Decimals to Fractions worksheet for converting decimal numbers to simplified fractions.
Worksheet titled "Decimals to Fractions" with 20 problems converting decimals to simplified fractions, featuring a cartoon doctor and "Stambo Resources" logo.
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Show Answer Key & Explanations
Step-by-step solution for: Grade 6 Decimal Worksheets | Free Printables | Math Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Grade 6 Decimal Worksheets | Free Printables | Math Worksheets
To solve the problem of converting decimals to fractions and simplifying the answers, we will follow these steps:
1. Identify the place value of the decimal to determine the denominator.
2. Write the decimal as a fraction with the denominator based on the place value.
3. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator.
Let's solve each problem step by step.
---
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{5}{10} \)
- Simplify: \( \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \)
Answer: \( \frac{1}{2} \)
---
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{3}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{3}{10} \)
---
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{9}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{9}{10} \)
---
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{4}{100} \)
- Simplify: \( \frac{4 \div 4}{100 \div 4} = \frac{1}{25} \)
Answer: \( \frac{1}{25} \)
---
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{13}{100} \)
- Simplify: Already in simplest form.
Answer: \( \frac{13}{100} \)
---
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{1}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{1}{10} \)
---
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{25}{100} \)
- Simplify: \( \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \)
Answer: \( \frac{1}{4} \)
---
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{75}{100} \)
- Simplify: \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{5}{100} \)
- Simplify: \( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \)
Answer: \( \frac{1}{20} \)
---
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{7}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{7}{10} \)
---
- Whole number part: 1
- Decimal part: 0.25
- Convert 0.25 to a fraction: \( \frac{25}{100} = \frac{1}{4} \)
- Combine: \( 1 \frac{1}{4} \) or \( \frac{5}{4} \)
Answer: \( \frac{5}{4} \)
---
- Whole number part: 1
- Decimal part: 0.3
- Convert 0.3 to a fraction: \( \frac{3}{10} \)
- Combine: \( 1 \frac{3}{10} \) or \( \frac{13}{10} \)
Answer: \( \frac{13}{10} \)
---
- Whole number part: 1
- Decimal part: 0.1
- Convert 0.1 to a fraction: \( \frac{1}{10} \)
- Combine: \( 1 \frac{1}{10} \) or \( \frac{11}{10} \)
Answer: \( \frac{11}{10} \)
---
- Whole number part: 1
- Decimal part: 0.5
- Convert 0.5 to a fraction: \( \frac{5}{10} = \frac{1}{2} \)
- Combine: \( 1 \frac{1}{2} \) or \( \frac{3}{2} \)
Answer: \( \frac{3}{2} \)
---
- Whole number part: 1
- Decimal part: 0.22
- Convert 0.22 to a fraction: \( \frac{22}{100} = \frac{11}{50} \)
- Combine: \( 1 \frac{11}{50} \) or \( \frac{61}{50} \)
Answer: \( \frac{61}{50} \)
---
- Whole number part: 2
- Decimal part: 0.3
- Convert 0.3 to a fraction: \( \frac{3}{10} \)
- Combine: \( 2 \frac{3}{10} \) or \( \frac{23}{10} \)
Answer: \( \frac{23}{10} \)
---
- Whole number part: 1
- Decimal part: 0.43
- Convert 0.43 to a fraction: \( \frac{43}{100} \)
- Combine: \( 1 \frac{43}{100} \) or \( \frac{143}{100} \)
Answer: \( \frac{143}{100} \)
---
- Whole number part: 4
- Decimal part: 0.15
- Convert 0.15 to a fraction: \( \frac{15}{100} = \frac{3}{20} \)
- Combine: \( 4 \frac{3}{20} \) or \( \frac{83}{20} \)
Answer: \( \frac{83}{20} \)
---
- Whole number part: 2
- Decimal part: 0.1
- Convert 0.1 to a fraction: \( \frac{1}{10} \)
- Combine: \( 2 \frac{1}{10} \) or \( \frac{21}{10} \)
Answer: \( \frac{21}{10} \)
---
- Whole number part: 1
- Decimal part: 0.7
- Convert 0.7 to a fraction: \( \frac{7}{10} \)
- Combine: \( 1 \frac{7}{10} \) or \( \frac{17}{10} \)
Answer: \( \frac{17}{10} \)
---
\[
\boxed{
\begin{array}{ll}
1. & \frac{1}{2} \\
2. & \frac{3}{10} \\
3. & \frac{9}{10} \\
4. & \frac{1}{25} \\
5. & \frac{13}{100} \\
6. & \frac{1}{10} \\
7. & \frac{1}{4} \\
8. & \frac{3}{4} \\
9. & \frac{1}{20} \\
10. & \frac{7}{10} \\
11. & \frac{5}{4} \\
12. & \frac{13}{10} \\
13. & \frac{11}{10} \\
14. & \frac{3}{2} \\
15. & \frac{61}{50} \\
16. & \frac{23}{10} \\
17. & \frac{143}{100} \\
18. & \frac{83}{20} \\
19. & \frac{21}{10} \\
20. & \frac{17}{10} \\
\end{array}
}
\]
Steps:
1. Identify the place value of the decimal to determine the denominator.
2. Write the decimal as a fraction with the denominator based on the place value.
3. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator.
Let's solve each problem step by step.
---
Problem 1: 0.5
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{5}{10} \)
- Simplify: \( \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \)
Answer: \( \frac{1}{2} \)
---
Problem 2: 0.3
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{3}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{3}{10} \)
---
Problem 3: 0.9
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{9}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{9}{10} \)
---
Problem 4: 0.04
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{4}{100} \)
- Simplify: \( \frac{4 \div 4}{100 \div 4} = \frac{1}{25} \)
Answer: \( \frac{1}{25} \)
---
Problem 5: 0.13
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{13}{100} \)
- Simplify: Already in simplest form.
Answer: \( \frac{13}{100} \)
---
Problem 6: 0.1
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{1}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{1}{10} \)
---
Problem 7: 0.25
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{25}{100} \)
- Simplify: \( \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \)
Answer: \( \frac{1}{4} \)
---
Problem 8: 0.75
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{75}{100} \)
- Simplify: \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
Problem 9: 0.05
- Place value: Hundredths (2 decimal places).
- Fraction: \( \frac{5}{100} \)
- Simplify: \( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \)
Answer: \( \frac{1}{20} \)
---
Problem 10: 0.7
- Place value: Tenths (1 decimal place).
- Fraction: \( \frac{7}{10} \)
- Simplify: Already in simplest form.
Answer: \( \frac{7}{10} \)
---
Problem 11: 1.25
- Whole number part: 1
- Decimal part: 0.25
- Convert 0.25 to a fraction: \( \frac{25}{100} = \frac{1}{4} \)
- Combine: \( 1 \frac{1}{4} \) or \( \frac{5}{4} \)
Answer: \( \frac{5}{4} \)
---
Problem 12: 1.3
- Whole number part: 1
- Decimal part: 0.3
- Convert 0.3 to a fraction: \( \frac{3}{10} \)
- Combine: \( 1 \frac{3}{10} \) or \( \frac{13}{10} \)
Answer: \( \frac{13}{10} \)
---
Problem 13: 1.1
- Whole number part: 1
- Decimal part: 0.1
- Convert 0.1 to a fraction: \( \frac{1}{10} \)
- Combine: \( 1 \frac{1}{10} \) or \( \frac{11}{10} \)
Answer: \( \frac{11}{10} \)
---
Problem 14: 1.5
- Whole number part: 1
- Decimal part: 0.5
- Convert 0.5 to a fraction: \( \frac{5}{10} = \frac{1}{2} \)
- Combine: \( 1 \frac{1}{2} \) or \( \frac{3}{2} \)
Answer: \( \frac{3}{2} \)
---
Problem 15: 1.22
- Whole number part: 1
- Decimal part: 0.22
- Convert 0.22 to a fraction: \( \frac{22}{100} = \frac{11}{50} \)
- Combine: \( 1 \frac{11}{50} \) or \( \frac{61}{50} \)
Answer: \( \frac{61}{50} \)
---
Problem 16: 2.3
- Whole number part: 2
- Decimal part: 0.3
- Convert 0.3 to a fraction: \( \frac{3}{10} \)
- Combine: \( 2 \frac{3}{10} \) or \( \frac{23}{10} \)
Answer: \( \frac{23}{10} \)
---
Problem 17: 1.43
- Whole number part: 1
- Decimal part: 0.43
- Convert 0.43 to a fraction: \( \frac{43}{100} \)
- Combine: \( 1 \frac{43}{100} \) or \( \frac{143}{100} \)
Answer: \( \frac{143}{100} \)
---
Problem 18: 4.15
- Whole number part: 4
- Decimal part: 0.15
- Convert 0.15 to a fraction: \( \frac{15}{100} = \frac{3}{20} \)
- Combine: \( 4 \frac{3}{20} \) or \( \frac{83}{20} \)
Answer: \( \frac{83}{20} \)
---
Problem 19: 2.1
- Whole number part: 2
- Decimal part: 0.1
- Convert 0.1 to a fraction: \( \frac{1}{10} \)
- Combine: \( 2 \frac{1}{10} \) or \( \frac{21}{10} \)
Answer: \( \frac{21}{10} \)
---
Problem 20: 1.7
- Whole number part: 1
- Decimal part: 0.7
- Convert 0.7 to a fraction: \( \frac{7}{10} \)
- Combine: \( 1 \frac{7}{10} \) or \( \frac{17}{10} \)
Answer: \( \frac{17}{10} \)
---
Final Answers:
\[
\boxed{
\begin{array}{ll}
1. & \frac{1}{2} \\
2. & \frac{3}{10} \\
3. & \frac{9}{10} \\
4. & \frac{1}{25} \\
5. & \frac{13}{100} \\
6. & \frac{1}{10} \\
7. & \frac{1}{4} \\
8. & \frac{3}{4} \\
9. & \frac{1}{20} \\
10. & \frac{7}{10} \\
11. & \frac{5}{4} \\
12. & \frac{13}{10} \\
13. & \frac{11}{10} \\
14. & \frac{3}{2} \\
15. & \frac{61}{50} \\
16. & \frac{23}{10} \\
17. & \frac{143}{100} \\
18. & \frac{83}{20} \\
19. & \frac{21}{10} \\
20. & \frac{17}{10} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of fraction and decimal worksheet.
