Introduction to Decimals and Fractions

Hello, Year 6! Today, we’re going to learn how to change decimals into fractions. This is an important skill in maths, and it will help you understand numbers better. Let’s dive in!

What is a Decimal?

A decimal is a way of showing numbers that are not whole. For example, 0.5, 0.75, and 1.2 are all decimals. The number after the decimal point shows a part of a whole.

What is a Fraction?

A fraction shows how many parts of a whole we have. For example, if we have 1/2, it means we have one part out of two equal parts.

How to Change Decimals to Fractions

Step 1: Write the Decimal Over 1

To turn a decimal into a fraction, we start by writing it over 1. For example:

  • For 0.5, we write it as \frac{0.5}{1}.

Step 2: Multiply to Remove the Decimal

Next, we need to get rid of the decimal point. We do this by multiplying both the top (numerator) and the bottom (denominator) by 10 for every number after the decimal point:

  • For 0.5, we multiply both the top and bottom by 10:\frac{0.5 \times 10}{1 \times 10} = \frac{5}{10}.

Step 3: Simplify the Fraction

Now, we simplify the fraction if possible. We do this by finding the greatest common divisor (GCD) of the numerator and the denominator.

  • In our example, the GCD of 5 and 10 is 5. So:\frac{5 \div 5}{10 \div 5} = \frac{1}{2}.

Example 1: Converting 0.75 to a Fraction

  1. Write it over 1: \frac{0.75}{1}.
  2. Multiply by 100 (since there are two decimal places):\frac{0.75 \times 100}{1 \times 100} = \frac{75}{100}.
  3. Simplify: The GCD of 75 and 100 is 25, so:\frac{75 \div 25}{100 \div 25} = \frac{3}{4}.

Example 2: Converting 1.2 to a Fraction

  1. Write it over 1: \frac{1.2}{1}.
  2. Multiply by 10 (since there is one decimal place):\frac{1.2 \times 10}{1 \times 10} = \frac{12}{10}.
  3. Simplify: The GCD of 12 and 10 is 2, so:\frac{12 \div 2}{10 \div 2} = \frac{6}{5} or 1\frac{1}{5}.

Key Rules to Remember

  1. Always write the decimal over 1 first.
  2. Multiply by 10, 100, or 1000 depending on how many decimal places are there.
  3. Simplify the fraction to its lowest form.

Tips and Tricks

  • Remember, every time you move the decimal point to the right, you multiply by 10.
  • Use a calculator if needed to help with larger numbers.
  • Practice makes perfect! The more you do it, the easier it becomes.

Practice Questions

Easy Level

  1. Convert 0.2 to a fraction.
  2. Convert 0.5 to a fraction.
  3. Convert 0.25 to a fraction.
  4. Convert 0.1 to a fraction.
  5. Convert 0.75 to a fraction.
  6. Convert 0.6 to a fraction.
  7. Convert 0.9 to a fraction.
  8. Convert 0.15 to a fraction.
  9. Convert 0.05 to a fraction.
  10. Convert 0.3 to a fraction.
  11. Convert 0.8 to a fraction.
  12. Convert 0.4 to a fraction.
  13. Convert 0.12 to a fraction.
  14. Convert 0.01 to a fraction.
  15. Convert 0.7 to a fraction.
  16. Convert 0.11 to a fraction.
  17. Convert 0.99 to a fraction.
  18. Convert 0.33 to a fraction.
  19. Convert 0.66 to a fraction.
  20. Convert 0.5 to a fraction (again for practice).

Medium Level

  1. Convert 0.85 to a fraction.
  2. Convert 1.5 to a fraction.
  3. Convert 1.25 to a fraction.
  4. Convert 2.75 to a fraction.
  5. Convert 3.1 to a fraction.
  6. Convert 0.125 to a fraction.
  7. Convert 0.45 to a fraction.
  8. Convert 0.99 to a fraction.
  9. Convert 0.55 to a fraction.
  10. Convert 0.2 to a fraction (again for practice).
  11. Convert 0.4 to a fraction (again for practice).
  12. Convert 0.08 to a fraction.
  13. Convert 1.1 to a fraction.
  14. Convert 0.3 to a fraction (again for practice).
  15. Convert 0.9 to a fraction (again for practice).
  16. Convert 2.5 to a fraction.
  17. Convert 0.6 to a fraction (again for practice).
  18. Convert 1.75 to a fraction.
  19. Convert 2.2 to a fraction.
  20. Convert 0.7 to a fraction (again for practice).

Hard Level

  1. Convert 0.625 to a fraction.
  2. Convert 1.125 to a fraction.
  3. Convert 1.875 to a fraction.
  4. Convert 0.333 to a fraction.
  5. Convert 0.875 to a fraction.
  6. Convert 2.33 to a fraction.
  7. Convert 0.04 to a fraction.
  8. Convert 3.75 to a fraction.
  9. Convert 0.2 to a fraction (again for practice).
  10. Convert 0.222 to a fraction.
  11. Convert 0.555 to a fraction.
  12. Convert 4.5 to a fraction.
  13. Convert 2.8 to a fraction.
  14. Convert 0.007 to a fraction.
  15. Convert 0.125 to a fraction (again for practice).
  16. Convert 1.01 to a fraction.
  17. Convert 0.001 to a fraction.
  18. Convert 5.5 to a fraction.
  19. Convert 0.03 to a fraction.
  20. Convert 1.5 to a fraction (again for practice).

Answers and Explanations

Easy Level Answers

  1. \frac{1}{5}
  2. \frac{1}{2}
  3. \frac{1}{4}
  4. \frac{1}{10}
  5. \frac{3}{4}
  6. \frac{3}{5}
  7. \frac{9}{10}
  8. \frac{3}{20}
  9. \frac{1}{20}
  10. \frac{3}{10}
  11. \frac{4}{5}
  12. \frac{2}{5}
  13. \frac{3}{25}
  14. \frac{1}{100}
  15. \frac{7}{10}
  16. \frac{11}{100}
  17. \frac{99}{100}
  18. \frac{1}{3}
  19. \frac{2}{3}
  20. \frac{1}{2}

Medium Level Answers

  1. \frac{17}{20}
  2. \frac{3}{2}
  3. \frac{5}{4}
  4. \frac{11}{4}
  5. \frac{31}{10}
  6. \frac{1}{8}
  7. \frac{9}{20}
  8. \frac{99}{100}
  9. \frac{11}{20}
  10. \frac{1}{5}
  11. \frac{2}{5}
  12. \frac{2}{25}
  13. \frac{11}{10}
  14. \frac{3}{30}
  15. \frac{9}{10}
  16. \frac{5}{2}
  17. \frac{11}{5}
  18. \frac{7}{4}
  19. \frac{11}{5}
  20. \frac{7}{10}

Hard Level Answers

  1. \frac{5}{8}
  2. \frac{9}{8}
  3. \frac{15}{8}
  4. \frac{1}{3}
  5. \frac{7}{8}
  6. \frac{7}{3}
  7. \frac{4}{100} = \frac{1}{25}
  8. \frac{15}{2}
  9. \frac{1}{5}
  10. \frac{2}{9}
  11. \frac{5}{9}
  12. \frac{11}{2}
  13. \frac{14}{5}
  14. \frac{1}{1000}
  15. \frac{1}{8}
  16. \frac{101}{100}
  17. \frac{1}{1000}
  18. \frac{11}{2}
  19. \frac{3}{100}
  20. \frac{3}{2}

I hope this helps you understand how to convert decimals to fractions better! Keep practicing, and you’ll become a pro at it!