Dividing Mixed Numbers worksheet with 20 division problems involving whole numbers and mixed fractions.

The task involves dividing whole numbers with mixed fractions and simplifying the results if possible. Let's solve a few of these problems step by step to illustrate the process.

General Steps for Dividing Mixed Numbers:

1. Convert mixed numbers to improper fractions.
2. Divide the fractions by multiplying by the reciprocal of the divisor.
3. Simplify the result if possible.
4. Convert back to a mixed number if needed.

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Example Problem: Solve \( 7 \div 1 \frac{7}{9} \) (Problem 1)

#### Step 1: Convert the mixed number to an improper fraction.
- The mixed number \( 1 \frac{7}{9} \) can be converted as follows:
\[
1 \frac{7}{9} = \frac{(1 \times 9) + 7}{9} = \frac{9 + 7}{9} = \frac{16}{9}
\]

#### Step 2: Rewrite the division problem.
- The problem now becomes:
\[
7 \div \frac{16}{9}
\]

#### Step 3: Divide by multiplying by the reciprocal.
- To divide by a fraction, multiply by its reciprocal:
\[
7 \div \frac{16}{9} = 7 \times \frac{9}{16}
\]
- Write 7 as a fraction: \( 7 = \frac{7}{1} \).
- Multiply:
\[
\frac{7}{1} \times \frac{9}{16} = \frac{7 \times 9}{1 \times 16} = \frac{63}{16}
\]

#### Step 4: Simplify and convert to a mixed number.
- The fraction \( \frac{63}{16} \) is already in simplest form. Convert it to a mixed number:
\[
\frac{63}{16} = 3 \frac{15}{16}
\]

#### Final Answer for Problem 1:
\[
\boxed{3 \frac{15}{16}}
\]

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Example Problem: Solve \( 4 + 4 \frac{2}{5} \) (Problem 2)

#### Step 1: Convert the mixed number to an improper fraction.
- The mixed number \( 4 \frac{2}{5} \) can be converted as follows:
\[
4 \frac{2}{5} = \frac{(4 \times 5) + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5}
\]

#### Step 2: Rewrite the division problem.
- The problem now becomes:
\[
4 \div \frac{22}{5}
\]

#### Step 3: Divide by multiplying by the reciprocal.
- To divide by a fraction, multiply by its reciprocal:
\[
4 \div \frac{22}{5} = 4 \times \frac{5}{22}
\]
- Write 4 as a fraction: \( 4 = \frac{4}{1} \).
- Multiply:
\[
\frac{4}{1} \times \frac{5}{22} = \frac{4 \times 5}{1 \times 22} = \frac{20}{22}
\]

#### Step 4: Simplify the fraction.
- Simplify \( \frac{20}{22} \) by dividing the numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{20}{22} = \frac{20 \div 2}{22 \div 2} = \frac{10}{11}
\]

#### Final Answer for Problem 2:
\[
\boxed{\frac{10}{11}}
\]

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Example Problem: Solve \( 6 \div 3 \frac{18}{23} \) (Problem 11)

#### Step 1: Convert the mixed number to an improper fraction.
- The mixed number \( 3 \frac{18}{23} \) can be converted as follows:
\[
3 \frac{18}{23} = \frac{(3 \times 23) + 18}{23} = \frac{69 + 18}{23} = \frac{87}{23}
\]

#### Step 2: Rewrite the division problem.
- The problem now becomes:
\[
6 \div \frac{87}{23}
\]

#### Step 3: Divide by multiplying by the reciprocal.
- To divide by a fraction, multiply by its reciprocal:
\[
6 \div \frac{87}{23} = 6 \times \frac{23}{87}
\]
- Write 6 as a fraction: \( 6 = \frac{6}{1} \).
- Multiply:
\[
\frac{6}{1} \times \frac{23}{87} = \frac{6 \times 23}{1 \times 87} = \frac{138}{87}
\]

#### Step 4: Simplify the fraction.
- Simplify \( \frac{138}{87} \) by dividing the numerator and denominator by their greatest common divisor (GCD), which is 3:
\[
\frac{138}{87} = \frac{138 \div 3}{87 \div 3} = \frac{46}{29}
\]

#### Final Answer for Problem 11:
\[
\boxed{\frac{46}{29}}
\]

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Summary of Solutions:

Here are the solutions for the first three problems:
1. \( 7 \div 1 \frac{7}{9} = \boxed{3 \frac{15}{16}} \)
2. \( 4 \div 4 \frac{2}{5} = \boxed{\frac{10}{11}} \)
3. \( 6 \div 3 \frac{18}{23} = \boxed{\frac{46}{29}} \)

You can follow the same steps to solve the remaining problems. If you need further assistance with any specific problem, feel free to ask!