Introduction to Dividing with Remainders

Hello Year 4! Today, we’re going to learn about dividing with remainders. This is an important skill in maths that helps us understand how numbers work when we share them.

What does “Dividing with Remainders” mean?

When we divide a number, we see how many times one number fits into another. Sometimes, after we divide, we have some left over. This leftover part is called the remainder.

Example of Dividing with Remainders

Let’s say we have 10 apples, and we want to share them equally among 3 friends.

  1. Divide the apples:
    • 3 goes into 10. How many times?
    • 3 fits into 10 three times because ( 3 \times 3 = 9 ).
  2. Count how many apples we have left:
    • We had 10 apples, and we used 9 apples to give to the friends.
    • So, ( 10 – 9 = 1 ) apple is left over.
  3. Write it down:
    • We can say that 10 divided by 3 equals 3 with a remainder of 1.
    • We write this as:
    $$ 10 \div 3 = 3 , R1 $$

Key Rules for Dividing with Remainders

  1. Divide normally first: Start by dividing the bigger number by the smaller number.
  2. Subtract to find the remainder: After you multiply, subtract to see what’s left.
  3. Remainder can be smaller than the divisor: The remainder should always be less than the number you divided by.

Tips and Tricks

  • Use your times tables: Knowing your times tables can help you divide faster!
  • Draw pictures: Sometimes drawing groups can help you see how many are left over.
  • Practice with real objects: Use toys or snacks to practice sharing and find remainders.

Practice Questions

Now that we understand dividing with remainders, let’s practice!

Easy Level Questions

  1. 8 ÷ 2 = ?
  2. 15 ÷ 4 = ?
  3. 7 ÷ 3 = ?
  4. 12 ÷ 5 = ?
  5. 9 ÷ 3 = ?
  6. 18 ÷ 6 = ?
  7. 20 ÷ 4 = ?
  8. 11 ÷ 2 = ?
  9. 5 ÷ 5 = ?
  10. 14 ÷ 3 = ?
  11. 16 ÷ 4 = ?
  12. 13 ÷ 5 = ?
  13. 10 ÷ 2 = ?
  14. 19 ÷ 4 = ?
  15. 21 ÷ 7 = ?
  16. 22 ÷ 3 = ?
  17. 6 ÷ 2 = ?
  18. 30 ÷ 8 = ?
  19. 25 ÷ 6 = ?
  20. 4 ÷ 4 = ?

Medium Level Questions

  1. 34 ÷ 5 = ?
  2. 27 ÷ 6 = ?
  3. 45 ÷ 8 = ?
  4. 33 ÷ 4 = ?
  5. 50 ÷ 9 = ?
  6. 29 ÷ 5 = ?
  7. 64 ÷ 7 = ?
  8. 72 ÷ 10 = ?
  9. 55 ÷ 6 = ?
  10. 78 ÷ 9 = ?
  11. 66 ÷ 8 = ?
  12. 90 ÷ 11 = ?
  13. 47 ÷ 7 = ?
  14. 39 ÷ 5 = ?
  15. 83 ÷ 12 = ?
  16. 52 ÷ 6 = ?
  17. 37 ÷ 4 = ?
  18. 80 ÷ 14 = ?
  19. 31 ÷ 6 = ?
  20. 70 ÷ 13 = ?

Hard Level Questions

  1. 98 ÷ 6 = ?
  2. 105 ÷ 9 = ?
  3. 123 ÷ 11 = ?
  4. 144 ÷ 12 = ?
  5. 154 ÷ 10 = ?
  6. 83 ÷ 7 = ?
  7. 67 ÷ 5 = ?
  8. 99 ÷ 8 = ?
  9. 115 ÷ 14 = ?
  10. 138 ÷ 12 = ?
  11. 126 ÷ 9 = ?
  12. 76 ÷ 7 = ?
  13. 88 ÷ 5 = ?
  14. 140 ÷ 13 = ?
  15. 157 ÷ 16 = ?
  16. 172 ÷ 15 = ?
  17. 195 ÷ 14 = ?
  18. 213 ÷ 17 = ?
  19. 164 ÷ 18 = ?
  20. 203 ÷ 19 = ?

Answers

Easy Level Answers

  1. 4 (0)
  2. 3 (3)
  3. 2 (1)
  4. 2 (2)
  5. 3 (0)
  6. 3 (0)
  7. 5 (0)
  8. 5 (1)
  9. 1 (0)
  10. 4 (2)
  11. 4 (0)
  12. 2 (3)
  13. 5 (0)
  14. 4 (3)
  15. 3 (0)
  16. 7 (1)
  17. 3 (0)
  18. 3 (6)
  19. 4 (1)
  20. 1 (0)

Medium Level Answers

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

Hard Level Answers

  1. 16 (2)
  2. 11 (6)
  3. 11 (2)
  4. 12 (0)
  5. 15 (4)
  6. 11 (6)
  7. 13 (2)
  8. 12 (3)
  9. 8 (7)
  10. 11 (6)
  11. 14 (0)
  12. 10 (6)
  13. 17 (3)
  14. 10 (10)
  15. 9 (1)
  16. 11 (7)
  17. 13 (12)
  18. 12 (9)
  19. 9 (1)
  20. 10 (13)

With these questions and answers, you can practice dividing with remainders. Remember to take your time and use the tips we discussed. Happy dividing!