What is a Mixed Number?

A mixed number is a number that has a whole part and a fractional part. For example, 2 3/4 means you have 2 whole parts and 3 out of 4 parts of another whole.

What is an Improper Fraction?

An improper fraction has a numerator that is larger than or equal to the denominator. For example, 11/4 is an improper fraction because 11 (the numerator) is greater than 4 (the denominator).

How to Convert a Mixed Number to an Improper Fraction

To change a mixed number into an improper fraction, follow these steps:

  1. Multiply the whole number by the denominator.For example, in 2 3/4:
    • Multiply 2 (the whole number) by 4 (the denominator):
    $$ 2 \times 4 = 8 $$
  2. Add the result to the numerator.Using the same example, add the 3 (the numerator):$$ 8 + 3 = 11 $$
  3. Write your answer as an improper fraction.You take the result from step 2 (which is 11) and place it over the original denominator (which is 4):$$ \frac{11}{4} $$

So, 2 3/4 as an improper fraction is 11/4.

Key Rules to Remember

  • The whole number is multiplied by the denominator.
  • The numerator is added to the result of the multiplication.
  • The improper fraction is formed by putting this total over the original denominator.

Tips and Tricks

  • Always check your multiplication and addition to avoid mistakes.
  • Practise with simple mixed numbers first, then move to more complicated ones.
  • Remember, the improper fraction can be converted back to a mixed number if needed!

Practice Questions

Easy Level Questions

  1. Convert 1 1/2 to an improper fraction.
  2. Convert 3 2/5 to an improper fraction.
  3. Convert 2 1/3 to an improper fraction.
  4. Convert 4 4/6 to an improper fraction.
  5. Convert 5 1/2 to an improper fraction.
  6. Convert 2 3/8 to an improper fraction.
  7. Convert 1 4/7 to an improper fraction.
  8. Convert 3 5/10 to an improper fraction.
  9. Convert 6 2/3 to an improper fraction.
  10. Convert 2 1/4 to an improper fraction.
  11. Convert 1 3/5 to an improper fraction.
  12. Convert 3 1/2 to an improper fraction.
  13. Convert 4 2/3 to an improper fraction.
  14. Convert 2 5/8 to an improper fraction.
  15. Convert 1 2/4 to an improper fraction.
  16. Convert 5 3/5 to an improper fraction.
  17. Convert 2 1/2 to an improper fraction.
  18. Convert 3 3/4 to an improper fraction.
  19. Convert 4 1/2 to an improper fraction.
  20. Convert 1 1/3 to an improper fraction.

Medium Level Questions

  1. Convert 2 2/3 to an improper fraction.
  2. Convert 5 4/5 to an improper fraction.
  3. Convert 3 7/10 to an improper fraction.
  4. Convert 4 3/5 to an improper fraction.
  5. Convert 6 1/4 to an improper fraction.
  6. Convert 5 2/3 to an improper fraction.
  7. Convert 3 8/9 to an improper fraction.
  8. Convert 7 1/2 to an improper fraction.
  9. Convert 2 4/7 to an improper fraction.
  10. Convert 3 6/8 to an improper fraction.
  11. Convert 1 5/12 to an improper fraction.
  12. Convert 4 4/9 to an improper fraction.
  13. Convert 2 2/5 to an improper fraction.
  14. Convert 5 1/8 to an improper fraction.
  15. Convert 6 3/4 to an improper fraction.
  16. Convert 1 7/8 to an improper fraction.
  17. Convert 3 2/3 to an improper fraction.
  18. Convert 2 6/7 to an improper fraction.
  19. Convert 5 5/6 to an improper fraction.
  20. Convert 4 1/4 to an improper fraction.

Hard Level Questions

  1. Convert 7 3/4 to an improper fraction.
  2. Convert 9 2/5 to an improper fraction.
  3. Convert 10 1/3 to an improper fraction.
  4. Convert 8 5/8 to an improper fraction.
  5. Convert 11 1/2 to an improper fraction.
  6. Convert 6 7/10 to an improper fraction.
  7. Convert 12 2/3 to an improper fraction.
  8. Convert 3 9/10 to an improper fraction.
  9. Convert 4 8/9 to an improper fraction.
  10. Convert 9 1/2 to an improper fraction.
  11. Convert 3 11/12 to an improper fraction.
  12. Convert 7 1/6 to an improper fraction.
  13. Convert 5 3/4 to an improper fraction.
  14. Convert 2 9/10 to an improper fraction.
  15. Convert 8 4/7 to an improper fraction.
  16. Convert 1 11/12 to an improper fraction.
  17. Convert 10 1/4 to an improper fraction.
  18. Convert 4 5/6 to an improper fraction.
  19. Convert 7 2/3 to an improper fraction.
  20. Convert 3 1/5 to an improper fraction.

Answers and Explanations

Easy Level Answers

  1. $$ \frac{3}{2} $$
  2. $$ \frac{17}{5} $$
  3. $$ \frac{7}{3} $$
  4. $$ \frac{28}{6} $$
  5. $$ \frac{11}{2} $$
  6. $$ \frac{19}{8} $$
  7. $$ \frac{11}{7} $$
  8. $$ \frac{32}{10} $$
  9. $$ \frac{20}{3} $$
  10. $$ \frac{9}{4} $$
  11. $$ \frac{8}{5} $$
  12. $$ \frac{7}{2} $$
  13. $$ \frac{14}{3} $$
  14. $$ \frac{21}{8} $$
  15. $$ \frac{5}{4} $$
  16. $$ \frac{33}{5} $$
  17. $$ \frac{5}{2} $$
  18. $$ \frac{15}{4} $$
  19. $$ \frac{9}{2} $$
  20. $$ \frac{4}{3} $$

Medium Level Answers

  1. $$ \frac{8}{3} $$
  2. $$ \frac{29}{5} $$
  3. $$ \frac{37}{10} $$
  4. $$ \frac{23}{5} $$
  5. $$ \frac{25}{4} $$
  6. $$ \frac{17}{3} $$
  7. $$ \frac{35}{9} $$
  8. $$ \frac{15}{2} $$
  9. $$ \frac{18}{7} $$
  10. $$ \frac{30}{8} $$
  11. $$ \frac{17}{12} $$
  12. $$ \frac{40}{9} $$
  13. $$ \frac{12}{5} $$
  14. $$ \frac{43}{8} $$
  15. $$ \frac{27}{4} $$
  16. $$ \frac{15}{8} $$
  17. $$ \frac{11}{3} $$
  18. $$ \frac{20}{7} $$
  19. $$ \frac{35}{6} $$
  20. $$ \frac{17}{4} $$

Hard Level Answers

  1. $$ \frac{31}{4} $$
  2. $$ \frac{47}{5} $$
  3. $$ \frac{31}{3} $$
  4. $$ \frac{69}{8} $$
  5. $$ \frac{23}{2} $$
  6. $$ \frac{67}{10} $$
  7. $$ \frac{38}{3} $$
  8. $$ \frac{39}{10} $$
  9. $$ \frac{44}{9} $$
  10. $$ \frac{19}{2} $$
  11. $$ \frac{47}{12} $$
  12. $$ \frac{43}{6} $$
  13. $$ \frac{23}{4} $$
  14. $$ \frac{29}{10} $$
  15. $$ \frac{60}{7} $$
  16. $$ \frac{23}{12} $$
  17. $$ \frac{41}{4} $$
  18. $$ \frac{29}{6} $$
  19. $$ \frac{23}{3} $$
  20. $$ \frac{16}{5} $$

Keep practising converting mixed numbers to improper fractions, and soon you’ll become a pro! If you have any questions, feel free to ask!