Year 4 Maths: Using Improper Fractions to Subtract

What are Improper Fractions?

Before we start subtracting, let’s understand what an improper fraction is. An improper fraction is when the top number (numerator) is bigger than the bottom number (denominator). For example:

• $$\frac{5}{4}$$
• $$\frac{7}{3}$$
• $$\frac{9}{2}$$

These fractions are improper because the numerator is greater than the denominator.

Why Use Improper Fractions?

Sometimes, it’s easier to work with improper fractions when we are adding or subtracting fractions. This is because we can convert mixed numbers (like $$1\frac{1}{2}$$) into improper fractions.

Example of Conversion

To convert a mixed number to an improper fraction, follow this rule:

1. Multiply the whole number by the denominator.
2. Add the numerator to that result.
3. Place that number over the original denominator.

For example, to convert $$1\frac{1}{2}$$:

1. Multiply: $$1 \times 2 = 2$$
2. Add: $$2 + 1 = 3$$
3. So, $$1\frac{1}{2}$$ becomes $$\frac{3}{2}$$.

Subtracting Improper Fractions

Steps to Subtract Improper Fractions

1. Make sure the fractions have the same denominator. If they don’t, find a common denominator.
2. Subtract the numerators. Keep the denominator the same.
3. Simplify the fraction if possible.

Example of Subtraction

Let’s subtract $$\frac{7}{3}$$ and $$\frac{2}{3}$$.

1. They have the same denominator (3).
2. Subtract the numerators: $$7 – 2 = 5$$.
3. So, $$\frac{7}{3} – \frac{2}{3} = \frac{5}{3}$$.

Another Example

Now, let’s subtract $$\frac{9}{4}$$ from $$\frac{11}{4}$$.

1. The denominators are the same (4).
2. Subtract the numerators: $$11 – 9 = 2$$.
3. So, $$\frac{11}{4} – \frac{9}{4} = \frac{2}{4}$$.
4. We can simplify $$\frac{2}{4}$$ to $$\frac{1}{2}$$.

Key Rules to Remember

• Always check if the denominators are the same.
• If they aren’t, find a common denominator first.
• Don’t forget to simplify your answer if you can!

Tips and Tricks

• Practice converting mixed numbers to improper fractions to get comfortable.
• Use visual aids like fraction bars to help understand the subtraction.
• Check your work by adding the answer back to the smaller fraction to see if you get the larger fraction.

Questions for Practice

Easy Level Questions

1. $$\frac{5}{3} – \frac{2}{3} = ?$$
2. $$\frac{7}{4} – \frac{3}{4} = ?$$
3. $$\frac{6}{5} – \frac{1}{5} = ?$$
4. $$\frac{8}{7} – \frac{3}{7} = ?$$
5. $$\frac{9}{6} – \frac{5}{6} = ?$$
6. $$\frac{10}{8} – \frac{4}{8} = ?$$
7. $$\frac{12}{9} – \frac{4}{9} = ?$$
8. $$\frac{15}{10} – \frac{6}{10} = ?$$
9. $$\frac{11}{5} – \frac{2}{5} = ?$$
10. $$\frac{14}{6} – \frac{7}{6} = ?$$
11. $$\frac{13}{8} – \frac{5}{8} = ?$$
12. $$\frac{9}{4} – \frac{3}{4} = ?$$
13. $$\frac{7}{6} – \frac{2}{6} = ?$$
14. $$\frac{4}{3} – \frac{1}{3} = ?$$
15. $$\frac{6}{4} – \frac{1}{4} = ?$$
16. $$\frac{10}{5} – \frac{4}{5} = ?$$
17. $$\frac{16}{12} – \frac{8}{12} = ?$$
18. $$\frac{18}{9} – \frac{6}{9} = ?$$
19. $$\frac{20}{15} – \frac{5}{15} = ?$$
20. $$\frac{22}{11} – \frac{9}{11} = ?$$

Medium Level Questions

1. $$\frac{5}{2} – \frac{1}{2} = ?$$
2. $$\frac{9}{3} – \frac{4}{3} = ?$$
3. $$\frac{13}{5} – \frac{3}{5} = ?$$
4. $$\frac{15}{7} – \frac{6}{7} = ?$$
5. $$\frac{18}{8} – \frac{9}{8} = ?$$
6. $$\frac{11}{6} – \frac{5}{6} = ?$$
7. $$\frac{14}{5} – \frac{4}{5} = ?$$
8. $$\frac{19}{10} – \frac{9}{10} = ?$$
9. $$\frac{12}{5} – \frac{4}{5} = ?$$
10. $$\frac{10}{6} – \frac{4}{6} = ?$$
11. $$\frac{17}{8} – \frac{7}{8} = ?$$
12. $$\frac{21}{12} – \frac{5}{12} = ?$$
13. $$\frac{16}{10} – \frac{3}{10} = ?$$
14. $$\frac{23}{15} – \frac{8}{15} = ?$$
15. $$\frac{15}{9} – \frac{5}{9} = ?$$
16. $$\frac{14}{11} – \frac{7}{11} = ?$$
17. $$\frac{20}{7} – \frac{10}{7} = ?$$
18. $$\frac{17}{5} – \frac{8}{5} = ?$$
19. $$\frac{24}{12} – \frac{9}{12} = ?$$
20. $$\frac{22}{13} – \frac{6}{13} = ?$$

Hard Level Questions

1. $$\frac{25}{12} – \frac{10}{12} = ?$$
2. $$\frac{30}{8} – \frac{15}{8} = ?$$
3. $$\frac{35}{20} – \frac{15}{20} = ?$$
4. $$\frac{18}{7} – \frac{6}{7} = ?$$
5. $$\frac{29}{10} – \frac{9}{10} = ?$$
6. $$\frac{26}{9} – \frac{10}{9} = ?$$
7. $$\frac{31}{15} – \frac{11}{15} = ?$$
8. $$\frac{28}{12} – \frac{16}{12} = ?$$
9. $$\frac{33}{11} – \frac{17}{11} = ?$$
10. $$\frac{40}{18} – \frac{20}{18} = ?$$
11. $$\frac{42}{15} – \frac{12}{15} = ?$$
12. $$\frac{39}{14} – \frac{21}{14} = ?$$
13. $$\frac{45}{20} – \frac{5}{20} = ?$$
14. $$\frac{49}{18} – \frac{15}{18} = ?$$
15. $$\frac{52}{24} – \frac{28}{24} = ?$$
16. $$\frac{55}{25} – \frac{20}{25} = ?$$
17. $$\frac{60}{22} – \frac{12}{22} = ?$$
18. $$\frac{65}{30} – \frac{25}{30} = ?$$
19. $$\frac{70}{40} – \frac{30}{40} = ?$$
20. $$\frac{75}{35} – \frac{15}{35} = ?$$

Answers

Easy Level Answers

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

Medium Level Answers

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

Hard Level Answers

1. $$\frac{15}{12} = \frac{5}{4}$$
2. $$\frac{15}{8}$$
3. $$\frac{20}{20} = 1$$
4. $$\frac{12}{7}$$
5. $$\frac{20}{10} = 2$$
6. $$\frac{16}{9}$$
7. $$\frac{20}{15} = \frac{4}{3}$$
8. $$\frac{12}{12} = 1$$
9. $$\frac{16}{11}$$
10. $$\frac{20}{18} = \frac{10}{9}$$
11. $$\frac{30}{15} = 2$$
12. $$\frac{28}{14} = 2$$
13. $$\frac{40}{20} = 2$$
14. $$\frac{34}{18} = \frac{17}{9}$$
15. $$\frac{24}{24} = 1$$
16. $$\frac{55}{25} = \frac{11}{5}$$
17. $$\frac{48}{22}$$
18. $$\frac{50}{30} = \frac{5}{3}$$
19. $$\frac{40}{40} = 1$$
20. $$\frac{60}{35} = \frac{12}{7}$$

Feel free to practice these questions and check your answers! Remember, the more you practice, the easier it gets! Happy learning!