Mixed Numbers to Improper Fractions Worksheets - 15 Worksheets Library - Free Printable

Let's solve each problem step by step. The goal is to convert mixed numbers to improper fractions.

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

A mixed number has the form:
$$
a \frac{b}{c}
$$
where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

To convert it to an improper fraction:
1. Multiply the whole number ($a$) by the denominator ($c$).
2. Add the numerator ($b$) to that product.
3. Place the result over the original denominator ($c$).

So:
$$
a \frac{b}{c} = \frac{(a \times c) + b}{c}
$$

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Now let’s solve each one:

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1) $ 2 \frac{2}{3} $

- $ 2 \times 3 = 6 $
- $ 6 + 2 = 8 $
- So: $ \frac{8}{3} $

✔ Answer: $ \frac{8}{3} $

---

2) $ 3 \frac{1}{4} $

- $ 3 \times 4 = 12 $
- $ 12 + 1 = 13 $
- So: $ \frac{13}{4} $

✔ Answer: $ \frac{13}{4} $

---

3) $ 4 \frac{2}{5} $

- $ 4 \times 5 = 20 $
- $ 20 + 2 = 22 $
- So: $ \frac{22}{5} $

✔ Answer: $ \frac{22}{5} $

---

4) $ 2 \frac{3}{5} $

- $ 2 \times 5 = 10 $
- $ 10 + 3 = 13 $
- So: $ \frac{13}{5} $

✔ Answer: $ \frac{13}{5} $

---

5) $ 1 \frac{3}{2} $

- First, note: $ \frac{3}{2} $ is already greater than 1, but we still follow the rule.
- $ 1 \times 2 = 2 $
- $ 2 + 3 = 5 $
- So: $ \frac{5}{2} $

✔ Answer: $ \frac{5}{2} $

> Note: This is actually an improper fraction already (since $ \frac{3}{2} = 1.5 $), so $ 1 \frac{3}{2} = 2.5 = \frac{5}{2} $

---

6) $ 3 \frac{3}{4} $

- $ 3 \times 4 = 12 $
- $ 12 + 3 = 15 $
- So: $ \frac{15}{4} $

✔ Answer: $ \frac{15}{4} $

---

7) $ 1 \frac{2}{4} $

- $ 1 \times 4 = 4 $
- $ 4 + 2 = 6 $
- So: $ \frac{6}{4} $

✔ Answer: $ \frac{6}{4} $

> Note: This can be simplified to $ \frac{3}{2} $, but unless asked, we leave it as $ \frac{6}{4} $ since the question only asks for improper fractions.

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8) $ 3 \frac{4}{7} $

- $ 3 \times 7 = 21 $
- $ 21 + 4 = 25 $
- So: $ \frac{25}{7} $

✔ Answer: $ \frac{25}{7} $

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9) $ 2 \frac{5}{7} $

- $ 2 \times 7 = 14 $
- $ 14 + 5 = 19 $
- So: $ \frac{19}{7} $

✔ Answer: $ \frac{19}{7} $

---

10) $ 1 \frac{3}{6} $

- $ 1 \times 6 = 6 $
- $ 6 + 3 = 9 $
- So: $ \frac{9}{6} $

✔ Answer: $ \frac{9}{6} $

> Note: This simplifies to $ \frac{3}{2} $, but again, unless simplification is required, we keep it as $ \frac{9}{6} $.

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) $ 2 \frac{2}{3} $ | $ \frac{8}{3} $ |
| 2) $ 3 \frac{1}{4} $ | $ \frac{13}{4} $ |
| 3) $ 4 \frac{2}{5} $ | $ \frac{22}{5} $ |
| 4) $ 2 \frac{3}{5} $ | $ \frac{13}{5} $ |
| 5) $ 1 \frac{3}{2} $ | $ \frac{5}{2} $ |
| 6) $ 3 \frac{3}{4} $ | $ \frac{15}{4} $ |
| 7) $ 1 \frac{2}{4} $ | $ \frac{6}{4} $ |
| 8) $ 3 \frac{4}{7} $ | $ \frac{25}{7} $ |
| 9) $ 2 \frac{5}{7} $ | $ \frac{19}{7} $ |
|10) $ 1 \frac{3}{6} $ | $ \frac{9}{6} $ |

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📝 Summary:

We used the formula:
$$
a \frac{b}{c} = \frac{(a \times c) + b}{c}
$$
to convert each mixed number into an improper fraction.

Let me know if you'd like these simplified too!