Dividing Mixed Numbers worksheet with 20 problems for practicing division of whole numbers and mixed fractions.

Here are the solutions to the 20 problems on the worksheet. To solve these, we convert the mixed numbers into improper fractions, flip the second fraction (the divisor), multiply, and then simplify the result back into a mixed number if needed.

1) $7 \div 1\frac{7}{9}$
* Convert: $7 = \frac{7}{1}$ and $1\frac{7}{9} = \frac{16}{9}$
* Multiply by reciprocal: $\frac{7}{1} \times \frac{9}{16} = \frac{63}{16}$
* Simplify: $63 \div 16 = 3$ with a remainder of $15$.
* Answer: $3\frac{15}{16}$

2) $4 \div 4\frac{2}{5}$
* Convert: $4 = \frac{4}{1}$ and $4\frac{2}{5} = \frac{22}{5}$
* Multiply by reciprocal: $\frac{4}{1} \times \frac{5}{22} = \frac{20}{22}$
* Simplify: Divide top and bottom by 2 to get $\frac{10}{11}$.
* Answer: $\frac{10}{11}$

3) $2 \div 2\frac{6}{11}$
* Convert: $2 = \frac{2}{1}$ and $2\frac{6}{11} = \frac{28}{11}$
* Multiply by reciprocal: $\frac{2}{1} \times \frac{11}{28} = \frac{22}{28}$
* Simplify: Divide top and bottom by 2 to get $\frac{11}{14}$.
* Answer: $\frac{11}{14}$

4) $9 \div 1\frac{3}{5}$
* Convert: $9 = \frac{9}{1}$ and $1\frac{3}{5} = \frac{8}{5}$
* Multiply by reciprocal: $\frac{9}{1} \times \frac{5}{8} = \frac{45}{8}$
* Simplify: $45 \div 8 = 5$ with a remainder of $5$.
* Answer: $5\frac{5}{8}$

5) $5 \div 5\frac{10}{19}$
* Convert: $5 = \frac{5}{1}$ and $5\frac{10}{19} = \frac{105}{19}$
* Multiply by reciprocal: $\frac{5}{1} \times \frac{19}{105}$
* Simplify before multiplying: 5 goes into 105 twenty-one times. So, $\frac{1}{1} \times \frac{19}{21} = \frac{19}{21}$.
* Answer: $\frac{19}{21}$

6) $2 \div 2\frac{8}{15}$
* Convert: $2 = \frac{2}{1}$ and $2\frac{8}{15} = \frac{38}{15}$
* Multiply by reciprocal: $\frac{2}{1} \times \frac{15}{38}$
* Simplify before multiplying: 2 goes into 38 nineteen times. So, $\frac{1}{1} \times \frac{15}{19} = \frac{15}{19}$.
* Answer: $\frac{15}{19}$

7) $4 \div 4\frac{2}{7}$
* Convert: $4 = \frac{4}{1}$ and $4\frac{2}{7} = \frac{30}{7}$
* Multiply by reciprocal: $\frac{4}{1} \times \frac{7}{30}$
* Simplify before multiplying: 2 goes into 4 twice and into 30 fifteen times. So, $\frac{2}{1} \times \frac{7}{15} = \frac{14}{15}$.
* Answer: $\frac{14}{15}$

8) $8 \div 8\frac{10}{13}$
* Convert: $8 = \frac{8}{1}$ and $8\frac{10}{13} = \frac{114}{13}$
* Multiply by reciprocal: $\frac{8}{1} \times \frac{13}{114}$
* Simplify before multiplying: 2 goes into 8 four times and into 114 fifty-seven times. So, $\frac{4}{1} \times \frac{13}{57} = \frac{52}{57}$.
* Answer: $\frac{52}{57}$

9) $2 \div 2\frac{8}{15}$
* This is the same as problem #6.
* Answer: $\frac{15}{19}$

10) $7 \div 7\frac{14}{15}$
* Convert: $7 = \frac{7}{1}$ and $7\frac{14}{15} = \frac{119}{15}$
* Multiply by reciprocal: $\frac{7}{1} \times \frac{15}{119}$
* Simplify before multiplying: 7 goes into 119 seventeen times. So, $\frac{1}{1} \times \frac{15}{17} = \frac{15}{17}$.
* Answer: $\frac{15}{17}$

11) $6 \div 3\frac{18}{23}$
* Convert: $6 = \frac{6}{1}$ and $3\frac{18}{23} = \frac{87}{23}$
* Multiply by reciprocal: $\frac{6}{1} \times \frac{23}{87}$
* Simplify before multiplying: 3 goes into 6 twice and into 87 twenty-nine times. So, $\frac{2}{1} \times \frac{23}{29} = \frac{46}{29}$.
* Simplify: $46 \div 29 = 1$ with a remainder of $17$.
* Answer: $1\frac{17}{29}$

12) $5 \div 3\frac{15}{17}$
* Convert: $5 = \frac{5}{1}$ and $3\frac{15}{17} = \frac{66}{17}$
* Multiply by reciprocal: $\frac{5}{1} \times \frac{17}{66} = \frac{85}{66}$
* Simplify: $85 \div 66 = 1$ with a remainder of $19$.
* Answer: $1\frac{19}{66}$

13) $3 \div 5\frac{9}{17}$
* Convert: $3 = \frac{3}{1}$ and $5\frac{9}{17} = \frac{94}{17}$
* Multiply by reciprocal: $\frac{3}{1} \times \frac{17}{94} = \frac{51}{94}$
* This cannot be simplified further.
* Answer: $\frac{51}{94}$

14) $8 \div 2\frac{4}{15}$
* Convert: $8 = \frac{8}{1}$ and $2\frac{4}{15} = \frac{34}{15}$
* Multiply by reciprocal: $\frac{8}{1} \times \frac{15}{34}$
* Simplify before multiplying: 2 goes into 8 four times and into 34 seventeen times. So, $\frac{4}{1} \times \frac{15}{17} = \frac{60}{17}$.
* Simplify: $60 \div 17 = 3$ with a remainder of $9$.
* Answer: $3\frac{9}{17}$

15) $4 \div 1\frac{12}{19}$
* Convert: $4 = \frac{4}{1}$ and $1\frac{12}{19} = \frac{31}{19}$
* Multiply by reciprocal: $\frac{4}{1} \times \frac{19}{31} = \frac{76}{31}$
* Simplify: $76 \div 31 = 2$ with a remainder of $14$.
* Answer: $2\frac{14}{31}$

16) $5 \div 3\frac{5}{8}$
* Convert: $5 = \frac{5}{1}$ and $3\frac{5}{8} = \frac{29}{8}$
* Multiply by reciprocal: $\frac{5}{1} \times \frac{8}{29} = \frac{40}{29}$
* Simplify: $40 \div 29 = 1$ with a remainder of $11$.
* Answer: $1\frac{11}{29}$

17) $3 \div 6\frac{1}{9}$
* Convert: $3 = \frac{3}{1}$ and $6\frac{1}{9} = \frac{55}{9}$
* Multiply by reciprocal: $\frac{3}{1} \times \frac{9}{55} = \frac{27}{55}$
* This cannot be simplified further.
* Answer: $\frac{27}{55}$

18) $7 \div 5\frac{14}{17}$
* Convert: $7 = \frac{7}{1}$ and $5\frac{14}{17} = \frac{99}{17}$
* Multiply by reciprocal: $\frac{7}{1} \times \frac{17}{99} = \frac{119}{99}$
* Simplify: $119 \div 99 = 1$ with a remainder of $20$.
* Answer: $1\frac{20}{99}$

19) $5 \div 3\frac{10}{19}$
* Convert: $5 = \frac{5}{1}$ and $3\frac{10}{19} = \frac{67}{19}$
* Multiply by reciprocal: $\frac{5}{1} \times \frac{19}{67} = \frac{95}{67}$
* Simplify: $95 \div 67 = 1$ with a remainder of $28$.
* Answer: $1\frac{28}{67}$

20) $4 \div 1\frac{8}{15}$
* Convert: $4 = \frac{4}{1}$ and $1\frac{8}{15} = \frac{23}{15}$
* Multiply by reciprocal: $\frac{4}{1} \times \frac{15}{23} = \frac{60}{23}$
* Simplify: $60 \div 23 = 2$ with a remainder of $14$.
* Answer: $2\frac{14}{23}$

Final Answer:
1) $3\frac{15}{16}$
2) $\frac{10}{11}$
3) $\frac{11}{14}$
4) $5\frac{5}{8}$
5) $\frac{19}{21}$
6) $\frac{15}{19}$
7) $\frac{14}{15}$
8) $\frac{52}{57}$
9) $\frac{15}{19}$
10) $\frac{15}{17}$
11) $1\frac{17}{29}$
12) $1\frac{19}{66}$
13) $\frac{51}{94}$
14) $3\frac{9}{17}$
15) $2\frac{14}{31}$
16) $1\frac{11}{29}$
17) $\frac{27}{55}$
18) $1\frac{20}{99}$
19) $1\frac{28}{67}$
20) $2\frac{14}{23}$