Division of Mixed Numbers worksheet with ten equations to solve.

To solve these problems, we need to divide mixed numbers. Here is the general method we will use for every problem:

1. Convert each mixed number into an improper fraction.
* Multiply the whole number by the denominator.
* Add the numerator.
* Place that result over the original denominator.
2. Keep, Change, Flip.
* Keep the first fraction as it is.
* Change the division sign ($\div$) to a multiplication sign ($\times$).
* Flip the second fraction (swap the top and bottom numbers) to get its reciprocal.
3. Multiply the numerators together and the denominators together.
4. Simplify the result. If the answer is an improper fraction (top number is bigger than the bottom), convert it back to a mixed number.

Let's solve them one by one.

1. $2\frac{1}{2} \div 1\frac{1}{4}$
* Convert: $2\frac{1}{2} = \frac{5}{2}$ and $1\frac{1}{4} = \frac{5}{4}$
* Equation: $\frac{5}{2} \div \frac{5}{4}$
* Keep, Change, Flip: $\frac{5}{2} \times \frac{4}{5}$
* Multiply: $\frac{20}{10}$
* Simplify: $2$

2. $1\frac{1}{5} \div 1\frac{4}{6}$
* First, simplify $1\frac{4}{6}$ to $1\frac{2}{3}$ to make it easier.
* Convert: $1\frac{1}{5} = \frac{6}{5}$ and $1\frac{2}{3} = \frac{5}{3}$
* Equation: $\frac{6}{5} \div \frac{5}{3}$
* Keep, Change, Flip: $\frac{6}{5} \times \frac{3}{5}$
* Multiply: $\frac{18}{25}$
* Simplify: It cannot be simplified further.

3. $4\frac{1}{4} \div 2\frac{1}{3}$
* Convert: $4\frac{1}{4} = \frac{17}{4}$ and $2\frac{1}{3} = \frac{7}{3}$
* Equation: $\frac{17}{4} \div \frac{7}{3}$
* Keep, Change, Flip: $\frac{17}{4} \times \frac{3}{7}$
* Multiply: $\frac{51}{28}$
* Convert to mixed number: $28$ goes into $51$ one time with $23$ left over.
* Answer: $1\frac{23}{28}$

4. $5\frac{2}{7} \div 1\frac{1}{2}$
* Convert: $5\frac{2}{7} = \frac{37}{7}$ and $1\frac{1}{2} = \frac{3}{2}$
* Equation: $\frac{37}{7} \div \frac{3}{2}$
* Keep, Change, Flip: $\frac{37}{7} \times \frac{2}{3}$
* Multiply: $\frac{74}{21}$
* Convert to mixed number: $21 \times 3 = 63$. $74 - 63 = 11$.
* Answer: $3\frac{11}{21}$

5. $3\frac{1}{3} \div 1\frac{8}{9}$
* Convert: $3\frac{1}{3} = \frac{10}{3}$ and $1\frac{8}{9} = \frac{17}{9}$
* Equation: $\frac{10}{3} \div \frac{17}{9}$
* Keep, Change, Flip: $\frac{10}{3} \times \frac{9}{17}$
* Cross-cancel before multiplying: The $3$ on the bottom and $9$ on top can both be divided by $3$. So, $3$ becomes $1$ and $9$ becomes $3$.
* New Equation: $\frac{10}{1} \times \frac{3}{17} = \frac{30}{17}$
* Convert to mixed number: $17$ goes into $30$ one time with $13$ left over.
* Answer: $1\frac{13}{17}$

6. $7\frac{1}{6} \div 1\frac{3}{4}$
* Convert: $7\frac{1}{6} = \frac{43}{6}$ and $1\frac{3}{4} = \frac{7}{4}$
* Equation: $\frac{43}{6} \div \frac{7}{4}$
* Keep, Change, Flip: $\frac{43}{6} \times \frac{4}{7}$
* Cross-cancel: $6$ and $4$ are both divisible by $2$. $6$ becomes $3$, $4$ becomes $2$.
* New Equation: $\frac{43}{3} \times \frac{2}{7} = \frac{86}{21}$
* Convert to mixed number: $21 \times 4 = 84$. $86 - 84 = 2$.
* Answer: $4\frac{2}{21}$

7. $3\frac{1}{5} \div 4\frac{2}{3}$
* Convert: $3\frac{1}{5} = \frac{16}{5}$ and $4\frac{2}{3} = \frac{14}{3}$
* Equation: $\frac{16}{5} \div \frac{14}{3}$
* Keep, Change, Flip: $\frac{16}{5} \times \frac{3}{14}$
* Cross-cancel: $16$ and $14$ are both divisible by $2$. $16$ becomes $8$, $14$ becomes $7$.
* New Equation: $\frac{8}{5} \times \frac{3}{7} = \frac{24}{35}$
* Simplify: Cannot be simplified.

8. $10\frac{1}{2} \div 1\frac{2}{3}$
* Convert: $10\frac{1}{2} = \frac{21}{2}$ and $1\frac{2}{3} = \frac{5}{3}$
* Equation: $\frac{21}{2} \div \frac{5}{3}$
* Keep, Change, Flip: $\frac{21}{2} \times \frac{3}{5}$
* Multiply: $\frac{63}{10}$
* Convert to mixed number: $10$ goes into $63$ six times with $3$ left over.
* Answer: $6\frac{3}{10}$

9. $2\frac{4}{10} \div 6\frac{2}{3}$
* First, simplify $2\frac{4}{10}$ to $2\frac{2}{5}$.
* Convert: $2\frac{2}{5} = \frac{12}{5}$ and $6\frac{2}{3} = \frac{20}{3}$
* Equation: $\frac{12}{5} \div \frac{20}{3}$
* Keep, Change, Flip: $\frac{12}{5} \times \frac{3}{20}$
* Cross-cancel: $12$ and $20$ are both divisible by $4$. $12$ becomes $3$, $20$ becomes $5$.
* New Equation: $\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}$
* Simplify: Cannot be simplified.

10. $10\frac{1}{2} \div 1\frac{1}{4}$
* Convert: $10\frac{1}{2} = \frac{21}{2}$ and $1\frac{1}{4} = \frac{5}{4}$
* Equation: $\frac{21}{2} \div \frac{5}{4}$
* Keep, Change, Flip: $\frac{21}{2} \times \frac{4}{5}$
* Cross-cancel: $2$ and $4$ are divisible by $2$. $2$ becomes $1$, $4$ becomes $2$.
* New Equation: $\frac{21}{1} \times \frac{2}{5} = \frac{42}{5}$
* Convert to mixed number: $5$ goes into $42$ eight times with $2$ left over.
* Answer: $8\frac{2}{5}$

Final Answer:
1. 2
2. $\frac{18}{25}$
3. $1\frac{23}{28}$
4. $3\frac{11}{21}$
5. $1\frac{13}{17}$
6. $4\frac{2}{21}$
7. $\frac{24}{35}$
8. $6\frac{3}{10}$
9. $\frac{9}{25}$
10. $8\frac{2}{5}$