Year 5 Maths: Comparing Fractions

Introduction to Comparing Fractions

Hello, Year 5! Today, we’re going to learn how to compare fractions. Comparing fractions means figuring out which fraction is bigger, smaller, or if they are equal.

What is a Fraction?

A fraction has two parts: the numerator and the denominator.

• The numerator (the top number) tells us how many parts we have.
• The denominator (the bottom number) tells us how many equal parts make a whole.

For example, in the fraction $$\frac{3}{4}$$ :

• 3 is the numerator.
• 4 is the denominator.

Why Compare Fractions?

Sometimes, we need to know which fraction is larger or if they are the same. This can help us in cooking, sharing, or measuring.

Key Rules for Comparing Fractions

1. Same Denominator:
   • If two fractions have the same denominator, the one with the larger numerator is the bigger fraction.
   • Example: Compare $$\frac{2}{5}$$ and $$\frac{4}{5}$$ . Since both have the same denominator (5), we look at the numerators. 2 is less than 4, so $$\frac{2}{5}$$ is smaller.
2. Different Denominators:
   • If the fractions have different denominators, we can:
     • Convert them to have a common denominator.
     • Or, convert them to decimals (but we will focus mainly on getting a common denominator).
   • Example: Compare $$\frac{1}{4}$$ and $$\frac{1}{2}$$ .
     • The denominators are different (4 and 2).
     • The common denominator for 4 and 2 is 4.
     • Convert $$\frac{1}{2}$$ to a fraction with 4 as the denominator: $$\frac{1}{2} = \frac{2}{4}$$ .
     • Now we compare $$\frac{1}{4}$$ to $$\frac{2}{4}$$ . Since 1 is less than 2, $$\frac{1}{4}$$ is smaller.
3. Equal Fractions:
   • If the fractions are equal, they will have the same value.
   • Example: $$\frac{2}{4}$$ is equal to $$\frac{1}{2}$$ .

Tips and Tricks

• Draw a Picture: Sometimes drawing a visual can help. You can shade in parts of a circle or a rectangle to see which fraction is larger.
• Use Fraction Strips: You can create strips of paper cut into different fractions to compare them physically.
• Practice: The more you practice comparing fractions, the easier it will become!

Questions

Easy Level (20 Questions)

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

Medium Level (20 Questions)

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

Hard Level (20 Questions)

1. Compare $$\frac{5}{8}$$ and $$\frac{7}{12}$$ .
2. Compare $$\frac{3}{7}$$ and $$\frac{5}{9}$$ .
3. Compare $$\frac{11}{18}$$ and $$\frac{7}{12}$$ .
4. Compare $$\frac{4}{5}$$ and $$\frac{3}{4}$$ .
5. Compare $$\frac{8}{15}$$ and $$\frac{5}{9}$$ .
6. Compare $$\frac{9}{16}$$ and $$\frac{7}{12}$$ .
7. Compare $$\frac{3}{10}$$ and $$\frac{4}{15}$$ .
8. Compare $$\frac{5}{6}$$ and $$\frac{11}{18}$$ .
9. Compare $$\frac{14}{25}$$ and $$\frac{9}{16}$$ .
10. Compare $$\frac{7}{10}$$ and $$\frac{4}{5}$$ .
11. Compare $$\frac{13}{20}$$ and $$\frac{7}{12}$$ .
12. Compare $$\frac{2}{5}$$ and $$\frac{3}{8}$$ .
13. Compare $$\frac{4}{7}$$ and $$\frac{5}{8}$$ .
14. Compare $$\frac{11}{24}$$ and $$\frac{7}{15}$$ .
15. Compare $$\frac{10}{21}$$ and $$\frac{3}{5}$$ .
16. Compare $$\frac{6}{11}$$ and $$\frac{7}{13}$$ .
17. Compare $$\frac{12}{19}$$ and $$\frac{14}{23}$$ .
18. Compare $$\frac{5}{12}$$ and $$\frac{7}{18}$$ .
19. Compare $$\frac{9}{14}$$ and $$\frac{11}{18}$$ .
20. Compare $$\frac{15}{28}$$ and $$\frac{7}{12}$$ .

Answers and Explanations

Easy Level Answers

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

Medium Level Answers

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

Hard Level Answers

1. $$\frac{5}{8} < \frac{7}{12}$$
2. $$\frac{3}{7} < \frac{5}{9}$$
3. $$\frac{11}{18} > \frac{7}{12}$$
4. $$\frac{4}{5} > \frac{3}{4}$$
5. $$\frac{8}{15} < \frac{5}{9}$$
6. $$\frac{9}{16} < \frac{7}{12}$$
7. $$\frac{3}{10} > \frac{4}{15}$$
8. $$\frac{5}{6} > \frac{11}{18}$$
9. $$\frac{14}{25} < \frac{9}{16}$$
10. $$\frac{7}{10} > \frac{4}{5}$$
11. $$\frac{13}{20} > \frac{7}{12}$$
12. $$\frac{2}{5} > \frac{3}{8}$$
13. $$\frac{4}{7} < \frac{5}{8}$$
14. $$\frac{11}{24} < \frac{7}{15}$$
15. $$\frac{10}{21} < \frac{3}{5}$$
16. $$\frac{6}{11} < \frac{7}{13}$$
17. $$\frac{12}{19} < \frac{14}{23}$$
18. $$\frac{5}{12} > \frac{7}{18}$$
19. $$\frac{9}{14} < \frac{11}{18}$$

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