Convert mixed numbers to improper fractions worksheets | Worsheets library - Free Printable

Let's solve the worksheet step by step. The task is to convert mixed numbers to improper fractions.

🔷 How to Convert a Mixed Number to an Improper Fraction:

A mixed number has the form:
Whole number + Fraction (e.g., $ 3 \frac{1}{2} $)

To convert it to an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator to that product.
3. Place the result over the original denominator.

$$
\text{Improper Fraction} = \frac{(Whole \times Denominator) + Numerator}{Denominator}
$$

---

Now, let’s solve each problem:

---

1. $ 3 \frac{1}{10} $
$ = \frac{(3 \times 10) + 1}{10} = \frac{30 + 1}{10} = \frac{31}{10} $

2. $ 3 \frac{1}{3} $
$ = \frac{(3 \times 3) + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} $

3. $ 2 \frac{5}{6} $
$ = \frac{(2 \times 6) + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} $

4. $ 2 \frac{2}{4} $
Simplify first: $ \frac{2}{4} = \frac{1}{2} $ → $ 2 \frac{1}{2} $
$ = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} $
*(Or directly: $ \frac{(2 \times 4) + 2}{4} = \frac{8 + 2}{4} = \frac{10}{4} = \frac{5}{2} $)*

5. $ 3 \frac{5}{6} $
$ = \frac{(3 \times 6) + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6} $

6. $ 2 \frac{2}{8} $
Simplify: $ \frac{2}{8} = \frac{1}{4} $ → $ 2 \frac{1}{4} $
$ = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} $
*(Or directly: $ \frac{(2 \times 8) + 2}{8} = \frac{16 + 2}{8} = \frac{18}{8} = \frac{9}{4} $)*

7. $ 3 \frac{1}{3} $
$ = \frac{(3 \times 3) + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} $

8. $ 1 \frac{3}{5} $
$ = \frac{(1 \times 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} $

9. $ 1 \frac{1}{4} $
$ = \frac{(1 \times 4) + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} $

10. $ 1 \frac{1}{4} $ → same as #9: $ \frac{5}{4} $

11. $ 1 \frac{1}{6} $
$ = \frac{(1 \times 6) + 1}{6} = \frac{6 + 1}{6} = \frac{7}{6} $

12. $ 2 \frac{5}{6} $
$ = \frac{(2 \times 6) + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} $

13. $ 2 \frac{11}{12} $
$ = \frac{(2 \times 12) + 11}{12} = \frac{24 + 11}{12} = \frac{35}{12} $

14. $ 2 \frac{1}{2} $
$ = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} $

15. $ 1 \frac{1}{2} $
$ = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} $

16. $ 1 \frac{5}{10} $
Simplify: $ \frac{5}{10} = \frac{1}{2} $ → $ 1 \frac{1}{2} $ → $ \frac{3}{2} $
*(Or: $ \frac{(1 \times 10) + 5}{10} = \frac{15}{10} = \frac{3}{2} $)*

17. $ 2 \frac{2}{3} $
$ = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} $

18. $ 1 \frac{1}{4} $ → same as #9 and #10: $ \frac{5}{4} $

19. $ 3 \frac{8}{10} $
Simplify: $ \frac{8}{10} = \frac{4}{5} $ → $ 3 \frac{4}{5} $
$ = \frac{(3 \times 5) + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} $
*(Or: $ \frac{(3 \times 10) + 8}{10} = \frac{38}{10} = \frac{19}{5} $)*

20. $ 3 \frac{2}{5} $
$ = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $

21. $ 2 \frac{2}{3} $
$ = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} $

---

✔ Final Answers:

1. $ \frac{31}{10} $
2. $ \frac{10}{3} $
3. $ \frac{17}{6} $
4. $ \frac{5}{2} $
5. $ \frac{23}{6} $
6. $ \frac{9}{4} $
7. $ \frac{10}{3} $
8. $ \frac{8}{5} $
9. $ \frac{5}{4} $
10. $ \frac{5}{4} $
11. $ \frac{7}{6} $
12. $ \frac{17}{6} $
13. $ \frac{35}{12} $
14. $ \frac{5}{2} $
15. $ \frac{3}{2} $
16. $ \frac{3}{2} $
17. $ \frac{8}{3} $
18. $ \frac{5}{4} $
19. $ \frac{19}{5} $
20. $ \frac{17}{5} $
21. $ \frac{8}{3} $

---

📝 Notes:

- Always simplify fractions when possible (like $ \frac{10}{4} \to \frac{5}{2} $).
- Some problems repeat (e.g., #9, #10, #18 are all $ 1 \frac{1}{4} $), so answers match.
- The key idea is consistent application of the formula:
$$
\text{Improper Fraction} = \frac{\text{Whole} \times \text{Denominator} + \text{Numerator}}{\text{Denominator}}
$$

Let me know if you'd like this in printable format or with visual explanations!