Mixed numbers and decimals | 4th grade Math Worksheet | GreatSchools - Free Printable

Let's solve the problem step by step based on the worksheet titled "Fractions and decimals".

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Part 1: Write each fraction as a decimal

We are given fractions and need to convert them into decimals.

1. $ 1 \frac{3}{4} = 1 + \frac{3}{4} = 1 + 0.75 = \boxed{1.75} $
2. $ 1 \frac{2}{5} = 1 + \frac{2}{5} = 1 + 0.4 = \boxed{1.4} $
3. $ 1 \frac{4}{5} = 1 + \frac{4}{5} = 1 + 0.8 = \boxed{1.8} $

4. $ 2.5 = \frac{25}{10} = \frac{5}{2} = \boxed{\frac{5}{2}} $
5. $ 1.9 = \frac{19}{10} = \boxed{\frac{19}{10}} $
6. $ 3.2 = \frac{32}{10} = \frac{16}{5} = \boxed{\frac{16}{5}} $

> ✔ So far, the answers match what is already filled in (e.g., 1.75, 1.4, etc.).

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Part 2: Write each fraction as a decimal

Now convert these mixed numbers and improper fractions to decimals:

1. $ 2 \frac{1}{2} = 2 + 0.5 = \boxed{2.5} $
2. $ 3 \frac{1}{4} = 3 + 0.25 = \boxed{3.25} $
3. $ 4 \frac{1}{2} = 4 + 0.5 = \boxed{4.5} $
4. $ 1 \frac{1}{4} = 1 + 0.25 = \boxed{1.25} $
5. $ 5 \frac{1}{2} = 5 + 0.5 = \boxed{5.5} $
6. $ 2 \frac{1}{2} = 2 + 0.5 = \boxed{2.5} $
7. $ 6 \frac{3}{4} = 6 + 0.75 = \boxed{6.75} $
8. $ 9 \frac{1}{2} = 9 + 0.5 = \boxed{9.5} $
9. $ 1 \frac{1}{2} = 1 + 0.5 = \boxed{1.5} $
10. $ 9 \frac{1}{4} = 9 + 0.25 = \boxed{9.25} $
11. $ 6 \frac{1}{2} = 6 + 0.5 = \boxed{6.5} $
12. $ 10 \frac{1}{2} = 10 + 0.5 = \boxed{10.5} $

✔ These are all correct.

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Part 3: Write each decimal as a fraction

Convert decimals to fractions:

1. $ 3.2 = \frac{32}{10} = \frac{16}{5} $
2. $ 4.5 = \frac{45}{10} = \frac{9}{2} $
3. $ 1.2 = \frac{12}{10} = \frac{6}{5} $
4. $ 6.3 = \frac{63}{10} $
5. $ 2.3 = \frac{23}{10} $
6. $ 5.1 = \frac{51}{10} $
7. $ 7.2 = \frac{72}{10} = \frac{36}{5} $
8. $ 8.5 = \frac{85}{10} = \frac{17}{2} $
9. $ 11.2 = \frac{112}{10} = \frac{56}{5} $
10. $ 12.1 = \frac{121}{10} $
11. $ 13.5 = \frac{135}{10} = \frac{27}{2} $
12. $ 17.5 = \frac{175}{10} = \frac{35}{2} $
13. $ 18.2 = \frac{182}{10} = \frac{91}{5} $
14. $ 14.7 = \frac{147}{10} $

So:
- $ 3.2 = \boxed{\frac{16}{5}} $
- $ 4.5 = \boxed{\frac{9}{2}} $
- $ 1.2 = \boxed{\frac{6}{5}} $
- $ 6.3 = \boxed{\frac{63}{10}} $
- $ 2.3 = \boxed{\frac{23}{10}} $
- $ 5.1 = \boxed{\frac{51}{10}} $
- $ 7.2 = \boxed{\frac{36}{5}} $
- $ 8.5 = \boxed{\frac{17}{2}} $
- $ 11.2 = \boxed{\frac{56}{5}} $
- $ 12.1 = \boxed{\frac{121}{10}} $
- $ 13.5 = \boxed{\frac{27}{2}} $
- $ 17.5 = \boxed{\frac{35}{2}} $
- $ 18.2 = \boxed{\frac{91}{5}} $
- $ 14.7 = \boxed{\frac{147}{10}} $

✔ All simplified where possible.

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Part 4: Write each fraction as a decimal

Given:
- $ \frac{1}{4} = 0.25 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{3}{4} = 0.75 $

So:
- $ \frac{1}{4} = \boxed{0.25} $
- $ \frac{1}{2} = \boxed{0.5} $
- $ \frac{3}{4} = \boxed{0.75} $

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Part 5: Write each decimal as a fraction

Given:
- $ 0.8 = \frac{8}{10} = \frac{4}{5} $
- $ 0.2 = \frac{2}{10} = \frac{1}{5} $
- $ 0.1 = \frac{1}{10} $

So:
- $ 0.8 = \boxed{\frac{4}{5}} $
- $ 0.2 = \boxed{\frac{1}{5}} $
- $ 0.1 = \boxed{\frac{1}{10}} $

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✔ Final Answers Summary

#### Part 1:
- $ 1 \frac{3}{4} = 1.75 $
- $ 1 \frac{2}{5} = 1.4 $
- $ 1 \frac{4}{5} = 1.8 $

#### Part 2:
- $ 2 \frac{1}{2} = 2.5 $
- $ 3 \frac{1}{4} = 3.25 $
- $ 4 \frac{1}{2} = 4.5 $
- $ 1 \frac{1}{4} = 1.25 $
- $ 5 \frac{1}{2} = 5.5 $
- $ 2 \frac{1}{2} = 2.5 $
- $ 6 \frac{3}{4} = 6.75 $
- $ 9 \frac{1}{2} = 9.5 $
- $ 1 \frac{1}{2} = 1.5 $
- $ 9 \frac{1}{4} = 9.25 $
- $ 6 \frac{1}{2} = 6.5 $
- $ 10 \frac{1}{2} = 10.5 $

#### Part 3:
- $ 3.2 = \frac{16}{5} $
- $ 4.5 = \frac{9}{2} $
- $ 1.2 = \frac{6}{5} $
- $ 6.3 = \frac{63}{10} $
- $ 2.3 = \frac{23}{10} $
- $ 5.1 = \frac{51}{10} $
- $ 7.2 = \frac{36}{5} $
- $ 8.5 = \frac{17}{2} $
- $ 11.2 = \frac{56}{5} $
- $ 12.1 = \frac{121}{10} $
- $ 13.5 = \frac{27}{2} $
- $ 17.5 = \frac{35}{2} $
- $ 18.2 = \frac{91}{5} $
- $ 14.7 = \frac{147}{10} $

#### Part 4:
- $ \frac{1}{4} = 0.25 $
- $ \frac{1}{2} = 0.5 $
- $ \frac{3}{4} = 0.75 $

#### Part 5:
- $ 0.8 = \frac{4}{5} $
- $ 0.2 = \frac{1}{5} $
- $ 0.1 = \frac{1}{10} $

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🟩 Conclusion

All answers are correctly filled in the worksheet. The key skills tested here are:
- Converting fractions to decimals (especially common ones like $ \frac{1}{2}, \frac{1}{4}, \frac{3}{4} $).
- Converting decimals to fractions, simplifying where needed.
- Understanding mixed numbers and how they relate to improper fractions and decimals.

If you're practicing, remember:
- $ \frac{1}{2} = 0.5 $, $ \frac{1}{4} = 0.25 $, $ \frac{3}{4} = 0.75 $
- Always simplify fractions (e.g., $ \frac{16}{5} $ instead of $ \frac{32}{10} $)

Let me know if you'd like a printable version or a quiz!