What is Partitioning?

Partitioning is a method we can use to help us add or subtract numbers by breaking them into smaller, easier parts. Instead of working with the whole number all at once, we split it into parts that are simpler to work with. This makes calculations more manageable!

How Does Partitioning Work?

When we partition numbers, we break them down into tens and ones (or hundreds, tens, and ones if we are working with bigger numbers).

Example of Partitioning in Addition

Let’s say we want to add 34 and 27.

  1. Partition the numbers:
    • 34 can be split into 30 (tens) and 4 (ones).
    • 27 can be split into 20 (tens) and 7 (ones).
  2. Add the tens together:
    • 30 + 20 = 50
  3. Add the ones together:
    • 4 + 7 = 11
  4. Combine the two results:
    • 50 + 11 = 61

So, 34 + 27 = 61!

Example of Partitioning in Subtraction

Now, let’s try subtraction with 56 – 29.

  1. Partition the numbers:
    • 56 can be split into 50 (tens) and 6 (ones).
    • 29 can be split into 20 (tens) and 9 (ones).
  2. Subtract the tens:
    • 50 – 20 = 30
  3. Subtract the ones:
    • 6 – 9 = -3 (We can’t have a negative, so we need to borrow!)
  4. So, we borrow 1 from the 30 to make it 29:
    • 29 + 6 = 35 (Now we have 29 – 9 = 20)
  5. Combine the results:
    • 30 – 3 = 27 (from the borrowing)

So, 56 – 29 = 27!

Key Rules for Partitioning

  1. Always break down the numbers into place value: Tens, Ones, Hundreds, etc.
  2. Make sure you add or subtract each part carefully.
  3. Don’t forget to combine your results at the end.

Tips and Tricks

  • Use a number line: This can help you see how numbers are split and combined.
  • Practice with real-life examples: Like adding prices when shopping!
  • Write it down: Visualising the partitioning on paper can help you understand better.

Questions to Practice Partitioning

Easy Level Questions

  1. 12 + 14
  2. 25 + 16
  3. 40 + 23
  4. 33 + 22
  5. 54 + 12
  6. 61 – 21
  7. 45 – 15
  8. 73 – 32
  9. 50 – 29
  10. 68 – 37
  11. 15 + 24
  12. 22 + 33
  13. 34 – 12
  14. 45 – 20
  15. 82 – 30
  16. 21 + 19
  17. 39 + 22
  18. 77 – 44
  19. 90 – 25
  20. 56 + 24

Medium Level Questions

  1. 83 + 29
  2. 67 – 38
  3. 58 + 36
  4. 91 – 54
  5. 74 + 18
  6. 99 – 48
  7. 62 + 39
  8. 44 – 26
  9. 71 + 19
  10. 85 – 42
  11. 55 + 27
  12. 90 – 56
  13. 48 + 37
  14. 76 – 49
  15. 99 – 72
  16. 22 + 58
  17. 33 + 44
  18. 67 – 29
  19. 51 + 39
  20. 82 – 55

Hard Level Questions

  1. 145 + 267
  2. 309 – 154
  3. 478 + 236
  4. 640 – 273
  5. 512 + 489
  6. 865 – 437
  7. 723 + 198
  8. 450 – 276
  9. 678 + 329
  10. 890 – 456
  11. 345 + 678
  12. 987 – 654
  13. 230 + 458
  14. 600 – 275
  15. 812 + 197
  16. 920 – 488
  17. 345 + 678
  18. 530 – 284
  19. 760 + 299
  20. 804 – 536

Answers and Explanations

Easy Level Answers

  1. 26
  2. 41
  3. 63
  4. 55
  5. 66
  6. 35
  7. 30
  8. 41
  9. 21
  10. 31
  11. 39
  12. 55
  13. 22
  14. 25
  15. 52
  16. 40
  17. 61
  18. 33
  19. 65
  20. 80

Medium Level Answers

  1. 112
  2. 29
  3. 94
  4. 37
  5. 92
  6. 51
  7. 101
  8. 18
  9. 90
  10. 43
  11. 82
  12. 34
  13. 85
  14. 27
  15. 27
  16. 80
  17. 77
  18. 38
  19. 90
  20. 27

Hard Level Answers

  1. 412
  2. 155
  3. 714
  4. 367
  5. 1001
  6. 428
  7. 921
  8. 174
  9. 1007
  10. 434
  11. 1023
  12. 333
  13. 688
  14. 325
  15. 1009
  16. 432
  17. 1023
  18. 246
  19. 1059
  20. 268

Now you have a great understanding of partitioning! Remember to practice and have fun with maths!