Year 6 Maths: Ordering Fractions

What Are Fractions?

Fractions are parts of a whole. For example, if you have a pizza and you eat 1 out of 4 equal slices, you have eaten $$\frac{1}{4}$$ of the pizza.

Why Do We Order Fractions?

Sometimes, we need to compare fractions to see which is bigger or smaller. Ordering fractions helps us understand which part of the whole is larger.

How To Order Fractions

Step 1: Common Denominator

To order fractions, it’s often easiest to find a common denominator. The denominator is the bottom number of a fraction.

Example:

If we want to order $$\frac{1}{4}$$ and $$\frac{1}{2}$$ , we can convert them to have the same denominator.

1. The denominators are 4 and 2.
2. The least common denominator (LCD) of 4 and 2 is 4.
3. Convert $$\frac{1}{2}$$ to have a denominator of 4.
   • $$\frac{1}{2} = \frac{2}{4}$$

Now we can compare $$\frac{1}{4}$$ and $$\frac{2}{4}$$ .

• So, $$\frac{1}{4} < \frac{2}{4}$$ .

Step 2: Compare Numerators

Once the fractions have the same denominator, you can compare the numerators (the top numbers).

Example:

If we have $$\frac{3}{5}$$ and $$\frac{1}{5}$$ :

• Both have a denominator of 5, so we just compare the numerators: 3 and 1.
• Since 3 is greater than 1, we can say $$\frac{3}{5} > \frac{1}{5}$$ .

Step 3: Mixed Numbers

Sometimes, you may also deal with mixed numbers (like $$1 \frac{1}{2}$$ ). First, convert them to improper fractions.

Example:

• $$1 \frac{1}{2} = \frac{3}{2}$$ .

Then, find a common denominator or compare numerators as before.

Key Tips and Tricks

• Visual Aids: Drawing pictures can help! For example, draw circles or bars to show how much each fraction represents.
• Simplify Fractions: Make sure your fractions are in their simplest form if possible before you start comparing.
• Practice: The more you order fractions, the better you will get!

Questions

Easy Level Questions

1. Order the fractions: $$\frac{1}{3}, \frac{1}{4}$$ .
2. Order the fractions: $$\frac{2}{5}, \frac{1}{5}$$ .
3. Order the fractions: $$\frac{3}{6}, \frac{1}{6}$$ .
4. Order the fractions: $$\frac{2}{8}, \frac{3}{8}$$ .
5. Order the fractions: $$\frac{1}{2}, \frac{1}{3}$$ .
6. Order the fractions: $$\frac{5}{10}, \frac{2}{10}$$ .
7. Order the fractions: $$\frac{1}{5}, \frac{3}{5}$$ .
8. Order the fractions: $$\frac{3}{4}, \frac{1}{4}$$ .
9. Order the fractions: $$\frac{1}{6}, \frac{5}{6}$$ .
10. Order the fractions: $$\frac{2}{3}, \frac{1}{3}$$ .
11. Order the fractions: $$\frac{3}{5}, \frac{2}{5}$$ .
12. Order the fractions: $$\frac{4}{8}, \frac{2}{8}$$ .
13. Order the fractions: $$\frac{1}{10}, \frac{2}{10}$$ .
14. Order the fractions: $$\frac{1}{1}, \frac{1}{2}$$ .
15. Order the fractions: $$\frac{1}{8}, \frac{1}{4}$$ .
16. Order the fractions: $$\frac{2}{6}, \frac{1}{6}$$ .
17. Order the fractions: $$\frac{3}{9}, \frac{2}{9}$$ .
18. Order the fractions: $$\frac{2}{2}, \frac{1}{2}$$ .
19. Order the fractions: $$\frac{5}{6}, \frac{3}{6}$$ .
20. Order the fractions: $$\frac{9}{10}, \frac{1}{10}$$ .

Medium Level Questions

1. Order the fractions: $$\frac{1}{3}, \frac{2}{6}, \frac{1}{2}$$ .
2. Order the fractions: $$\frac{1}{4}, \frac{3}{8}, \frac{1}{8}$$ .
3. Order the fractions: $$\frac{2}{5}, \frac{4}{10}, \frac{1}{5}$$ .
4. Order the fractions: $$\frac{3}{6}, \frac{2}{4}, \frac{5}{12}$$ .
5. Order the fractions: $$\frac{7}{10}, \frac{1}{2}, \frac{3}{5}$$ .
6. Order the fractions: $$\frac{3}{4}, \frac{1}{2}, \frac{5}{8}$$ .
7. Order the fractions: $$\frac{2}{3}, \frac{3}{9}, \frac{1}{2}$$ .
8. Order the fractions: $$\frac{4}{5}, \frac{2}{5}, \frac{3}{10}$$ .
9. Order the fractions: $$\frac{2}{8}, \frac{1}{4}, \frac{1}{2}$$ .
10. Order the fractions: $$\frac{5}{12}, \frac{1}{3}, \frac{1}{4}$$ .
11. Order the fractions: $$\frac{3}{5}, \frac{4}{5}, \frac{2}{5}$$ .
12. Order the fractions: $$\frac{1}{6}, \frac{2}{3}, \frac{3}{6}$$ .
13. Order the fractions: $$\frac{3}{8}, \frac{1}{2}, \frac{5}{8}$$ .
14. Order the fractions: $$\frac{1}{5}, \frac{4}{10}, \frac{3}{10}$$ .
15. Order the fractions: $$\frac{1}{4}, \frac{3}{16}, \frac{1}{2}$$ .
16. Order the fractions: $$\frac{5}{8}, \frac{7}{10}, \frac{4}{5}$$ .
17. Order the fractions: $$\frac{1}{2}, \frac{2}{4}, \frac{3}{8}$$ .
18. Order the fractions: $$\frac{9}{10}, \frac{3}{5}, \frac{1}{2}$$ .
19. Order the fractions: $$\frac{2}{7}, \frac{1}{3}, \frac{3}{10}$$ .
20. Order the fractions: $$\frac{2}{9}, \frac{5}{12}, \frac{1}{4}$$ .

Hard Level Questions

1. Order the fractions: $$\frac{7}{12}, \frac{5}{8}, \frac{1}{2}$$ .
2. Order the fractions: $$\frac{3}{10}, \frac{4}{15}, \frac{1}{3}$$ .
3. Order the fractions: $$\frac{9}{20}, \frac{11}{30}, \frac{7}{10}$$ .
4. Order the fractions: $$\frac{2}{5}, \frac{3}{8}, \frac{1}{2}$$ .
5. Order the fractions: $$\frac{1}{2}, \frac{3}{5}, \frac{5}{12}$$ .
6. Order the fractions: $$\frac{8}{15}, \frac{5}{9}, \frac{7}{10}$$ .
7. Order the fractions: $$\frac{4}{7}, \frac{2}{3}, \frac{5}{12}$$ .
8. Order the fractions: $$\frac{3}{8}, \frac{5}{12}, \frac{7}{20}$$ .
9. Order the fractions: $$\frac{3}{4}, \frac{5}{6}, \frac{2}{3}$$ .
10. Order the fractions: $$\frac{9}{14}, \frac{5}{8}, \frac{1}{2}$$ .
11. Order the fractions: $$\frac{12}{25}, \frac{1}{2}, \frac{9}{20}$$ .
12. Order the fractions: $$\frac{5}{12}, \frac{10}{24}, \frac{4}{9}$$ .
13. Order the fractions: $$\frac{7}{15}, \frac{1}{3}, \frac{2}{5}$$ .
14. Order the fractions: $$\frac{4}{11}, \frac{9}{22}, \frac{3}{8}$$ .
15. Order the fractions: $$\frac{8}{18}, \frac{2}{5}, \frac{3}{7}$$ .
16. Order the fractions: $$\frac{5}{24}, \frac{11}{30}, \frac{2}{4}$$ .
17. Order the fractions: $$\frac{13}{16}, \frac{7}{10}, \frac{3}{5}$$ .
18. Order the fractions: $$\frac{7}{18}, \frac{11}{30}, \frac{2}{5}$$ .
19. Order the fractions: $$\frac{2}{3}, \frac{3}{5}, \frac{5}{12}$$ .
20. Order the fractions: $$\frac{5}{16}, \frac{9}{20}, \frac{3}{5}$$ .

Answers with Explanations

Easy Level Answers

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

Medium Level Answers

1. $$\frac{1}{3} < \frac{2}{6} < \frac{1}{2}$$
2. $$\frac{1}{8} < \frac{1}{4} < \frac{3}{8}$$
3. $$\frac{1}{5} < \frac{2}{5} < \frac{4}{10}$$
4. $$\frac{5}{12} < \frac{2}{4} = \frac{3}{6}$$
5. $$\frac{1}{2} < \frac{3}{5} < \frac{7}{10}$$
6. $$\frac{4}{5} > \frac{3}{10} > \frac{2}{5}$$
7. $$\frac{2}{3} > \frac{3}{9} < \frac{1}{2}$$
8. $$\frac{2}{5} < \frac{4}{5} > \frac{3}{10}$$
9. $$\frac{2}{8} < \frac{1}{4} < \frac{1}{2}$$
10. $$\frac{1}{4} < \frac{5}{12} < \frac{1}{3}$$
11. $$\frac{2}{5} < \frac{3}{5} < \frac{4}{5}$$
12. $$\frac{1}{6} < \frac{3}{6} < \frac{2}{3}$$
13. $$\frac{3}{8} < \frac{5}{12} < \frac{7}{20}$$
14. $$\frac{1}{5} < \frac{3}{10} < \frac{4}{10}$$
15. $$\frac{3}{16} < \frac{1}{4} < \frac{1}{2}$$
16. $$\frac{5}{8} < \frac{7}{10} < \frac{4}{5}$$
17. $$\frac{3}{8} < \frac{2}{4} < \frac{1}{2}$$
18. $$\frac{1}{2} < \frac{3}{5} < \frac{9}{10}$$
19. $$\frac{2}{5} < \frac{3}{10} < \frac{1}{4}$$
20. $$\frac{2}{9} < \frac{1}{4} < \frac{5}{12}$$

Hard Level Answers

1. $$\frac{1}{2} < \frac{5}{8} < \frac{7}{12}$$
2. $$\frac{4}{15} < \frac{3}{10} < \frac{1}{3}$$
3. $$\frac{9}{20} < \frac{11}{30} < \frac{7}{10}$$
4. $$\frac{1}{2} < \frac{2}{5} < \frac{3}{8}$$
5. $$\frac{5}{12} < \frac{1}{2} < \frac{3}{5}$$
6. $$\frac{8}{15} < \frac{5}{9} < \frac{7}{10}$$
7. $$\frac{4}{11} < \frac{2}{3} < \frac{5}{12}$$
8. $$\frac{3}{8} < \frac{7}{20} < \frac{5}{12}$$
9. $$\frac{2}{3} < \frac{3}{4} < \frac{5}{6}$$
10. $$\frac{1}{2} < \frac{9}{14} < \frac{5}{8}$$
11. $$\frac{12}{25} < \frac{9}{20} < \frac{1}{2}$$
12. $$\frac{5}{12} < \frac{10}{24} < \frac{4}{9}$$
13. $$\frac{2}{5} < \frac{5}{12} < \frac{7}{15}$$
14. $$\frac{4}{11} < \frac{3}{8} < \frac{9}{22}$$
15. $$\frac{2}{5} < \frac{8}{18} < \frac{3}{7}$$
16. $$\frac{5}{24} < \frac{11}{30} < \frac{2}{4}$$
17. $$\frac{7}{10} < \frac{13}{16} < \frac{3}{5}$$
18. $$\frac{7}{18} < \frac{11}{30} < \frac{2}{5}$$
19. $$\frac{5}{12} < \frac{2}{3} < \frac{3}{5}$$
20. $$\frac{5}{16} < \frac{9}{20} < \frac{3}{5}$$

Now you have a complete guide to ordering fractions! Remember to practice, and soon it will become easy!