Year 6 Maths: Ordering Fractions, Decimals, and Percentages

Introduction

Hello, Year 6! Today, we’re going to learn about ordering fractions, decimals, and percentages. These are different ways to represent parts of a whole. Sometimes, we need to put them in order from smallest to largest (or largest to smallest). Let’s get started!

Understanding Fractions, Decimals, and Percentages

What is a Fraction?

A fraction shows a part of a whole. For example, if you have a pizza divided into 4 equal slices and you eat 1 slice, you have eaten

$$\frac{1}{4}$$ of the pizza.

What is a Decimal?

A decimal is another way to show a part of a whole, using a dot. For example,

$$\frac{1}{4}$$ can also be written as 0.25.

What is a Percentage?

A percentage is a way to express a number as a part of 100. For example,

$$\frac{1}{4}$$ is the same as 25%, because 1 slice out of 4 is the same as 25 out of 100 slices.

Key Relationships

• $$\frac{1}{4} = 0.25 = 25%$$
• $$\frac{1}{2} = 0.5 = 50%$$
• $$\frac{3}{4} = 0.75 = 75%$$

How to Order Them

When you want to order fractions, decimals, and percentages, it’s easiest to convert them to the same form. You can choose to convert everything into:

1. Fractions
2. Decimals
3. Percentages

Tips for Ordering

1. Convert all to the same type: Choose one type (fractions, decimals, or percentages) and change the others to match it.
2. Use a number line: This can help you visually see where each number falls.
3. Compare two at a time: It can be easier to compare two numbers before moving on to the next.

Examples

Let’s order these numbers:

$$\frac{1}{2}, 0.75, 50%$$ .

Step 1: Convert to Decimals

• $$\frac{1}{2} = 0.5$$
• $$0.75 = 0.75$$
• $$50% = 0.5$$

Step 2: Order Them

Now we have:

• 0.5
• 0.75
• 0.5

Ordering them gives us: 0.5 (or

$$\frac{1}{2}$$ and 50%), 0.75.

Final Order: $$\frac{1}{2} = 50% < 0.75$$

Practice Questions

Easy Level Questions

1. Order: $$\frac{1}{4}, 0.5, 25%$$
2. Order: $$\frac{1}{3}, 0.33, 33%$$
3. Order: $$\frac{1}{2}, 60%, 0.6$$
4. Order: $$\frac{3}{4}, 0.75, 75%$$
5. Order: $$\frac{1}{5}, 0.2, 20%$$
6. Order: $$\frac{2}{5}, 0.4, 40%$$
7. Order: $$\frac{0}{1}, 0, 0%$$
8. Order: $$\frac{1}{10}, 0.1, 10%$$
9. Order: $$\frac{1}{8}, 0.125, 12.5%$$
10. Order: $$\frac{1}{2}, 0.55, 55%$$

Medium Level Questions

11. Order: $$\frac{2}{3}, 0.66, 66%$$
12. Order: $$\frac{5}{8}, 0.625, 62.5%$$
13. Order: $$\frac{3}{10}, 0.3, 30%$$
14. Order: $$\frac{7}{10}, 0.7, 70%$$
15. Order: $$\frac{4}{5}, 0.8, 80%$$
16. Order: $$\frac{1}{6}, 0.16, 16%$$
17. Order: $$\frac{2}{7}, 0.285, 28.5%$$
18. Order: $$\frac{9}{10}, 0.9, 90%$$
19. Order: $$\frac{3}{5}, 0.6, 60%$$
20. Order: $$\frac{5}{6}, 0.83, 83%$$

Hard Level Questions

21. Order: $$\frac{3}{8}, 0.375, 37.5%$$
22. Order: $$\frac{2}{9}, 0.222, 22.2%$$
23. Order: $$\frac{11}{20}, 0.55, 55%$$
24. Order: $$\frac{7}{12}, 0.583, 58.3%$$
25. Order: $$\frac{13}{16}, 0.8125, 81.25%$$
26. Order: $$\frac{17}{20}, 0.85, 85%$$
27. Order: $$\frac{5}{12}, 0.416, 41.6%$$
28. Order: $$\frac{4}{11}, 0.363, 36.3%$$
29. Order: $$\frac{19}{20}, 0.95, 95%$$
30. Order: $$\frac{8}{15}, 0.533, 53.3%$$

Answers to Questions

Easy Level Answers

1. $$\frac{1}{4} < 25% = 0.5$$
2. $$\frac{1}{3} = 33% < 0.33$$
3. $$\frac{1}{2} = 50% = 0.6$$
4. $$\frac{3}{4} = 75% = 0.75$$
5. $$\frac{1}{5} < 20% = 0.2$$
6. $$\frac{2}{5} = 40% = 0.4$$
7. $$0 < 0 = 0%$$
8. $$\frac{1}{10} < 0.1 = 10%$$
9. $$\frac{1}{8} < 0.125 = 12.5%$$
10. $$\frac{1}{2} < 55% < 0.55$$

Medium Level Answers

11. $$\frac{2}{3} = 66% = 0.66$$
12. $$\frac{5}{8} = 62.5% < 0.625$$
13. $$\frac{3}{10} = 30% < 0.3$$
14. $$\frac{7}{10} = 70% < 0.7$$
15. $$\frac{4}{5} = 80% < 0.8$$
16. $$\frac{1}{6} < 0.16 = 16%$$
17. $$\frac{2}{7} < 0.285 = 28.5%$$
18. $$\frac{9}{10} = 90% < 0.9$$
19. $$\frac{3}{5} = 60% < 0.6$$
20. $$\frac{5}{6} = 83.3% < 0.83$$

Hard Level Answers

21. $$\frac{3}{8} = 37.5% < 0.375$$
22. $$\frac{2}{9} = 22.2% < 0.222$$
23. $$\frac{11}{20} = 55% < 0.55$$
24. $$\frac{7}{12} = 58.3% < 0.583$$
25. $$\frac{13}{16} = 81.25% < 0.8125$$
26. $$\frac{17}{20} = 85% < 0.85$$
27. $$\frac{5}{12} = 41.6% < 0.416$$
28. $$\frac{4}{11} = 36.3% < 0.363$$
29. $$\frac{19}{20} = 95% < 0.95$$
30. $$\frac{8}{15} = 53.3% < 0.533$$

Conclusion

Great job today, Year 6! You’ve learned how to order fractions, decimals, and percentages. Remember to practice converting between them, and soon you’ll be an expert!