SOLUTION: Mixed operations fractions - Studypool - Free Printable

Here are the step-by-step solutions for each problem on your worksheet.

1. $9 \frac{3}{5} - 4 \frac{4}{5}$
* You cannot subtract $\frac{4}{5}$ from $\frac{3}{5}$, so you need to borrow from the whole number.
* Change $9$ into $8 + 1$. Since $1 = \frac{5}{5}$, add that to the fraction: $\frac{3}{5} + \frac{5}{5} = \frac{8}{5}$.
* Now the problem is $8 \frac{8}{5} - 4 \frac{4}{5}$.
* Subtract whole numbers: $8 - 4 = 4$.
* Subtract fractions: $\frac{8}{5} - \frac{4}{5} = \frac{4}{5}$.
* Answer: $4 \frac{4}{5}$

2. $9 \frac{2}{3} + 3 \frac{1}{3}$
* Add the whole numbers: $9 + 3 = 12$.
* Add the fractions: $\frac{2}{3} + \frac{1}{3} = \frac{3}{3}$.
* $\frac{3}{3}$ equals $1$ whole.
* Add that 1 to the 12.
* Answer: $13$

3. $2 \frac{1}{3} + 5 \frac{1}{3}$
* Add the whole numbers: $2 + 5 = 7$.
* Add the fractions: $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$.
* Answer: $7 \frac{2}{3}$

4. $9 \frac{2}{4} \div 1 \frac{2}{4}$
* First, simplify the fractions if possible. $\frac{2}{4}$ is the same as $\frac{1}{2}$. So, $9 \frac{1}{2} \div 1 \frac{1}{2}$.
* Turn mixed numbers into improper fractions:
* $9 \frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{19}{2}$
* $1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$
* Divide by flipping the second fraction (multiply by reciprocal): $\frac{19}{2} \times \frac{2}{3}$.
* The 2s cancel out. You are left with $\frac{19}{3}$.
* Convert back to a mixed number: 3 goes into 19 six times with 1 left over.
* Answer: $6 \frac{1}{3}$

5. $6 \frac{4}{6} \div 4 \frac{1}{6}$
* Simplify $\frac{4}{6}$ to $\frac{2}{3}$. The problem is $6 \frac{2}{3} \div 4 \frac{1}{6}$.
* Turn into improper fractions:
* $6 \frac{2}{3} = \frac{20}{3}$
* $4 \frac{1}{6} = \frac{25}{6}$
* Flip and multiply: $\frac{20}{3} \times \frac{6}{25}$.
* Simplify before multiplying: 20 and 25 both divide by 5 (becomes 4 and 5). 6 and 3 both divide by 3 (becomes 2 and 1).
* New equation: $\frac{4}{1} \times \frac{2}{5} = \frac{8}{5}$.
* Convert to mixed number: 5 goes into 8 once with 3 left over.
* Answer: $1 \frac{3}{5}$

6. $4 \frac{1}{8} \div 3 \frac{5}{8}$
* Turn into improper fractions:
* $4 \frac{1}{8} = \frac{33}{8}$
* $3 \frac{5}{8} = \frac{29}{8}$
* Flip and multiply: $\frac{33}{8} \times \frac{8}{29}$.
* The 8s cancel out. You are left with $\frac{33}{29}$.
* Convert to mixed number: 29 goes into 33 one time with 4 left over.
* Answer: $1 \frac{4}{29}$

7. $5 \frac{2}{5} \times 5 \frac{4}{5}$
* Turn into improper fractions:
* $5 \frac{2}{5} = \frac{27}{5}$
* $5 \frac{4}{5} = \frac{29}{5}$
* Multiply straight across:
* Top: $27 \times 29 = 783$
* Bottom: $5 \times 5 = 25$
* Result: $\frac{783}{25}$.
* Convert to mixed number: 25 goes into 783 thirty-one times ($31 \times 25 = 775$) with 8 left over.
* Answer: $31 \frac{8}{25}$

8. $3 \frac{4}{6} \div 6 \frac{3}{6}$
* Simplify fractions first: $\frac{4}{6} = \frac{2}{3}$ and $\frac{3}{6} = \frac{1}{2}$.
* Problem: $3 \frac{2}{3} \div 6 \frac{1}{2}$.
* Turn into improper fractions:
* $3 \frac{2}{3} = \frac{11}{3}$
* $6 \frac{1}{2} = \frac{13}{2}$
* Flip and multiply: $\frac{11}{3} \times \frac{2}{13}$.
* Top: $11 \times 2 = 22$. Bottom: $3 \times 13 = 39$.
* Result: $\frac{22}{39}$. This cannot be simplified further.
* Answer: $\frac{22}{39}$

9. $3 \frac{3}{4} \times 9 \frac{3}{4}$
* Turn into improper fractions:
* $3 \frac{3}{4} = \frac{15}{4}$
* $9 \frac{3}{4} = \frac{39}{4}$
* Multiply straight across:
* Top: $15 \times 39 = 585$
* Bottom: $4 \times 4 = 16$
* Result: $\frac{585}{16}$.
* Convert to mixed number: 16 goes into 585 thirty-six times ($36 \times 16 = 576$) with 9 left over.
* Answer: $36 \frac{9}{16}$

10. $1 \frac{6}{8} \times 8 \frac{2}{8}$
* Simplify fractions: $\frac{6}{8} = \frac{3}{4}$ and $\frac{2}{8} = \frac{1}{4}$.
* Problem: $1 \frac{3}{4} \times 8 \frac{1}{4}$.
* Turn into improper fractions:
* $1 \frac{3}{4} = \frac{7}{4}$
* $8 \frac{1}{4} = \frac{33}{4}$
* Multiply straight across:
* Top: $7 \times 33 = 231$
* Bottom: $4 \times 4 = 16$
* Result: $\frac{231}{16}$.
* Convert to mixed number: 16 goes into 231 fourteen times ($14 \times 16 = 224$) with 7 left over.
* Answer: $14 \frac{7}{16}$

11. $2 \frac{3}{5} + 7 \frac{2}{5}$
* Add whole numbers: $2 + 7 = 9$.
* Add fractions: $\frac{3}{5} + \frac{2}{5} = \frac{5}{5}$.
* $\frac{5}{5}$ equals 1 whole.
* Add 1 to 9.
* Answer: $10$

12. $4 \frac{1}{3} \times 8 \frac{1}{3}$
* Turn into improper fractions:
* $4 \frac{1}{3} = \frac{13}{3}$
* $8 \frac{1}{3} = \frac{25}{3}$
* Multiply straight across:
* Top: $13 \times 25 = 325$
* Bottom: $3 \times 3 = 9$
* Result: $\frac{325}{9}$.
* Convert to mixed number: 9 goes into 325 thirty-six times ($36 \times 9 = 324$) with 1 left over.
* Answer: $36 \frac{1}{9}$

13. $8 \frac{1}{2} \times 7 \frac{1}{2}$
* Turn into improper fractions:
* $8 \frac{1}{2} = \frac{17}{2}$
* $7 \frac{1}{2} = \frac{15}{2}$
* Multiply straight across:
* Top: $17 \times 15 = 255$
* Bottom: $2 \times 2 = 4$
* Result: $\frac{255}{4}$.
* Convert to mixed number: 4 goes into 255 sixty-three times ($63 \times 4 = 252$) with 3 left over.
* Answer: $63 \frac{3}{4}$

14. $8 \frac{1}{2} + 9 \frac{1}{2}$
* Add whole numbers: $8 + 9 = 17$.
* Add fractions: $\frac{1}{2} + \frac{1}{2} = \frac{2}{2}$.
* $\frac{2}{2}$ equals 1 whole.
* Add 1 to 17.
* Answer: $18$

15. $9 \frac{4}{5} + 3 \frac{2}{5}$
* Add whole numbers: $9 + 3 = 12$.
* Add fractions: $\frac{4}{5} + \frac{2}{5} = \frac{6}{5}$.
* $\frac{6}{5}$ is an improper fraction. It equals $1 \frac{1}{5}$.
* Add the 1 to the 12.
* Answer: $13 \frac{1}{5}$

Final Answer:
1. $4 \frac{4}{5}$
2. $13$
3. $7 \frac{2}{3}$
4. $6 \frac{1}{3}$
5. $1 \frac{3}{5}$
6. $1 \frac{4}{29}$
7. $31 \frac{8}{25}$
8. $\frac{22}{39}$
9. $36 \frac{9}{16}$
10. $14 \frac{7}{16}$
11. $10$
12. $36 \frac{1}{9}$
13. $63 \frac{3}{4}$
14. $18$
15. $13 \frac{1}{5}$