Introduction to Mixed Numbers

Hello, Year 6! Today, we’re going to learn how to multiply a mixed number by a whole number.

What is a Mixed Number?

A mixed number is a number that has both a whole part and a fractional part. For example, in the mixed number (2 \frac{1}{3}), the whole part is 2, and the fraction is (\frac{1}{3}).

Steps to Multiply a Mixed Number by a Whole Number

Here’s how to do it step by step:

  1. Convert the Mixed Number to an Improper Fraction:
    • To convert a mixed number to an improper fraction, multiply the whole number by the denominator (the bottom number of the fraction) and then add the numerator (the top number of the fraction).
    • For example, to convert (2 \frac{1}{3}):
      • Multiply (2) (the whole number) by (3) (the denominator): (2 \times 3 = 6).
      • Add the (1) (the numerator): (6 + 1 = 7).
      • So, (2 \frac{1}{3} = \frac{7}{3}).
  2. Multiply the Improper Fraction by the Whole Number:
    • Now, multiply the improper fraction by the whole number.
    • If we have (2 \frac{1}{3} \times 4), we can do:
      • (\frac{7}{3} \times 4 = \frac{7 \times 4}{3} = \frac{28}{3}).
  3. Convert Back to a Mixed Number (if needed):
    • Sometimes, you might want to convert your answer back to a mixed number.
    • For (\frac{28}{3}):
      • Divide (28) by (3): (28 \div 3 = 9) remainder (1).
      • So, (9 \frac{1}{3}) is the mixed number.

Key Rules

  • Always convert the mixed number to an improper fraction first.
  • Multiply the numerator of the fraction by the whole number.
  • Simplify your answer if possible.

Tips and Tricks

  • Remember, when you convert a mixed number, you multiply the whole number by the denominator and add the numerator.
  • Keep your fractions in their simplest form if you can.
  • Practice makes perfect! The more you practice, the easier it will become.

Practice Questions

Easy Level Questions

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

Medium Level Questions

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

Hard Level Questions

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

Answers and Explanations

Easy Level Answers

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

Medium Level Answers

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

Hard Level Answers

  1. (7 \frac{3}{4} \times 2 = 15 \frac{1}{2})
  2. (5 \frac{1}{2} \times 3 = 16 \frac{1}{2})
  3. (4 \frac{5}{6} \times 5 = 29 \frac{1}{6})
  4. (2 \frac{7}{8} \times 4 = 11 \frac{3}{2})
  5. (3 \frac{2}{3} \times 6 = 22)
  6. (1 \frac{9}{10} \times 7 = 8 \frac{3}{10})
  7. (6 \frac{5}{6} \times 3 = 20 \frac{1}{2})
  8. (2 \frac{1}{3} \times 9 = 21)
  9. (5 \frac{1}{4} \times 4 = 21)
  10. (3 \frac{5}{8} \times 2 = 7 \frac{1}{4})
  11. (8 \frac{1}{2} \times 1 = 8 \frac{1}{2})
  12. (4 \frac{2}{3} \times 3 = 14)
  13. (3 \frac{2}{5} \times 5 = 16)
  14. (2 \frac{9}{10} \times 2 = 5 \frac{8}{10} = 5 \frac{4}{5})
  15. (1 \frac{3}{4} \times 8 = 14)
  16. (5 \frac{3}{4} \times 3 = 17 \frac{1}{4})
  17. (6 \frac{2}{3} \times 1 = 6 \frac{2}{3})
  18. (2 \frac{5}{6} \times 6 = 15)
  19. (7 \frac{1}{2} \times 4 = 30)
  20. (1 \frac{8}{9} \times 9 = 10)

I hope this helps you understand how to multiply a mixed number by a whole number! Keep practicing, and you’ll get even better! If you have any questions, feel free to ask!