Convert mixed numbers to improper fractions with this Grade 4 Fractions Worksheet from K5 Learning.

Problem: Convert mixed numbers to improper fractions

The task is to convert each mixed number in the worksheet into an improper fraction. Here's how to solve it step by step:

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#### Step-by-Step Process to Convert Mixed Numbers to Improper Fractions:

1. Identify the parts of the mixed number:
- A mixed number consists of a whole number and a proper fraction.
- Example: \( 3 \frac{4}{10} \)
- Whole number: \( 3 \)
- Fraction: \( \frac{4}{10} \)

2. Multiply the whole number by the denominator of the fraction:
- This gives you the total number of fractional parts represented by the whole number.
- Example: For \( 3 \frac{4}{10} \):
- Whole number: \( 3 \)
- Denominator: \( 10 \)
- Calculation: \( 3 \times 10 = 30 \)

3. Add the result to the numerator of the fraction:
- This gives you the new numerator for the improper fraction.
- Example: For \( 3 \frac{4}{10} \):
- Numerator of the fraction: \( 4 \)
- Add: \( 30 + 4 = 34 \)

4. Keep the same denominator:
- The denominator of the improper fraction remains the same as the denominator of the original fraction.
- Example: For \( 3 \frac{4}{10} \):
- Denominator: \( 10 \)

5. Write the improper fraction:
- Combine the new numerator and the denominator.
- Example: For \( 3 \frac{4}{10} \):
- New numerator: \( 34 \)
- Denominator: \( 10 \)
- Improper fraction: \( \frac{34}{10} \)

6. Simplify the fraction if possible:
- Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
- Example: For \( \frac{34}{10} \):
- GCD of 34 and 10 is 2.
- Simplify: \( \frac{34 \div 2}{10 \div 2} = \frac{17}{5} \)

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#### Solutions for Each Problem:

1. \( 3 \frac{4}{10} \)
- Whole number: \( 3 \)
- Denominator: \( 10 \)
- Numerator: \( 4 \)
- Calculation:
\[
3 \times 10 + 4 = 30 + 4 = 34
\]
- Improper fraction: \( \frac{34}{10} \)
- Simplify: \( \frac{34 \div 2}{10 \div 2} = \frac{17}{5} \)
- Answer: \( \frac{17}{5} \)

2. \( 3 \frac{1}{3} \)
- Whole number: \( 3 \)
- Denominator: \( 3 \)
- Numerator: \( 1 \)
- Calculation:
\[
3 \times 3 + 1 = 9 + 1 = 10
\]
- Improper fraction: \( \frac{10}{3} \)
- Answer: \( \frac{10}{3} \)

3. \( 2 \frac{5}{8} \)
- Whole number: \( 2 \)
- Denominator: \( 8 \)
- Numerator: \( 5 \)
- Calculation:
\[
2 \times 8 + 5 = 16 + 5 = 21
\]
- Improper fraction: \( \frac{21}{8} \)
- Answer: \( \frac{21}{8} \)

4. \( 2 \frac{2}{4} \)
- Whole number: \( 2 \)
- Denominator: \( 4 \)
- Numerator: \( 2 \)
- Calculation:
\[
2 \times 4 + 2 = 8 + 2 = 10
\]
- Improper fraction: \( \frac{10}{4} \)
- Simplify: \( \frac{10 \div 2}{4 \div 2} = \frac{5}{2} \)
- Answer: \( \frac{5}{2} \)

5. \( 3 \frac{5}{6} \)
- Whole number: \( 3 \)
- Denominator: \( 6 \)
- Numerator: \( 5 \)
- Calculation:
\[
3 \times 6 + 5 = 18 + 5 = 23
\]
- Improper fraction: \( \frac{23}{6} \)
- Answer: \( \frac{23}{6} \)

6. \( 2 \frac{2}{8} \)
- Whole number: \( 2 \)
- Denominator: \( 8 \)
- Numerator: \( 2 \)
- Calculation:
\[
2 \times 8 + 2 = 16 + 2 = 18
\]
- Improper fraction: \( \frac{18}{8} \)
- Simplify: \( \frac{18 \div 2}{8 \div 2} = \frac{9}{4} \)
- Answer: \( \frac{9}{4} \)

7. \( 3 \frac{2}{3} \)
- Whole number: \( 3 \)
- Denominator: \( 3 \)
- Numerator: \( 2 \)
- Calculation:
\[
3 \times 3 + 2 = 9 + 2 = 11
\]
- Improper fraction: \( \frac{11}{3} \)
- Answer: \( \frac{11}{3} \)

8. \( 1 \frac{3}{6} \)
- Whole number: \( 1 \)
- Denominator: \( 6 \)
- Numerator: \( 3 \)
- Calculation:
\[
1 \times 6 + 3 = 6 + 3 = 9
\]
- Improper fraction: \( \frac{9}{6} \)
- Simplify: \( \frac{9 \div 3}{6 \div 3} = \frac{3}{2} \)
- Answer: \( \frac{3}{2} \)

9. \( 1 \frac{7}{8} \)
- Whole number: \( 1 \)
- Denominator: \( 8 \)
- Numerator: \( 7 \)
- Calculation:
\[
1 \times 8 + 7 = 8 + 7 = 15
\]
- Improper fraction: \( \frac{15}{8} \)
- Answer: \( \frac{15}{8} \)

10. \( 1 \frac{1}{4} \)
- Whole number: \( 1 \)
- Denominator: \( 4 \)
- Numerator: \( 1 \)
- Calculation:
\[
1 \times 4 + 1 = 4 + 1 = 5
\]
- Improper fraction: \( \frac{5}{4} \)
- Answer: \( \frac{5}{4} \)

11. \( 1 \frac{1}{6} \)
- Whole number: \( 1 \)
- Denominator: \( 6 \)
- Numerator: \( 1 \)
- Calculation:
\[
1 \times 6 + 1 = 6 + 1 = 7
\]
- Improper fraction: \( \frac{7}{6} \)
- Answer: \( \frac{7}{6} \)

12. \( 2 \frac{4}{5} \)
- Whole number: \( 2 \)
- Denominator: \( 5 \)
- Numerator: \( 4 \)
- Calculation:
\[
2 \times 5 + 4 = 10 + 4 = 14
\]
- Improper fraction: \( \frac{14}{5} \)
- Answer: \( \frac{14}{5} \)

13. \( 2 \frac{11}{12} \)
- Whole number: \( 2 \)
- Denominator: \( 12 \)
- Numerator: \( 11 \)
- Calculation:
\[
2 \times 12 + 11 = 24 + 11 = 35
\]
- Improper fraction: \( \frac{35}{12} \)
- Answer: \( \frac{35}{12} \)

14. \( 2 \frac{1}{2} \)
- Whole number: \( 2 \)
- Denominator: \( 2 \)
- Numerator: \( 1 \)
- Calculation:
\[
2 \times 2 + 1 = 4 + 1 = 5
\]
- Improper fraction: \( \frac{5}{2} \)
- Answer: \( \frac{5}{2} \)

15. \( 1 \frac{1}{2} \)
- Whole number: \( 1 \)
- Denominator: \( 2 \)
- Numerator: \( 1 \)
- Calculation:
\[
1 \times 2 + 1 = 2 + 1 = 3
\]
- Improper fraction: \( \frac{3}{2} \)
- Answer: \( \frac{3}{2} \)

16. \( 1 \frac{6}{10} \)
- Whole number: \( 1 \)
- Denominator: \( 10 \)
- Numerator: \( 6 \)
- Calculation:
\[
1 \times 10 + 6 = 10 + 6 = 16
\]
- Improper fraction: \( \frac{16}{10} \)
- Simplify: \( \frac{16 \div 2}{10 \div 2} = \frac{8}{5} \)
- Answer: \( \frac{8}{5} \)

17. \( 2 \frac{1}{3} \)
- Whole number: \( 2 \)
- Denominator: \( 3 \)
- Numerator: \( 1 \)
- Calculation:
\[
2 \times 3 + 1 = 6 + 1 = 7
\]
- Improper fraction: \( \frac{7}{3} \)
- Answer: \( \frac{7}{3} \)

18. \( 1 \frac{3}{4} \)
- Whole number: \( 1 \)
- Denominator: \( 4 \)
- Numerator: \( 3 \)
- Calculation:
\[
1 \times 4 + 3 = 4 + 3 = 7
\]
- Improper fraction: \( \frac{7}{4} \)
- Answer: \( \frac{7}{4} \)

19. \( 3 \frac{8}{10} \)
- Whole number: \( 3 \)
- Denominator: \( 10 \)
- Numerator: \( 8 \)
- Calculation:
\[
3 \times 10 + 8 = 30 + 8 = 38
\]
- Improper fraction: \( \frac{38}{10} \)
- Simplify: \( \frac{38 \div 2}{10 \div 2} = \frac{19}{5} \)
- Answer: \( \frac{19}{5} \)

20. \( 3 \frac{2}{5} \)
- Whole number: \( 3 \)
- Denominator: \( 5 \)
- Numerator: \( 2 \)
- Calculation:
\[
3 \times 5 + 2 = 15 + 2 = 17
\]
- Improper fraction: \( \frac{17}{5} \)
- Answer: \( \frac{17}{5} \)

21. \( 2 \frac{2}{3} \)
- Whole number: \( 2 \)
- Denominator: \( 3 \)
- Numerator: \( 2 \)
- Calculation:
\[
2 \times 3 + 2 = 6 + 2 = 8
\]
- Improper fraction: \( \frac{8}{3} \)
- Answer: \( \frac{8}{3} \)

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Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & \frac{17}{5} & 2. & \frac{10}{3} & 3. & \frac{21}{8} \\
4. & \frac{5}{2} & 5. & \frac{23}{6} & 6. & \frac{9}{4} \\
7. & \frac{11}{3} & 8. & \frac{3}{2} & 9. & \frac{15}{8} \\
10. & \frac{5}{4} & 11. & \frac{7}{6} & 12. & \frac{14}{5} \\
13. & \frac{35}{12} & 14. & \frac{5}{2} & 15. & \frac{3}{2} \\
16. & \frac{8}{5} & 17. & \frac{7}{3} & 18. & \frac{7}{4} \\
19. & \frac{19}{5} & 20. & \frac{17}{5} & 21. & \frac{8}{3} \\
\end{array}
}
\]