Introduction to Fractions and Percentages

Hello Year 5! Today, we are going to learn how to convert fractions into percentages. This is a really useful skill that helps us understand parts of a whole in different ways. Let’s break it down step by step.

What is a Fraction?

A fraction is a way to show a part of something. For example, if you have a pizza cut into 4 equal slices and you eat 1 slice, you have eaten $$\frac{1}{4}$$ of the pizza. The top number (1) is called the numerator, and the bottom number (4) is called the denominator.

What is a Percentage?

A percentage is another way to talk about parts of a whole, but it uses 100 as the whole. For example, if you have 25 out of 100 marbles that are red, you can say that 25% of the marbles are red.

How to Convert Fractions to Percentages

To convert a fraction to a percentage, you can follow these simple steps:

  1. Divide the numerator by the denominator.
    • This gives you a decimal.
    • For example, for the fraction $$\frac{1}{4}$$, you would do $$1 \div 4 = 0.25$$.
  2. Multiply the decimal by 100.
    • This will convert the decimal into a percentage.
    • Using our example, $$0.25 \times 100 = 25$$. So, $$\frac{1}{4}$$ is equal to 25%.
  3. Add the percentage sign (%).
    • Don’t forget to write the percentage sign! So, we say that $$\frac{1}{4} = 25%$$.

Example

Let’s look at another example: converting $$\frac{3}{5}$$ to a percentage.

  1. Divide: $$3 \div 5 = 0.6$$
  2. Multiply: $$0.6 \times 100 = 60$$
  3. Write it as a percentage: $$\frac{3}{5} = 60%$$.

Key Rules

  • Always divide the top number (numerator) by the bottom number (denominator).
  • Remember to multiply the decimal by 100 to get your percentage.
  • Always add the % sign at the end.

Tips and Tricks

  • If you can’t remember the steps, you can use this phrase: “Divide, Multiply, and Add the %!”
  • Practice with different fractions to get comfortable with the process.
  • You can use a calculator for larger numbers to make it easier.

Practice Questions

Easy Level Questions

  1. Convert $$\frac{1}{2}$$ to a percentage.
  2. Convert $$\frac{3}{4}$$ to a percentage.
  3. Convert $$\frac{1}{5}$$ to a percentage.
  4. Convert $$\frac{2}{10}$$ to a percentage.
  5. Convert $$\frac{1}{3}$$ to a percentage.
  6. Convert $$\frac{2}{5}$$ to a percentage.
  7. Convert $$\frac{1}{10}$$ to a percentage.
  8. Convert $$\frac{3}{5}$$ to a percentage.
  9. Convert $$\frac{5}{10}$$ to a percentage.
  10. Convert $$\frac{4}{5}$$ to a percentage.

Medium Level Questions

  1. Convert $$\frac{7}{10}$$ to a percentage.
  2. Convert $$\frac{9}{20}$$ to a percentage.
  3. Convert $$\frac{2}{8}$$ to a percentage.
  4. Convert $$\frac{5}{12}$$ to a percentage.
  5. Convert $$\frac{1}{6}$$ to a percentage.
  6. Convert $$\frac{8}{15}$$ to a percentage.
  7. Convert $$\frac{11}{25}$$ to a percentage.
  8. Convert $$\frac{3}{8}$$ to a percentage.
  9. Convert $$\frac{4}{12}$$ to a percentage.
  10. Convert $$\frac{2}{3}$$ to a percentage.

Hard Level Questions

  1. Convert $$\frac{13}{50}$$ to a percentage.
  2. Convert $$\frac{15}{28}$$ to a percentage.
  3. Convert $$\frac{9}{16}$$ to a percentage.
  4. Convert $$\frac{17}{40}$$ to a percentage.
  5. Convert $$\frac{23}{60}$$ to a percentage.
  6. Convert $$\frac{5}{18}$$ to a percentage.
  7. Convert $$\frac{14}{33}$$ to a percentage.
  8. Convert $$\frac{19}{30}$$ to a percentage.
  9. Convert $$\frac{21}{45}$$ to a percentage.
  10. Convert $$\frac{27}{70}$$ to a percentage.

Answers with Explanations

Easy Level Answers

  1. $$\frac{1}{2} = 50%$$
    • $$1 \div 2 = 0.5$$, $$0.5 \times 100 = 50$$.
  2. $$\frac{3}{4} = 75%$$
    • $$3 \div 4 = 0.75$$, $$0.75 \times 100 = 75$$.
  3. $$\frac{1}{5} = 20%$$
    • $$1 \div 5 = 0.2$$, $$0.2 \times 100 = 20$$.
  4. $$\frac{2}{10} = 20%$$
    • $$2 \div 10 = 0.2$$, $$0.2 \times 100 = 20$$.
  5. $$\frac{1}{3} \approx 33.33%$$
    • $$1 \div 3 \approx 0.333$$, $$0.333 \times 100 \approx 33.33$$.
  6. $$\frac{2}{5} = 40%$$
    • $$2 \div 5 = 0.4$$, $$0.4 \times 100 = 40$$.
  7. $$\frac{1}{10} = 10%$$
    • $$1 \div 10 = 0.1$$, $$0.1 \times 100 = 10$$.
  8. $$\frac{3}{5} = 60%$$
    • $$3 \div 5 = 0.6$$, $$0.6 \times 100 = 60$$.
  9. $$\frac{5}{10} = 50%$$
    • $$5 \div 10 = 0.5$$, $$0.5 \times 100 = 50$$.
  10. $$\frac{4}{5} = 80%$$
    • $$4 \div 5 = 0.8$$, $$0.8 \times 100 = 80$$.

Medium Level Answers

  1. $$\frac{7}{10} = 70%$$
    • $$7 \div 10 = 0.7$$, $$0.7 \times 100 = 70$$.
  2. $$\frac{9}{20} = 45%$$
    • $$9 \div 20 = 0.45$$, $$0.45 \times 100 = 45$$.
  3. $$\frac{2}{8} = 25%$$
    • $$2 \div 8 = 0.25$$, $$0.25 \times 100 = 25$$.
  4. $$\frac{5}{12} \approx 41.67%$$
    • $$5 \div 12 \approx 0.4167$$, $$0.4167 \times 100 \approx 41.67$$.
  5. $$\frac{1}{6} \approx 16.67%$$
    • $$1 \div 6 \approx 0.1667$$, $$0.1667 \times 100 \approx 16.67$$.
  6. $$\frac{8}{15} \approx 53.33%$$
    • $$8 \div 15 \approx 0.5333$$, $$0.5333 \times 100 \approx 53.33$$.
  7. $$\frac{11}{25} = 44%$$
    • $$11 \div 25 = 0.44$$, $$0.44 \times 100 = 44$$.
  8. $$\frac{3}{8} = 37.5%$$
    • $$3 \div 8 = 0.375$$, $$0.375 \times 100 = 37.5$$.
  9. $$\frac{4}{12} \approx 33.33%$$
    • $$4 \div 12 \approx 0.3333$$, $$0.3333 \times 100 \approx 33.33$$.
  10. $$\frac{2}{3} \approx 66.67%$$
    • $$2 \div 3 \approx 0.6667$$, $$0.6667 \times 100 \approx 66.67$$.

Hard Level Answers

  1. $$\frac{13}{50} = 26%$$
    • $$13 \div 50 = 0.26$$, $$0.26 \times 100 = 26$$.
  2. $$\frac{15}{28} \approx 53.57%$$
    • $$15 \div 28 \approx 0.5357$$, $$0.5357 \times 100 \approx 53.57$$.
  3. $$\frac{9}{16} = 56.25%$$
    • $$9 \div 16 = 0.5625$$, $$0.5625 \times 100 = 56.25$$.
  4. $$\frac{17}{40} = 42.5%$$
    • $$17 \div 40 = 0.425$$, $$0.425 \times 100 = 42.5$$.
  5. $$\frac{23}{60} \approx 38.33%$$
    • $$23 \div 60 \approx 0.3833$$, $$0.3833 \times 100 \approx 38.33$$.
  6. $$\frac{5}{18} \approx 27.78%$$
    • $$5 \div 18 \approx 0.2778$$, $$0.2778 \times 100 \approx 27.78$$.
  7. $$\frac{14}{33} \approx 42.42%$$
    • $$14 \div 33 \approx 0.4242$$, $$0.4242 \times 100 \approx 42.42$$.
  8. $$\frac{19}{30} \approx 63.33%$$
    • $$19 \div 30 \approx 0.6333$$, $$0.6333 \times 100 \approx 63.33$$.
  9. $$\frac{21}{45} \approx 46.67%$$
    • $$21 \div 45 \approx 0.4667$$, $$0.4667 \times 100 \approx 46.67$$.
  10. $$\frac{27}{70} \approx 38.57%$$
    • $$27 \div 70 \approx 0.3857$$, $$0.3857 \times 100 \approx 38.57$$.

Conclusion

Great job today, Year 5! You’ve learned how to convert fractions to percentages. Remember to practice these skills to become even better at maths. Keep up the good work!