Grade 6 Decimal Worksheets | Free Printables | Math Worksheets - Free Printable

To solve the problem of converting decimals to fractions and simplifying the answers, we will follow these steps:

Steps:

1. Write the decimal as a fraction: The decimal represents a number of parts out of a power of 10.
2. Simplify the fraction: Reduce the fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD).

Let's solve each problem step by step.

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Problem 1: 0.12

- Write as a fraction: \( 0.12 = \frac{12}{100} \)
- Simplify: The GCD of 12 and 100 is 4.
\[
\frac{12 \div 4}{100 \div 4} = \frac{3}{25}
\]
- Answer: \( \frac{3}{25} \)

---

Problem 2: 0.15

- Write as a fraction: \( 0.15 = \frac{15}{100} \)
- Simplify: The GCD of 15 and 100 is 5.
\[
\frac{15 \div 5}{100 \div 5} = \frac{3}{20}
\]
- Answer: \( \frac{3}{20} \)

---

Problem 3: 0.45

- Write as a fraction: \( 0.45 = \frac{45}{100} \)
- Simplify: The GCD of 45 and 100 is 5.
\[
\frac{45 \div 5}{100 \div 5} = \frac{9}{20}
\]
- Answer: \( \frac{9}{20} \)

---

Problem 4: 0.01

- Write as a fraction: \( 0.01 = \frac{1}{100} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{1}{100} \)

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Problem 5: 0.04

- Write as a fraction: \( 0.04 = \frac{4}{100} \)
- Simplify: The GCD of 4 and 100 is 4.
\[
\frac{4 \div 4}{100 \div 4} = \frac{1}{25}
\]
- Answer: \( \frac{1}{25} \)

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Problem 6: 0.77

- Write as a fraction: \( 0.77 = \frac{77}{100} \)
- Simplify: The GCD of 77 and 100 is 1 (they are coprime).
- Answer: \( \frac{77}{100} \)

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Problem 7: 0.16

- Write as a fraction: \( 0.16 = \frac{16}{100} \)
- Simplify: The GCD of 16 and 100 is 4.
\[
\frac{16 \div 4}{100 \div 4} = \frac{4}{25}
\]
- Answer: \( \frac{4}{25} \)

---

Problem 8: 0.07

- Write as a fraction: \( 0.07 = \frac{7}{100} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{7}{100} \)

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Problem 9: 0.63

- Write as a fraction: \( 0.63 = \frac{63}{100} \)
- Simplify: The GCD of 63 and 100 is 1 (they are coprime).
- Answer: \( \frac{63}{100} \)

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Problem 10: 0.19

- Write as a fraction: \( 0.19 = \frac{19}{100} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{19}{100} \)

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Problem 11: 1.3

- Write as a fraction: \( 1.3 = \frac{13}{10} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{13}{10} \)

---

Problem 12: 6.2

- Write as a fraction: \( 6.2 = \frac{62}{10} \)
- Simplify: The GCD of 62 and 10 is 2.
\[
\frac{62 \div 2}{10 \div 2} = \frac{31}{5}
\]
- Answer: \( \frac{31}{5} \)

---

Problem 13: 3.5

- Write as a fraction: \( 3.5 = \frac{35}{10} \)
- Simplify: The GCD of 35 and 10 is 5.
\[
\frac{35 \div 5}{10 \div 5} = \frac{7}{2}
\]
- Answer: \( \frac{7}{2} \)

---

Problem 14: 2.1

- Write as a fraction: \( 2.1 = \frac{21}{10} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{21}{10} \)

---

Problem 15: 1.8

- Write as a fraction: \( 1.8 = \frac{18}{10} \)
- Simplify: The GCD of 18 and 10 is 2.
\[
\frac{18 \div 2}{10 \div 2} = \frac{9}{5}
\]
- Answer: \( \frac{9}{5} \)

---

Problem 16: 1.5

- Write as a fraction: \( 1.5 = \frac{15}{10} \)
- Simplify: The GCD of 15 and 10 is 5.
\[
\frac{15 \div 5}{10 \div 5} = \frac{3}{2}
\]
- Answer: \( \frac{3}{2} \)

---

Problem 17: 4.5

- Write as a fraction: \( 4.5 = \frac{45}{10} \)
- Simplify: The GCD of 45 and 10 is 5.
\[
\frac{45 \div 5}{10 \div 5} = \frac{9}{2}
\]
- Answer: \( \frac{9}{2} \)

---

Problem 18: 2.7

- Write as a fraction: \( 2.7 = \frac{27}{10} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{27}{10} \)

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Problem 19: 5.5

- Write as a fraction: \( 5.5 = \frac{55}{10} \)
- Simplify: The GCD of 55 and 10 is 5.
\[
\frac{55 \div 5}{10 \div 5} = \frac{11}{2}
\]
- Answer: \( \frac{11}{2} \)

---

Problem 20: 2.3

- Write as a fraction: \( 2.3 = \frac{23}{10} \)
- Simplify: Already in simplest form.
- Answer: \( \frac{23}{10} \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. \frac{3}{25} & 11. \frac{13}{10} \\
2. \frac{3}{20} & 12. \frac{31}{5} \\
3. \frac{9}{20} & 13. \frac{7}{2} \\
4. \frac{1}{100} & 14. \frac{21}{10} \\
5. \frac{1}{25} & 15. \frac{9}{5} \\
6. \frac{77}{100} & 16. \frac{3}{2} \\
7. \frac{4}{25} & 17. \frac{9}{2} \\
8. \frac{7}{100} & 18. \frac{27}{10} \\
9. \frac{63}{100} & 19. \frac{11}{2} \\
10. \frac{19}{100} & 20. \frac{23}{10} \\
\end{array}
}
\]