3}{4} = \frac{3+3}{4} = \frac{6}{4} \)

- Step 2: Simplify the fraction.
- \( \frac{6}{4} \) is an improper fraction, so convert it to a mixed number: \( \frac{6}{4} = 1 \frac{2}{4} \).
- Further simplify \( \frac{2}{4} \) by dividing both numerator and denominator by their GCD, which is 2: \( \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \).
- So, \( \frac{6}{4} = 1 \frac{1}{2} \).

- Step 3: Combine the results.
- \( 17 + 1 \frac{1}{2} = 18 \frac{1}{2} \)

Answer: \( 18 \frac{1}{2} \)

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Problem 9: \( 3 \frac{7}{8} + 7 \frac{5}{8} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 3 + 7 = 10 \)
- Fractions: \( \frac{7}{8} + \frac{5}{8} = \frac{7+5}{8} = \frac{12}{8} \)

- Step 2: Simplify the fraction.
- \( \frac{12}{8} \) is an improper fraction, so convert it to a mixed number: \( \frac{12}{8} = 1 \frac{4}{8} \).
- Further simplify \( \frac{4}{8} \) by dividing both numerator and denominator by their GCD, which is 4: \( \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \).
- So, \( \frac{12}{8} = 1 \frac{1}{2} \).

- Step 3: Combine the results.
- \( 10 + 1 \frac{1}{2} = 11 \frac{1}{2} \)

Answer: \( 11 \frac{1}{2} \)

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Problem 10: \( 10 \frac{1}{2} + 7 \frac{1}{2} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 10 + 7 = 17 \)
- Fractions: \( \frac{1}{2} + \frac{1}{2} = \frac{1+1}{2} = \frac{2}{2} = 1 \)

- Step 2: Combine the results.
- \( 17 + 1 = 18 \)

Answer: \( 18 \)

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Problem 11: \( 4 \frac{2}{16} + 6 \frac{13}{16} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 4 + 6 = 10 \)
- Fractions: \( \frac{2}{16} + \frac{13}{16} = \frac{2+13}{16} = \frac{15}{16} \)

- Step 2: Simplify the fraction.
- \( \frac{15}{16} \) is already in simplest form.

- Step 3: Combine the results.
- \( 10 + \frac{15}{16} = 10 \frac{15}{16} \)

Answer: \( 10 \frac{15}{16} \)

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Problem 12: \( 6 \frac{19}{25} + 1 \frac{13}{25} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 6 + 1 = 7 \)
- Fractions: \( \frac{19}{25} + \frac{13}{25} = \frac{19+13}{25} = \frac{32}{25} \)

- Step 2: Simplify the fraction.
- \( \frac{32}{25} \) is an improper fraction, so convert it to a mixed number: \( \frac{32}{25} = 1 \frac{7}{25} \).

- Step 3: Combine the results.
- \( 7 + 1 \frac{7}{25} = 8 \frac{7}{25} \)

Answer: \( 8 \frac{7}{25} \)

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Problem 13: \( 3 \frac{4}{9} + 1 \frac{1}{9} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 3 + 1 = 4 \)
- Fractions: \( \frac{4}{9} + \frac{1}{9} = \frac{4+1}{9} = \frac{5}{9} \)

- Step 2: Simplify the fraction.
- \( \frac{5}{9} \) is already in simplest form.

- Step 3: Combine the results.
- \( 4 + \frac{5}{9} = 4 \frac{5}{9} \)

Answer: \( 4 \frac{5}{9} \)

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Problem 14: \( 4 \frac{17}{100} + 4 \frac{84}{100} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 4 + 4 = 8 \)
- Fractions: \( \frac{17}{100} + \frac{84}{100} = \frac{17+84}{100} = \frac{101}{100} \)

- Step 2: Simplify the fraction.
- \( \frac{101}{100} \) is an improper fraction, so convert it to a mixed number: \( \frac{101}{100} = 1 \frac{1}{100} \).

- Step 3: Combine the results.
- \( 8 + 1 \frac{1}{100} = 9 \frac{1}{100} \)

Answer: \( 9 \frac{1}{100} \)

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Problem 15: \( 1 \frac{6}{8} + 2 \frac{5}{8} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 1 + 2 = 3 \)
- Fractions: \( \frac{6}{8} + \frac{5}{8} = \frac{6+5}{8} = \frac{11}{8} \)

- Step 2: Simplify the fraction.
- \( \frac{11}{8} \) is an improper fraction, so convert it to a mixed number: \( \frac{11}{8} = 1 \frac{3}{8} \).

- Step 3: Combine the results.
- \( 3 + 1 \frac{3}{8} = 4 \frac{3}{8} \)

Answer: \( 4 \frac{3}{8} \)

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Problem 16: \( 9 \frac{11}{50} + 3 \frac{7}{50} \)

- Step 1: Separate the whole numbers and fractions.
- Whole numbers: \( 9 + 3 = 12 \)
- Fractions: \( \frac{11}{50} + \frac{7}{50} = \frac{11+7}{50} = \frac{18}{50} \)

- Step 2: Simplify the fraction.
- \( \frac{18}{50} \) can be simplified by dividing both numerator and denominator by their GCD, which is 2: \( \frac{18 \div 2}{50 \div 2} = \frac{9}{25} \).

- Step 3: Combine the results.
- \( 12 + \frac{9}{25} = 12 \frac{9}{25} \)

Answer: \( 12 \frac{9}{25} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 9 \frac{2}{5} \\
2. & 11 \frac{2}{7} \\
3. & 10 \frac{7}{9} \\
4. & 8 \frac{2}{3} \\
5. & 8 \frac{3}{4} \\
6. & 10 \frac{13}{14} \\
7. & 10 \frac{3}{4} \\
8. & 18 \frac{1}{2} \\
9. & 11 \frac{1}{2} \\
10. & 18 \\
11. & 10 \frac{15}{16} \\
12. & 8 \frac{7}{25} \\
13. & 4 \frac{5}{9} \\
14. & 9 \frac{1}{100} \\
15. & 4 \frac{3}{8} \\
16. & 12 \frac{9}{25} \\
\end{array}
}
\]