Year 6 Maths: Percentages as Fractions

Introduction to Percentages

Hello, Year 6! Today, we’re going to learn about percentages and how we can turn them into fractions. Understanding percentages as fractions is a useful skill that helps us in many real-life situations, like shopping, cooking, and even sports!

What is a Percentage?

A percentage means “out of 100.” For example, if you say 25%, it means 25 out of every 100. It’s a way to compare things easily.

Converting Percentages to Fractions

Step 1: Write the Percentage as a Fraction

To convert a percentage to a fraction, you write it over 100. For example:

• 25% = $$\frac{25}{100}$$

Step 2: Simplify the Fraction

Next, we simplify the fraction if possible. This means we make the fraction smaller while keeping it equal.

For example:

• 25% = $$\frac{25}{100}$$
• Both numbers can be divided by 25: $$\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$$

So, 25% is the same as

Key Rules and Tips

1. Always write the percentage over 100: This is the first step to convert it into a fraction.
2. Look for the greatest common divisor (GCD): This helps you simplify the fraction. It’s the biggest number that can divide both the numerator and denominator.
3. Check if your fraction can be simplified: Not all fractions can be simplified, but many can!

Examples

• Example 1: Convert 50% to a fraction. $$50% = \frac{50}{100} = \frac{1}{2}$$
• Example 2: Convert 10% to a fraction. $$10% = \frac{10}{100} = \frac{1}{10}$$
• Example 3: Convert 75% to a fraction. $$75% = \frac{75}{100} = \frac{3}{4}$$

Practice Questions

Now it’s time for you to try converting percentages to fractions! Below are questions divided into easy, medium, and hard levels.

Easy Level Questions

1. Convert 20% to a fraction.
2. Convert 30% to a fraction.
3. Convert 40% to a fraction.
4. Convert 60% to a fraction.
5. Convert 80% to a fraction.
6. Convert 10% to a fraction.
7. Convert 50% to a fraction.
8. Convert 70% to a fraction.
9. Convert 90% to a fraction.
10. Convert 100% to a fraction.

Medium Level Questions

11. Convert 15% to a fraction.
12. Convert 25% to a fraction.
13. Convert 35% to a fraction.
14. Convert 45% to a fraction.
15. Convert 55% to a fraction.
16. Convert 65% to a fraction.
17. Convert 85% to a fraction.
18. Convert 95% to a fraction.
19. Convert 12% to a fraction.
20. Convert 18% to a fraction.

Hard Level Questions

21. Convert 22% to a fraction.
22. Convert 33% to a fraction.
23. Convert 44% to a fraction.
24. Convert 66% to a fraction.
25. Convert 99% to a fraction.
26. Convert 27% to a fraction.
27. Convert 48% to a fraction.
28. Convert 55% to a fraction.
29. Convert 73% to a fraction.
30. Convert 82% to a fraction.

Answers

Easy Level Answers

1. $$\frac{1}{5}$$
2. $$\frac{3}{10}$$
3. $$\frac{2}{5}$$
4. $$\frac{3}{5}$$
5. $$\frac{4}{5}$$
6. $$\frac{1}{10}$$
7. $$\frac{1}{2}$$
8. $$\frac{7}{10}$$
9. $$\frac{9}{10}$$
10. $$\frac{100}{100} = 1$$

Medium Level Answers

11. $$\frac{3}{20}$$
12. $$\frac{1}{4}$$
13. $$\frac{7}{20}$$
14. $$\frac{9}{20}$$
15. $$\frac{11}{20}$$
16. $$\frac{13}{20}$$
17. $$\frac{17}{20}$$
18. $$\frac{19}{20}$$
19. $$\frac{3}{25}$$
20. $$\frac{9}{50}$$

Hard Level Answers

21. $$\frac{11}{50}$$
22. $$\frac{1}{3}$$
23. $$\frac{11}{25}$$
24. $$\frac{2}{3}$$
25. $$\frac{99}{100}$$
26. $$\frac{27}{100}$$
27. $$\frac{12}{25}$$
28. $$\frac{11}{20}$$
29. $$\frac{73}{100}$$
30. $$\frac{41}{50}$$

Conclusion

Great job today, Year 6! Remember, converting percentages to fractions is just about writing them over 100 and simplifying. Keep practising, and you’ll get even better!