What is Subtraction with Decomposition?

Hello Year 4! Today, we are going to learn about subtraction with decomposition. This is a method that helps us subtract bigger numbers, especially when the top number is smaller than the bottom number in any column.

Why Do We Need Decomposition?

Sometimes when we subtract, we can’t take one number away from another because the top number is smaller. This is where decomposition comes in! It allows us to break down numbers into smaller parts to make subtraction easier.

How to Do Subtraction with Decomposition

Let’s break it down step by step!

Step 1: Write the Numbers Vertically

When we subtract, we write the larger number on top and the smaller number underneath it.

Example: 

   54 - 28

Step 2: Start from the Right

We will start subtracting from the rightmost column (the units). If the top number is smaller than the bottom number, we need to decompose.

Example: Subtracting Units

In our example, we have:

  • 4 (from 54) minus 8

We need to borrow from the next column (the tens).

  1. The 5 in 54 becomes 4 (we take 1 ten away).
  2. The 4 in 54 becomes 14 (we add 10 to the 4).

Now it looks like this: 

   4(14) -  28

Step 4: Subtract

Now we subtract:

  • 14 minus 8 equals 6.
  • 4 minus 2 equals 2.

So, 54 minus 28 equals 26. 

   54 - 28 _____   26

Key Rules to Remember

  1. Always start from the right.
  2. If the top number is smaller, borrow from the next column.
  3. Don’t forget to reduce the next column by one!

Tips and Tricks

  • Practice makes perfect! The more you practice, the easier it will become.
  • Use your fingers or draw dots to help you visualize the numbers.
  • Check your work! After you finish, add the answer to the smaller number to see if you get back to the larger number.

Practice Questions

Let’s practice what we learned! Here are some subtraction problems for you to try.

Easy Level Questions

  1. 34 – 12 = ?
  2. 45 – 23 = ?
  3. 51 – 30 = ?
  4. 62 – 21 = ?
  5. 73 – 14 = ?
  6. 82 – 45 = ?
  7. 90 – 11 = ?
  8. 76 – 28 = ?
  9. 58 – 29 = ?
  10. 67 – 38 = ?
  11. 53 – 22 = ?
  12. 84 – 36 = ?
  13. 73 – 24 = ?
  14. 44 – 13 = ?
  15. 32 – 15 = ?
  16. 61 – 20 = ?
  17. 95 – 57 = ?
  18. 88 – 19 = ?
  19. 47 – 26 = ?
  20. 29 – 14 = ?

Medium Level Questions

  1. 63 – 47 = ?
  2. 81 – 36 = ?
  3. 74 – 59 = ?
  4. 92 – 45 = ?
  5. 65 – 28 = ?
  6. 57 – 29 = ?
  7. 48 – 37 = ?
  8. 79 – 53 = ?
  9. 94 – 78 = ?
  10. 86 – 39 = ?
  11. 72 – 54 = ?
  12. 53 – 46 = ?
  13. 91 – 62 = ?
  14. 85 – 58 = ?
  15. 66 – 49 = ?
  16. 77 – 68 = ?
  17. 69 – 32 = ?
  18. 58 – 47 = ?
  19. 45 – 29 = ?
  20. 99 – 84 = ?

Hard Level Questions

  1. 125 – 67 = ?
  2. 156 – 79 = ?
  3. 134 – 88 = ?
  4. 142 – 95 = ?
  5. 213 – 157 = ?
  6. 300 – 128 = ?
  7. 245 – 189 = ?
  8. 154 – 78 = ?
  9. 198 – 127 = ?
  10. 275 – 134 = ?
  11. 360 – 245 = ?
  12. 480 – 299 = ?
  13. 512 – 279 = ?
  14. 623 – 487 = ?
  15. 770 – 456 = ?
  16. 850 – 579 = ?
  17. 934 – 748 = ?
  18. 1010 – 673 = ?
  19. 1200 – 845 = ?
  20. 1500 – 999 = ?

Answers

Easy Level Answers

  1. 22
  2. 22
  3. 21
  4. 41
  5. 59
  6. 37
  7. 79
  8. 48
  9. 29
  10. 29
  11. 31
  12. 48
  13. 49
  14. 31
  15. 17
  16. 41
  17. 38
  18. 69
  19. 21
  20. 15

Medium Level Answers

  1. 16
  2. 45
  3. 15
  4. 47
  5. 37
  6. 28
  7. 11
  8. 26
  9. 16
  10. 47
  11. 18
  12. 7
  13. 29
  14. 27
  15. 17
  16. 11
  17. 37
  18. 11
  19. 16
  20. 15

Hard Level Answers

  1. 58
  2. 77
  3. 46
  4. 47
  5. 56
  6. 172
  7. 56
  8. 76
  9. 71
  10. 141
  11. 115
  12. 181
  13. 233
  14. 136
  15. 314
  16. 394
  17. 186
  18. 337
  19. 501
  20. 501

Now, practice these questions, and remember to use decomposition when you need to! Happy subtracting!