Math worksheet for converting improper fractions to mixed numbers and vice versa.

It looks like you've uploaded a worksheet that includes two types of fraction conversion problems:

1. Converting improper fractions to mixed numbers
2. Converting mixed numbers to improper fractions

Let’s go through each problem step by step and solve them.

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🔹 Part 1: Converting Improper Fractions to Mixed Numbers

We convert an improper fraction (where the numerator is greater than or equal to the denominator) into a mixed number by dividing the numerator by the denominator.

The result is:
- Quotient = whole number
- Remainder = new numerator
- Denominator stays the same

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#### 1) \( \frac{47}{10} \)

Divide 47 ÷ 10 = 4 with remainder 7
So, \( \frac{47}{10} = 4 \frac{7}{10} \)

✔ Answer: \( 4 \frac{7}{10} \)

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#### 2) \( \frac{33}{9} \)

Divide 33 ÷ 9 = 3 with remainder 6
Simplify \( \frac{6}{9} = \frac{2}{3} \)
So, \( \frac{33}{9} = 3 \frac{2}{3} \)

✔ Answer: \( 3 \frac{2}{3} \)

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#### 3) \( \frac{12}{5} \)

Divide 12 ÷ 5 = 2 with remainder 2
So, \( \frac{12}{5} = 2 \frac{2}{5} \)

✔ Answer: \( 2 \frac{2}{5} \)

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#### 4) \( \frac{25}{6} \)

Divide 25 ÷ 6 = 4 with remainder 1
So, \( \frac{25}{6} = 4 \frac{1}{6} \)

✔ Answer: \( 4 \frac{1}{6} \)

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#### 5) \( \frac{58}{9} \)

Divide 58 ÷ 9 = 6 with remainder 4
So, \( \frac{58}{9} = 6 \frac{4}{9} \)

✔ Answer: \( 6 \frac{4}{9} \)

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#### 6) \( \frac{27}{10} \)

Divide 27 ÷ 10 = 2 with remainder 7
So, \( \frac{27}{10} = 2 \frac{7}{10} \)

✔ Answer: \( 2 \frac{7}{10} \)

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#### 7) \( \frac{19}{5} \)

Divide 19 ÷ 5 = 3 with remainder 4
So, \( \frac{19}{5} = 3 \frac{4}{5} \)

✔ Answer: \( 3 \frac{4}{5} \)

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#### 8) \( \frac{34}{12} \)

Divide 34 ÷ 12 = 2 with remainder 10
Simplify \( \frac{10}{12} = \frac{5}{6} \)
So, \( \frac{34}{12} = 2 \frac{5}{6} \)

✔ Answer: \( 2 \frac{5}{6} \)

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#### 9) \( \frac{26}{8} \)

Divide 26 ÷ 8 = 3 with remainder 2
Simplify \( \frac{2}{8} = \frac{1}{4} \)
So, \( \frac{26}{8} = 3 \frac{1}{4} \)

✔ Answer: \( 3 \frac{1}{4} \)

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🔹 Part 2: Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction:
- Multiply the whole number by the denominator
- Add the numerator
- Place the result over the original denominator

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#### 1) \( 8 \frac{1}{6} \)

\( 8 \times 6 + 1 = 48 + 1 = 49 \) → \( \frac{49}{6} \)

✔ Answer: \( \frac{49}{6} \)

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#### 2) \( 7 \frac{1}{5} \)

\( 7 \times 5 + 1 = 35 + 1 = 36 \) → \( \frac{36}{5} \)

✔ Answer: \( \frac{36}{5} \)

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#### 3) \( 2 \frac{4}{11} \)

\( 2 \times 11 + 4 = 22 + 4 = 26 \) → \( \frac{26}{11} \)

✔ Answer: \( \frac{26}{11} \)

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#### 4) \( 9 \frac{2}{3} \)

\( 9 \times 3 + 2 = 27 + 2 = 29 \) → \( \frac{29}{3} \)

✔ Answer: \( \frac{29}{3} \)

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#### 5) \( 8 \frac{3}{4} \)

\( 8 \times 4 + 3 = 32 + 3 = 35 \) → \( \frac{35}{4} \)

✔ Answer: \( \frac{35}{4} \)

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#### 6) \( 2 \frac{2}{3} \)

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

✔ Answer: \( \frac{8}{3} \)

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#### 7) \( 8 \frac{4}{5} \)

\( 8 \times 5 + 4 = 40 + 4 = 44 \) → \( \frac{44}{5} \)

✔ Answer: \( \frac{44}{5} \)

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#### 8) \( 4 \frac{2}{5} \)

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

✔ Answer: \( \frac{22}{5} \)

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#### 9) \( 2 \frac{3}{4} \)

\( 2 \times 4 + 3 = 8 + 3 = 11 \) → \( \frac{11}{4} \)

✔ Answer: \( \frac{11}{4} \)

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#### 10) \( 3 \frac{12}{2} \)

Wait — this is unusual. \( \frac{12}{2} = 6 \), so \( 3 + 6 = 9 \). But let's assume it's a typo or meant to be \( 3 \frac{1}{2} \)? Or perhaps \( 3 \frac{12}{2} \) is not standard.

But if we interpret it literally:
\( 3 \frac{12}{2} = 3 + \frac{12}{2} = 3 + 6 = 9 \) → \( \frac{9}{1} \)

Alternatively, maybe it was meant to be \( 3 \frac{1}{2} \)? But as written:
→ \( \frac{12}{2} = 6 \), so total value is 9.

But in improper fraction form:
\( 3 \times 2 + 12 = 6 + 12 = 18 \), then \( \frac{18}{2} = 9 \)

So \( 3 \frac{12}{2} = \frac{18}{2} = 9 \), but this is not a proper mixed number since \( \frac{12}{2} = 6 \).

Possibly a typo. Let's assume it's meant to be \( 3 \frac{1}{2} \) → then \( \frac{7}{2} \)

But as written:
\( 3 \frac{12}{2} \) → improper fraction:
Whole number × denominator + numerator = \( 3 \times 2 + 12 = 6 + 12 = 18 \) → \( \frac{18}{2} \)

✔ Answer: \( \frac{18}{2} \) (or simplified: \( 9 \))

But likely a typo — probably meant \( 3 \frac{1}{2} \), which would be \( \frac{7}{2} \)

Let’s move on.

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#### 11) \( 4 \frac{4}{5} \)

\( 4 \times 5 + 4 = 20 + 4 = 24 \) → \( \frac{24}{5} \)

✔ Answer: \( \frac{24}{5} \)

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#### 12) \( 5 \frac{5}{12} \)

\( 5 \times 12 + 5 = 60 + 5 = 65 \) → \( \frac{65}{12} \)

✔ Answer: \( \frac{65}{12} \)

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#### 13) \( 4 \frac{5}{5} \)

Note: \( \frac{5}{5} = 1 \), so \( 4 + 1 = 5 \) → \( \frac{5}{1} \)

Or compute: \( 4 \times 5 + 5 = 20 + 5 = 25 \) → \( \frac{25}{5} = 5 \)

✔ Answer: \( \frac{25}{5} \) or simplified \( 5 \)

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#### 14) \( 5 \frac{3}{5} \)

\( 5 \times 5 + 3 = 25 + 3 = 28 \) → \( \frac{28}{5} \)

✔ Answer: \( \frac{28}{5} \)

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#### 15) \( 2 \frac{5}{8} \)

\( 2 \times 8 + 5 = 16 + 5 = 21 \) → \( \frac{21}{8} \)

✔ Answer: \( \frac{21}{8} \)

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✔ Final Answers Summary

#### Improper to Mixed Numbers:
1. \( \frac{47}{10} = 4 \frac{7}{10} \)
2. \( \frac{33}{9} = 3 \frac{2}{3} \)
3. \( \frac{12}{5} = 2 \frac{2}{5} \)
4. \( \frac{25}{6} = 4 \frac{1}{6} \)
5. \( \frac{58}{9} = 6 \frac{4}{9} \)
6. \( \frac{27}{10} = 2 \frac{7}{10} \)
7. \( \frac{19}{5} = 3 \frac{4}{5} \)
8. \( \frac{34}{12} = 2 \frac{5}{6} \)
9. \( \frac{26}{8} = 3 \frac{1}{4} \)

#### Mixed to Improper Fractions:
1. \( 8 \frac{1}{6} = \frac{49}{6} \)
2. \( 7 \frac{1}{5} = \frac{36}{5} \)
3. \( 2 \frac{4}{11} = \frac{26}{11} \)
4. \( 9 \frac{2}{3} = \frac{29}{3} \)
5. \( 8 \frac{3}{4} = \frac{35}{4} \)
6. \( 2 \frac{2}{3} = \frac{8}{3} \)
7. \( 8 \frac{4}{5} = \frac{44}{5} \)
8. \( 4 \frac{2}{5} = \frac{22}{5} \)
9. \( 2 \frac{3}{4} = \frac{11}{4} \)
10. \( 3 \frac{12}{2} = \frac{18}{2} = 9 \) *(likely typo)*
11. \( 4 \frac{4}{5} = \frac{24}{5} \)
12. \( 5 \frac{5}{12} = \frac{65}{12} \)
13. \( 4 \frac{5}{5} = \frac{25}{5} = 5 \)
14. \( 5 \frac{3}{5} = \frac{28}{5} \)
15. \( 2 \frac{5}{8} = \frac{21}{8} \)

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