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

Let's solve the problem of converting mixed numbers to improper fractions step by step.

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🔷 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,
- $ 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. The result becomes the new numerator.
4. Keep the same denominator.

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

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Now, let’s solve each problem:

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

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

✔ Answer: $ \frac{8}{3} $

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

$$
= \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
$$

✔ Answer: $ \frac{13}{4} $

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

$$
= \frac{(4 \times 5) + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5}
$$

✔ Answer: $ \frac{22}{5} $

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

$$
= \frac{(2 \times 5) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}
$$

✔ Answer: $ \frac{13}{5} $

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

Wait! This one is interesting — $ \frac{3}{2} $ is already an improper fraction, but it's part of a mixed number.

But $ 1 \frac{3}{2} $ means:
$$
= \frac{(1 \times 2) + 3}{2} = \frac{2 + 3}{2} = \frac{5}{2}
$$

✔ Answer: $ \frac{5}{2} $

> Note: Even though $ \frac{3}{2} > 1 $, we still follow the rule.

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

$$
= \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}
$$

✔ Answer: $ \frac{15}{4} $

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

$$
= \frac{(1 \times 4) + 2}{4} = \frac{4 + 2}{4} = \frac{6}{4}
$$

We can simplify this:
$$
\frac{6}{4} = \frac{3}{2}
$$

But since the question just asks for improper fraction (not simplified), both are acceptable. But usually, we reduce if possible.

✔ Answer: $ \frac{6}{4} $ or simplified $ \frac{3}{2} $ → $ \frac{3}{2} $ (recommended)

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

$$
= \frac{(3 \times 7) + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7}
$$

✔ Answer: $ \frac{25}{7} $

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

$$
= \frac{(2 \times 7) + 5}{7} = \frac{14 + 5}{7} = \frac{19}{7}
$$

✔ Answer: $ \frac{19}{7} $

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

$$
= \frac{(1 \times 6) + 3}{6} = \frac{6 + 3}{6} = \frac{9}{6}
$$

Simplify:
$$
\frac{9}{6} = \frac{3}{2}
$$

✔ Answer: $ \frac{9}{6} $ or simplified $ \frac{3}{2} $ → $ \frac{3}{2} $ (recommended)

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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{3}{2} $ |
| 8) $ 3 \frac{4}{7} $ | $ \frac{25}{7} $ |
| 9) $ 2 \frac{5}{7} $ | $ \frac{19}{7} $ |
|10) $ 1 \frac{3}{6} $ | $ \frac{3}{2} $ |

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💡 Tip: Always check if the final improper fraction can be simplified (like #7 and #10). It's good practice!

Let me know if you'd like this as a printable worksheet or with visual aids!