Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

To solve the problems involving division of mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions.
2. Divide the fractions by multiplying the first fraction by the reciprocal of the second fraction.
3. Simplify the result and convert it back to a mixed number if necessary.

Let's solve each problem step by step.

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \)
- \( 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \)

#### Step 2: Divide the fractions.
\[ \frac{14}{3} \div \frac{7}{2} = \frac{14}{3} \times \frac{2}{7} = \frac{14 \times 2}{3 \times 7} = \frac{28}{21} \]

#### Step 3: Simplify and convert to a mixed number.
- Simplify \( \frac{28}{21} \): Both numerator and denominator are divisible by 7.
\[ \frac{28}{21} = \frac{4}{3} \]
- Convert \( \frac{4}{3} \) to a mixed number:
\[ \frac{4}{3} = 1 \frac{1}{3} \]

Answer: \( 1 \frac{1}{3} \)

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \)
- \( 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{7}{2} \div \frac{9}{4} = \frac{7}{2} \times \frac{4}{9} = \frac{7 \times 4}{2 \times 9} = \frac{28}{18} \]

#### Step 3: Simplify and convert to a mixed number.
- Simplify \( \frac{28}{18} \): Both numerator and denominator are divisible by 2.
\[ \frac{28}{18} = \frac{14}{9} \]
- Convert \( \frac{14}{9} \) to a mixed number:
\[ \frac{14}{9} = 1 \frac{5}{9} \]

Answer: \( 1 \frac{5}{9} \)

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \)
- \( 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \)

#### Step 2: Divide the fractions.
\[ \frac{9}{2} \div \frac{11}{4} = \frac{9}{2} \times \frac{4}{11} = \frac{9 \times 4}{2 \times 11} = \frac{36}{22} \]

#### Step 3: Simplify and convert to a mixed number.
- Simplify \( \frac{36}{22} \): Both numerator and denominator are divisible by 2.
\[ \frac{36}{22} = \frac{18}{11} \]
- Convert \( \frac{18}{11} \) to a mixed number:
\[ \frac{18}{11} = 1 \frac{7}{11} \]

Answer: \( 1 \frac{7}{11} \)

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Problem 4: \( 4 \frac{2}{3} \div 2 \frac{5}{6} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \)
- \( 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \)

#### Step 2: Divide the fractions.
\[ \frac{14}{3} \div \frac{17}{6} = \frac{14}{3} \times \frac{6}{17} = \frac{14 \times 6}{3 \times 17} = \frac{84}{51} \]

#### Step 3: Simplify and convert to a mixed number.
- Simplify \( \frac{84}{51} \): Both numerator and denominator are divisible by 3.
\[ \frac{84}{51} = \frac{28}{17} \]
- Convert \( \frac{28}{17} \) to a mixed number:
\[ \frac{28}{17} = 1 \frac{11}{17} \]

Answer: \( 1 \frac{11}{17} \)

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Final Answers:

\[
\boxed{
\begin{aligned}
&1 \frac{1}{3}, \quad 1 \frac{5}{9}, \quad 1 \frac{7}{11}, \quad 1 \frac{11}{17}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}, \quad 1 \frac{1}{3}, \quad 1 \frac{1}{2}
\end{aligned}
}
\]