Multiplying Mixed Fractions - Free Printable

To solve the problems involving the multiplication of mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions.
2. Multiply the numerators and the denominators.
3. Simplify the resulting fraction if possible.
4. Convert the result back to a mixed fraction if necessary.

Let's solve each problem step by step.

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

#### Step 1: Convert \( 2 \frac{1}{3} \) to an improper fraction.
\[ 2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

#### Step 2: Multiply the fractions.
\[ \frac{7}{3} \times \frac{3}{8} = \frac{7 \times 3}{3 \times 8} = \frac{21}{24} \]

#### Step 3: Simplify the fraction.
The greatest common divisor (GCD) of 21 and 24 is 3.
\[ \frac{21}{24} = \frac{21 \div 3}{24 \div 3} = \frac{7}{8} \]

#### Step 4: Convert to a mixed fraction.
Since \( \frac{7}{8} \) is already in its simplest form and is a proper fraction, it remains as is.

Answer:
\[ \boxed{\frac{7}{8}} \]

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Problem 2: \( 1 \frac{5}{9} \times \frac{2}{7} \)

#### Step 1: Convert \( 1 \frac{5}{9} \) to an improper fraction.
\[ 1 \frac{5}{9} = \frac{(1 \times 9) + 5}{9} = \frac{9 + 5}{9} = \frac{14}{9} \]

#### Step 2: Multiply the fractions.
\[ \frac{14}{9} \times \frac{2}{7} = \frac{14 \times 2}{9 \times 7} = \frac{28}{63} \]

#### Step 3: Simplify the fraction.
The GCD of 28 and 63 is 7.
\[ \frac{28}{63} = \frac{28 \div 7}{63 \div 7} = \frac{4}{9} \]

#### Step 4: Convert to a mixed fraction.
Since \( \frac{4}{9} \) is already in its simplest form and is a proper fraction, it remains as is.

Answer:
\[ \boxed{\frac{4}{9}} \]

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Problem 3: \( 2 \frac{1}{4} \times \frac{7}{10} \)

#### Step 1: Convert \( 2 \frac{1}{4} \) to an improper fraction.
\[ 2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]

#### Step 2: Multiply the fractions.
\[ \frac{9}{4} \times \frac{7}{10} = \frac{9 \times 7}{4 \times 10} = \frac{63}{40} \]

#### Step 3: Simplify the fraction.
\( \frac{63}{40} \) is already in its simplest form.

#### Step 4: Convert to a mixed fraction.
\[ \frac{63}{40} = 1 \frac{23}{40} \]

Answer:
\[ \boxed{1 \frac{23}{40}} \]

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Problem 4: \( 1 \frac{6}{7} \times \frac{5}{6} \)

#### Step 1: Convert \( 1 \frac{6}{7} \) to an improper fraction.
\[ 1 \frac{6}{7} = \frac{(1 \times 7) + 6}{7} = \frac{7 + 6}{7} = \frac{13}{7} \]

#### Step 2: Multiply the fractions.
\[ \frac{13}{7} \times \frac{5}{6} = \frac{13 \times 5}{7 \times 6} = \frac{65}{42} \]

#### Step 3: Simplify the fraction.
\( \frac{65}{42} \) is already in its simplest form.

#### Step 4: Convert to a mixed fraction.
\[ \frac{65}{42} = 1 \frac{23}{42} \]

Answer:
\[ \boxed{1 \frac{23}{42}} \]

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

#### Step 1: Convert \( 2 \frac{2}{3} \) to an improper fraction.
\[ 2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \]

#### Step 2: Multiply the fractions.
\[ 4 \times \frac{8}{3} = \frac{4 \times 8}{3} = \frac{32}{3} \]

#### Step 3: Simplify the fraction.
\( \frac{32}{3} \) is already in its simplest form.

#### Step 4: Convert to a mixed fraction.
\[ \frac{32}{3} = 10 \frac{2}{3} \]

Answer:
\[ \boxed{10 \frac{2}{3}} \]

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Problem 6: \( 1 \frac{7}{10} \times \frac{3}{8} \)

#### Step 1: Convert \( 1 \frac{7}{10} \) to an improper fraction.
\[ 1 \frac{7}{10} = \frac{(1 \times 10) + 7}{10} = \frac{10 + 7}{10} = \frac{17}{10} \]

#### Step 2: Multiply the fractions.
\[ \frac{17}{10} \times \frac{3}{8} = \frac{17 \times 3}{10 \times 8} = \frac{51}{80} \]

#### Step 3: Simplify the fraction.
\( \frac{51}{80} \) is already in its simplest form.

#### Step 4: Convert to a mixed fraction.
Since \( \frac{51}{80} \) is a proper fraction, it remains as is.

Answer:
\[ \boxed{\frac{51}{80}} \]

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

#### Step 1: Convert \( 5 \frac{1}{2} \) to an improper fraction.
\[ 5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]

#### Step 2: Convert \( 1 \frac{3}{4} \) to an improper fraction.
\[ 1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \]

#### Step 3: Multiply the fractions.
\[ \frac{11}{2} \times \frac{7}{4} = \frac{11 \times 7}{2 \times 4} = \frac{77}{8} \]

#### Step 4: Simplify the fraction.
\( \frac{77}{8} \) is already in its simplest form.

#### Step 5: Convert to a mixed fraction.
\[ \frac{77}{8} = 9 \frac{5}{8} \]

Answer:
\[ \boxed{9 \frac{5}{8}} \]

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Problem 8: \( 4 \frac{2}{3} \times \frac{5}{12} \)

#### Step 1: Convert \( 4 \frac{2}{3} \) to an improper fraction.
\[ 4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]

#### Step 2: Multiply the fractions.
\[ \frac{14}{3} \times \frac{5}{12} = \frac{14 \times 5}{3 \times 12} = \frac{70}{36} \]

#### Step 3: Simplify the fraction.
The GCD of 70 and 36 is 2.
\[ \frac{70}{36} = \frac{70 \div 2}{36 \div 2} = \frac{35}{18} \]

#### Step 4: Convert to a mixed fraction.
\[ \frac{35}{18} = 1 \frac{17}{18} \]

Answer:
\[ \boxed{1 \frac{17}{18}} \]

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Problem 9: \( 4 \frac{1}{5} \times 2 \frac{2}{9} \)

#### Step 1: Convert \( 4 \frac{1}{5} \) to an improper fraction.
\[ 4 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \]

#### Step 2: Convert \( 2 \frac{2}{9} \) to an improper fraction.
\[ 2 \frac{2}{9} = \frac{(2 \times 9) + 2}{9} = \frac{18 + 2}{9} = \frac{20}{9} \]

#### Step 3: Multiply the fractions.
\[ \frac{21}{5} \times \frac{20}{9} = \frac{21 \times 20}{5 \times 9} = \frac{420}{45} \]

#### Step 4: Simplify the fraction.
The GCD of 420 and 45 is 15.
\[ \frac{420}{45} = \frac{420 \div 15}{45 \div 15} = \frac{28}{3} \]

#### Step 5: Convert to a mixed fraction.
\[ \frac{28}{3} = 9 \frac{1}{3} \]

Answer:
\[ \boxed{9 \frac{1}{3}} \]

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Final Answers:

1. \( \boxed{\frac{7}{8}} \)
2. \( \boxed{\frac{4}{9}} \)
3. \( \boxed{1 \frac{23}{40}} \)
4. \( \boxed{1 \frac{23}{42}} \)
5. \( \boxed{10 \frac{2}{3}} \)
6. \( \boxed{\frac{51}{80}} \)
7. \( \boxed{9 \frac{5}{8}} \)
8. \( \boxed{1 \frac{17}{18}} \)
9. \( \boxed{9 \frac{1}{3}} \)