Grade 5 math worksheet on multiplying mixed numbers, designed for learning and practice.

Problem: Multiplying Mixed Numbers

The task is to solve the multiplication problems involving mixed numbers. Here are the steps to solve each problem, along with explanations.

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#### Step 1: Convert Mixed Numbers to Improper Fractions
A mixed number consists of a whole number and a fraction. To convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator of the fraction.
- Add the result to the numerator.
- Write the new numerator over the original denominator.

For example, $ 2 \frac{1}{2} $ becomes:
$$
2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}
$$

#### Step 2: Multiply the Fractions
To multiply two fractions:
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the resulting fraction if possible.

For example, multiplying $ \frac{5}{2} \times \frac{3}{4} $:
$$
\frac{5}{2} \times \frac{3}{4} = \frac{5 \times 3}{2 \times 4} = \frac{15}{8}
$$

#### Step 3: Convert Back to a Mixed Number (if necessary)
If the result is an improper fraction, convert it back to a mixed number:
- Divide the numerator by the denominator.
- The quotient becomes the whole number part.
- The remainder becomes the numerator of the fractional part.
- The denominator remains the same.

For example, $ \frac{15}{8} $ becomes:
$$
\frac{15}{8} = 1 \frac{7}{8}
$$

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Solutions to Each Problem

#### Problem 1: $ 1 \frac{1}{4} \times 3 \frac{6}{7} $
1. Convert mixed numbers to improper fractions:
- $ 1 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4} $
- $ 3 \frac{6}{7} = \frac{(3 \times 7) + 6}{7} = \frac{27}{7} $
2. Multiply the fractions:
$$
\frac{5}{4} \times \frac{27}{7} = \frac{5 \times 27}{4 \times 7} = \frac{135}{28}
$$
3. Convert back to a mixed number:
- $ 135 \div 28 = 4 $ remainder $ 23 $
- So, $ \frac{135}{28} = 4 \frac{23}{28} $

Answer: $ 4 \frac{23}{28} $

#### Problem 2: $ 1 \frac{1}{6} \times 2 \frac{6}{12} $
1. Simplify $ 2 \frac{6}{12} $ first:
- $ \frac{6}{12} = \frac{1}{2} $, so $ 2 \frac{6}{12} = 2 \frac{1}{2} $
2. Convert mixed numbers to improper fractions:
- $ 1 \frac{1}{6} = \frac{(1 \times 6) + 1}{6} = \frac{7}{6} $
- $ 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2} $
3. Multiply the fractions:
$$
\frac{7}{6} \times \frac{5}{2} = \frac{7 \times 5}{6 \times 2} = \frac{35}{12}
$$
4. Convert back to a mixed number:
- $ 35 \div 12 = 2 $ remainder $ 11 $
- So, $ \frac{35}{12} = 2 \frac{11}{12} $

Answer: $ 2 \frac{11}{12} $

#### Problem 3: $ 2 \frac{1}{2} \times 3 \frac{5}{9} $
1. Convert mixed numbers to improper fractions:
- $ 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2} $
- $ 3 \frac{5}{9} = \frac{(3 \times 9) + 5}{9} = \frac{32}{9} $
2. Multiply the fractions:
$$
\frac{5}{2} \times \frac{32}{9} = \frac{5 \times 32}{2 \times 9} = \frac{160}{18}
$$
3. Simplify $ \frac{160}{18} $:
- Both 160 and 18 are divisible by 2:
$$
\frac{160 \div 2}{18 \div 2} = \frac{80}{9}
$$
4. Convert back to a mixed number:
- $ 80 \div 9 = 8 $ remainder $ 8 $
- So, $ \frac{80}{9} = 8 \frac{8}{9} $

Answer: $ 8 \frac{8}{9} $

#### Problem 4: $ 3 \frac{1}{3} \times \frac{4}{10} $
1. Convert mixed numbers to improper fractions:
- $ 3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{10}{3} $
2. Multiply the fractions:
$$
\frac{10}{3} \times \frac{4}{10} = \frac{10 \times 4}{3 \times 10} = \frac{40}{30}
$$
3. Simplify $ \frac{40}{30} $:
- Both 40 and 30 are divisible by 10:
$$
\frac{40 \div 10}{30 \div 10} = \frac{4}{3}
$$
4. Convert back to a mixed number:
- $ 4 \div 3 = 1 $ remainder $ 1 $
- So, $ \frac{4}{3} = 1 \frac{1}{3} $

Answer: $ 1 \frac{1}{3} $

#### Problem 5: $ 3 \frac{3}{4} \times 3 \frac{3}{9} $
1. Simplify $ 3 \frac{3}{9} $ first:
- $ \frac{3}{9} = \frac{1}{3} $, so $ 3 \frac{3}{9} = 3 \frac{1}{3} $
2. Convert mixed numbers to improper fractions:
- $ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4} $
- $ 3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{10}{3} $
3. Multiply the fractions:
$$
\frac{15}{4} \times \frac{10}{3} = \frac{15 \times 10}{4 \times 3} = \frac{150}{12}
$$
4. Simplify $ \frac{150}{12} $:
- Both 150 and 12 are divisible by 6:
$$
\frac{150 \div 6}{12 \div 6} = \frac{25}{2}
$$
5. Convert back to a mixed number:
- $ 25 \div 2 = 12 $ remainder $ 1 $
- So, $ \frac{25}{2} = 12 \frac{1}{2} $

Answer: $ 12 \frac{1}{2} $

#### Problem 6: $ 3 \frac{2}{5} \times 2 \frac{2}{7} $
1. Convert mixed numbers to improper fractions:
- $ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{17}{5} $
- $ 2 \frac{2}{7} = \frac{(2 \times 7) + 2}{7} = \frac{16}{7} $
2. Multiply the fractions:
$$
\frac{17}{5} \times \frac{16}{7} = \frac{17 \times 16}{5 \times 7} = \frac{272}{35}
$$
3. Convert back to a mixed number:
- $ 272 \div 35 = 7 $ remainder $ 27 $
- So, $ \frac{272}{35} = 7 \frac{27}{35} $

Answer: $ 7 \frac{27}{35} $

#### Problem 7: $ 1 \frac{1}{2} \times 3 \frac{2}{2} $
1. Simplify $ 3 \frac{2}{2} $ first:
- $ \frac{2}{2} = 1 $, so $ 3 \frac{2}{2} = 4 $
2. Convert mixed numbers to improper fractions:
- $ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2} $
3. Multiply the fractions:
$$
\frac{3}{2} \times 4 = \frac{3}{2} \times \frac{4}{1} = \frac{3 \times 4}{2 \times 1} = \frac{12}{2} = 6
$$

Answer: $ 6 $

#### Problem 8: $ 1 \frac{6}{13} \times 3 \frac{10}{13} $
1. Convert mixed numbers to improper fractions:
- $ 1 \frac{6}{13} = \frac{(1 \times 13) + 6}{13} = \frac{19}{13} $
- $ 3 \frac{10}{13} = \frac{(3 \times 13) + 10}{13} = \frac{49}{13} $
2. Multiply the fractions:
$$
\frac{19}{13} \times \frac{49}{13} = \frac{19 \times 49}{13 \times 13} = \frac{931}{169}
$$
3. Convert back to a mixed number:
- $ 931 \div 169 = 5 $ remainder $ 86 $
- So, $ \frac{931}{169} = 5 \frac{86}{169} $

Answer: $ 5 \frac{86}{169} $

#### Problem 9: $ 3 \frac{3}{5} \times 3 \frac{3}{5} $
1. Convert mixed numbers to improper fractions:
- $ 3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{18}{5} $
2. Multiply the fractions:
$$
\frac{18}{5} \times \frac{18}{5} = \frac{18 \times 18}{5 \times 5} = \frac{324}{25}
$$
3. Convert back to a mixed number:
- $ 324 \div 25 = 12 $ remainder $ 24 $
- So, $ \frac{324}{25} = 12 \frac{24}{25} $

Answer: $ 12 \frac{24}{25} $

#### Problem 10: $ 3 \frac{3}{4} \times 2 \frac{2}{4} $
1. Simplify $ 2 \frac{2}{4} $ first:
- $ \frac{2}{4} = \frac{1}{2} $, so $ 2 \frac{2}{4} = 2 \frac{1}{2} $
2. Convert mixed numbers to improper fractions:
- $ 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4} $
- $ 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2} $
3. Multiply the fractions:
$$
\frac{15}{4} \times \frac{5}{2} = \frac{15 \times 5}{4 \times 2} = \frac{75}{8}
$$
4. Convert back to a mixed number:
- $ 75 \div 8 = 9 $ remainder $ 3 $
- So, $ \frac{75}{8} = 9 \frac{3}{8} $

Answer: $ 9 \frac{3}{8} $

#### Problem 11: $ 1 \frac{2}{3} \times 1 \frac{2}{4} $
1. Simplify $ 1 \frac{2}{4} $ first:
- $ \frac{2}{4} = \frac{1}{2} $, so $ 1 \frac{2}{4} = 1 \frac{1}{2} $
2. Convert mixed numbers to improper fractions:
- $ 1 \frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{5}{3} $
- $ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2} $
3. Multiply the fractions:
$$
\frac{5}{3} \times \frac{3}{2} = \frac{5 \times 3}{3 \times 2} = \frac{15}{6}
$$
4. Simplify $ \frac{15}{6} $:
- Both 15 and 6 are divisible by 3:
$$
\frac{15 \div 3}{6 \div 3} = \frac{5}{2}
$$
5. Convert back to a mixed number:
- $ 5 \div 2 = 2 $ remainder $ 1 $
- So, $ \frac{5}{2} = 2 \frac{1}{2} $

Answer: $ 2 \frac{1}{2} $

#### Problem 12: $ 2 \frac{4}{5} \times 1 \frac{1}{12} $
1. Convert mixed numbers to improper fractions:
- $ 2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{14}{5} $
- $ 1 \frac{1}{12} = \frac{(1 \times 12) + 1}{12} = \frac{13}{12} $
2. Multiply the fractions:
$$
\frac{14}{5} \times \frac{13}{12} = \frac{14 \times 13}{5 \times 12} = \frac{182}{60}
$$
3. Simplify $ \frac{182}{60} $:
- Both 182 and 60 are divisible by 2:
$$
\frac{182 \div 2}{60 \div 2} = \frac{91}{30}
$$
4. Convert back to a mixed number:
- $ 91 \div 30 = 3 $ remainder $ 1 $
- So, $ \frac{91}{30} = 3 \frac{1}{30} $

Answer: $ 3 \frac{1}{30} $

#### Problem 13: $ 1 \frac{3}{8} \times 2 \frac{6}{8} $
1. Simplify $ 2 \frac{6}{8} $ first:
- $ \frac{6}{8} = \frac{3}{4} $, so $ 2 \frac{6}{8} = 2 \frac{3}{4} $
2. Convert mixed numbers to improper fractions:
- $ 1 \frac{3}{8} = \frac{(1 \times 8) + 3}{8} = \frac{11}{8} $
- $ 2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{11}{4} $
3. Multiply the fractions:
$$
\frac{11}{8} \times \frac{11}{4} = \frac{11 \times 11}{8 \times 4} = \frac{121}{32}
$$
4. Convert back to a mixed number:
- $ 121 \div 32 = 3 $ remainder $ 25 $
- So, $ \frac{121}{32} = 3 \frac{25}{32} $

Answer: $ 3 \frac{25}{32} $

#### Problem 14: $ 3 \frac{3}{7} \times 1 \frac{1}{2} $
1. Convert mixed numbers to improper fractions:
- $ 3 \frac{3}{7} = \frac{(3 \times 7) + 3}{7} = \frac{24}{7} $
- $ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2} $
2. Multiply the fractions:
$$
\frac{24}{7} \times \frac{3}{2} = \frac{24 \times 3}{7 \times 2} = \frac{72}{14}
$$
3. Simplify $ \frac{72}{14} $:
- Both 72 and 14 are divisible by 2:
$$
\frac{72 \div 2}{14 \div 2} = \frac{36}{7}
$$
4. Convert back to a mixed number:
- $ 36 \div 7 = 5 $ remainder $ 1 $
- So, $ \frac{36}{7} = 5 \frac{1}{7} $

Answer: $ 5 \frac{1}{7} $

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Final Answers:

1. $ 4 \frac{23}{28} $
2. $ 2 \frac{11}{12} $
3. $ 8 \frac{8}{9} $
4. $ 1 \frac{1}{3} $
5. $ 12 \frac{1}{2} $
6. $ 7 \frac{27}{35} $
7. $ 6 $
8. $ 5 \frac{86}{169} $
9. $ 12 \frac{24}{25} $
10. $ 9 \frac{3}{8} $
11. $ 2 \frac{1}{2} $
12. $ 3 \frac{1}{30} $
13. $ 3 \frac{25}{32} $
14. $ 5 \frac{1}{7} $

$$
\boxed{4 \frac{23}{28}, 2 \frac{11}{12}, 8 \frac{8}{9}, 1 \frac{1}{3}, 12 \frac{1}{2}, 7 \frac{27}{35}, 6, 5 \frac{86}{169}, 12 \frac{24}{25}, 9 \frac{3}{8}, 2 \frac{1}{2}, 3 \frac{1}{30}, 3 \frac{25}{32}, 5 \frac{1}{7}}
$$