1.3: Subtraction of Larger Numbers

You can find the difference between two large numbers using the subtraction facts you have been practicing. Always take away or subtract the number after the minus sign.

Use these steps to complete each subtraction question:

  1. Subtract the ones from the ones.
  2. Subtract the tens from the tens.
  3. Subtract the hundreds from the hundreds.
  4. Subtract the thousands from the thousands.
  5. Subtract the ten thousands from the ten thousands, and so on.

Example A

[latex]\begin{array}[t]{rr}&57\\-&26\\ \hline \\\end{array}[/latex]

Step 1: Subtract the ones from the ones.

[latex]7 \text{ ones }- 6 \text{ ones }= 1 \text{ one}[/latex]

Write the answer in line with the ones in the question.

[latex]\begin{array}[t]{rr}&57\\-&26\\ \hline &1 \\\end{array}[/latex]

Step 2: Subtract the tens from the tens.

[latex]5 \text{ tens }- 2 \text{ tens }= 3 \text{ tens}[/latex]

The difference between 57 and 26 is 31.

[latex]\begin{array}[t]{rr}&57\\-&26\\ \hline &31 \\\end{array}[/latex]

Exercise 1

Find the differences. Check your work by adding and then by using the answer key at the end of the exercise.

  1. [latex]\begin{array}[t]{rr}&36\\-&13\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&72\\-&42\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&48\\-&22\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&55\\-&31\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&93\\-&40\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&76\\-&71\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&95\\-&62\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&39\\-&26\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&64\\-&21\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&85\\-&64\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&98\\-&73\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&76\\-&64\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&86\\-&50\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&95\\-&35\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&28\\-&17\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&69\\-&52\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&84\\-&40\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&74\\-&53\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&97\\-&83\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&89\\-&80\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&79\\-&29\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&89\\-&80\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}&67\\-&61\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}&48\\-&40\\ \hline \\ \end{array}[/latex]

Exercise 1 Answers

  1. 23
  2. 30
  3. 26
  4. 24
  5. 53
  6. 5
  7. 33
  8. 13
  9. 43
  10. 21
  11. 25
  12. 12
  13. 36
  14. 60
  15. 11
  16. 17
  17. 44
  18. 21
  19. 14
  20. 9
  21. 50
  22. 9
  23. 6
  24. 8

Checking Subtraction

You can check your subtraction. Add the answer (the difference) to the number you took away (the second number). If your subtracting was correct, the adding will result in the number you started with (the top number) in the subtraction question.

Example B

The difference is

[latex]\begin{array}[t]{rr}&928\\-&416\\ \hline&512\end{array}[/latex]

Check: Add 512 to 416.

[latex]\begin{array}[t]{rr}&512\\+&416\\ \hline&928\end{array}[/latex]

Exercise 2

Find the differences.

  1. [latex]\begin{array}[t]{rr}&87\\-&36\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&29\\-&21\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&48\\-&40\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&99\\-&63\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&75\\-&45\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&73\\-&20\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&92\\-&21\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&58\\-&27\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&84\\-&23\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&69\\-&38\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&45\\-&23\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&49\\-&19\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&59\\-&14\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&89\\-&63\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&88\\-&15\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&56\\-&44\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&96\\-&75\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&37\\-&17\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&70\\-&50\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&38\\-&24\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&31\\-&10\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&27\\-&12\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}&74\\-&53\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}&45\\-&20\\ \hline \\ \end{array}[/latex]

Exercise 2 Answers

  1. 51
  2. 8
  3. 8
  4. 36
  5. 30
  6. 53
  7. 71
  8. 31
  9. 61
  10. 31
  11. 22
  12. 30
  13. 45
  14. 24
  15. 73
  16. 12
  17. 21
  18. 20
  19. 20
  20. 14
  21. 21
  22. 15
  23. 21
  24. 25

Example C

[latex]\begin{array}[t]{rr}&696\\-&251\\ \hline \\ \end{array}[/latex]

Step 1: Subtract the ones from the ones.

[latex]6 \text{ ones }- 1 \text{ one }= 5 \text{ ones}[/latex]

[latex]\begin{array}[t]{rr}&696\\-&251\\ \hline &5 \\ \end{array}[/latex]

Step 2: Subtract the tens from the tens.

[latex]9 \text{ tens }- 5 \text{ tens }= 4 \text{ tens}[/latex]

[latex]\begin{array}[t]{rr}& 696\\-&251\\ \hline &45 \\ \end{array}[/latex]

Step 3: Subtract the hundreds from the hundreds.

[latex]6 \text{ hundreds }- 2 \text{ hundreds }= 4 \text{ hundreds}[/latex]

[latex]\begin{array}[t]{rr}& 696\\-&251\\ \hline &445 \\ \end{array}[/latex]

The difference between 696 and 251 is 445.

Exercise 3

Find the differences.

  1. [latex]\begin{array}[t]{rr}&995\\-&452\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&877\\-&342\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&788\\-&615\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&987\\-&243\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&549\\-&131\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&806\\-&204\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&953\\-&603\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&569\\-&403\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&874\\-&650\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&269\\-&159\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&485\\-&203\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&381\\-&270\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&796\\-&172\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&864\\-&531\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&963\\-&810\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&957\\-&342\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&837\\-&410\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&528\\-&208\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&549\\-&120\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&627\\-&523\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&849\\-&246\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&175\\-&163\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}&937\\-&224\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}&875\\-&252\\ \hline \\ \end{array}[/latex]

Exercise 3 Answers

  1. 543
  2. 535
  3. 173
  4. 744
  5. 418
  6. 602
  7. 350
  8. 166
  9. 224
  10. 110
  11. 282
  12. 111
  13. 624
  14. 333
  15. 153
  16. 615
  17. 427
  18. 320
  19. 429
  20. 104
  21. 603
  22. 12
  23. 713
  24. 623

Exercise 4

Find the differences.

  1. [latex]\begin{array}[t]{rr}&543\\-&132\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&752\\-&150\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 328\\-&115\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 758\\-&341\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&587\\-&425\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&857\\-&143\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&545\\-&302\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&466\\-&115\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&964\\-&231\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&679\\-&424\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&757\\-&136\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&467\\-&132\\ \hline \\ \end{array}[/latex]

Exercise 4 Answers

  1. 411
  2. 602
  3. 213
  4. 417
  5. 162
  6. 714
  7. 243
  8. 351
  9. 733
  10. 255
  11. 621
  12. 335

Example D

[latex]\begin{array}[t]{rr}&4\, 628 \\− &2\, 604\\ \hline \\ \end{array}[/latex]

Step 1: Subtract the ones from the ones.

[latex]8 \text{ ones }- 4 \text{ ones }= 4 \text{ ones}[/latex]

[latex]\begin{array}[t]{rr}&4\, 628 \\− &2\, 604\\ \hline& 4 \\ \end{array}[/latex]

Step 2: Subtract the tens from the tens.

[latex]2 \text{ tens }- 0 \text{ tens }= 2 \text{ tens}[/latex]

[latex]\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &24 \\ \end{array}[/latex]

Step 3: Subtract the hundreds from the hundreds.

[latex]6 \text{ hundreds }- 6 \text{ hundreds }= 0 \text{ hundreds}[/latex]

[latex]\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &024 \\ \end{array}[/latex]

The 0 must be placed in the answer to hold the hundreds place.

Step 4: Subtract the thousands from the thousands.

[latex]4 \text{ thousands }- 2 \text{ thousands }= 2 \text{ thousands}[/latex]

[latex]\begin{array}[t]{rr}&4\, 628 \\−& 2\, 604\\ \hline &2\,024 \\ \end{array}[/latex]

The difference between 4628 and 2604 is 2024.

Example E

[latex]\begin{array}[t]{rr}&79\, 486 \\−& 42\, 104\\ \hline \\ \end{array}[/latex]

Step 1: Subtract the ones from the ones.

[latex]6 \text{ ones }- 4 \text{ ones }= 2 \text{ ones}[/latex]

[latex]\begin{array}[t]{rr}&79\, 486 \\−& 42\, 104\\ \hline& 2 \\ \end{array}[/latex]

Step 2: Subtract the tens from the tens.

[latex]8 \text{ tens }- 0 \text{ tens }= 8 \text{ tens}[/latex]

[latex]\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &82 \\ \end{array}[/latex]

Step 3: Subtract the hundreds from the hundreds.

[latex]4 \text{ hundreds }- 1 \text{ hundreds }= 3 \text{ hundreds}[/latex]

[latex]\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &382 \\ \end{array}[/latex]

Step 4: Subtract the thousands from the thousands.

[latex]9 \text{ thousands }- 2 \text{ thousands }= 7 \text{ thousands}[/latex]

[latex]\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline& 7\,382 \\ \end{array}[/latex]

Step 5: Subtract the ten thousands from the ten thousands.

[latex]7 \text{ ten thousands }- 4 \text{ ten thousands }= 3 \text{ ten thousands}[/latex]

[latex]\begin{array}[t]{rr}&79\, 486 \\− &42\, 104\\ \hline &37\,382 \\ \end{array}[/latex]

The difference between 79486 and 42104 is 37382.

Exercise 5

Find the differences.

  1. [latex]\begin{array}[t]{rr}&8\, 646 \\-& 542\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&7\, 295 \\-& 231\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&9\, 738 \\-& 215\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&6\, 498 \\-& 253\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&3\, 674 \\-& 2\, 503\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&3 \,219 \\-& 2\, 116\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&6\, 456 \\-& 5\,\ 234\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&1\, 758 \\-& 1\, 431\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&8\, 954 \\-& 2\, 151\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&8\, 975 \\-& 4\, 732\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&7\, 296 \\-& 5\, 081\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&9\, 678 \\-& 4\, 316\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&9\, 489 \\-& 2\, 079\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&7\, 638 \\-& 6\, 218\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&4\, 759 \\-& 1\, 136\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&8\, 275 \\-& 4\, 073\\ \hline \\ \end{array}[/latex]

Exercise 5 Answers

  1. 8104
  2. 7064
  3. 9523
  4. 6245
  5. 1171
  6. 1103
  7. 1222
  8. 327
  9. 6803
  10. 4243
  11. 2215
  12. 5362
  13. 7410
  14. 1420
  15. 3623
  16. 4202

If a subtraction question is written with the numbers side by side, rewrite the question in columns. Put the ones under the ones, the tens under the tens, the hundreds under the hundreds, and so on. The first number is always the top number, and the second number is always written below the first number.

Example F

[latex]\begin{array}[t]{rr} &687\\-&52\\ \hline &635\end{array}[/latex]

Example G

[latex]\begin{array}[t]{rr}&9\,756\\-&420\\ \hline &9\, 336\end{array}[/latex]

Exercise 6

Rewrite each question in columns and find the differences.

  1. [latex]\begin{array}[t]{rr}&43\\-&21\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&84\\-&30\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&975\\-&21\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&779\\-&54\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&695\\-&173\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&863\\-&701\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&965\\-&152\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&849\\-&212\\ \hline \\ \end{array}[/latex]

Exercise 6 Answers

  1. 22
  2. 54
  3. 954
  4. 725
  5. 522
  6. 162
  7. 813
  8. 637

1.3: Practice Questions

  1. Find the differences. Check your answers.
    1. [latex]\begin{array}[t]{rr}&39\\-&15\\ \hline \\ \end{array}[/latex]
    2. [latex]\begin{array}[t]{rr}&58\\-&24\\ \hline \\ \end{array}[/latex]
    3. [latex]\begin{array}[t]{rr}&72\\-&60\\ \hline \\ \end{array}[/latex]
    4. [latex]\begin{array}[t]{rr}&49\\-&23\\ \hline \\ \end{array}[/latex]
    5. [latex]\begin{array}[t]{rr}&64\\-&10\\ \hline \\ \end{array}[/latex]
    6. [latex]\begin{array}[t]{rr}&85\\-&71\\ \hline \\ \end{array}[/latex]

     

  2. Find the differences. Check your answers.
    1. [latex]\begin{array}[t]{rr}&896\\-& 385\\ \hline \\ \end{array}[/latex]
    2. [latex]\begin{array}[t]{rr}&698\\-& 461\\ \hline \\ \end{array}[/latex]
    3. [latex]\begin{array}[t]{rr}&399\\-& 202\\ \hline \\ \end{array}[/latex]
    4. [latex]\begin{array}[t]{rr}&467\\-& 124\\ \hline \\ \end{array}[/latex]
    5. [latex]\begin{array}[t]{rr}&752\\-& 231\\ \hline \\ \end{array}[/latex]
    6. [latex]\begin{array}[t]{rr}&497\\-& 341\\ \hline \\ \end{array}[/latex]

     

  3. Find the differences. Check your answers.
    1. [latex]\begin{array}[t]{rr}&8 \,627\\-& 323\\ \hline \\ \end{array}[/latex]
    2. [latex]\begin{array}[t]{rr}&9 \,875\\-& 9 \,251\\ \hline \\ \end{array}[/latex]
    3. [latex]\begin{array}[t]{rr}&9 \,751\\-& 7 \,340\\ \hline \\ \end{array}[/latex]
    4. [latex]\begin{array}[t]{rr}&34\, 859\\-& 1\, 336\\ \hline \\ \end{array}[/latex]
    5. [latex]\begin{array}[t]{rr}&37\, 698 \\-& 12\, 540\\ \hline \\ \end{array}[/latex]
    6. [latex]\begin{array}[t]{rr}&96 \,723\\-& 51\, 403\\ \hline \\ \end{array}[/latex]

     

  4. Subtract these numbers.
    1. [latex]85 - 61 =[/latex]
    2. [latex]724 - 13 =[/latex]
    3. [latex]879  - 152 =[/latex]
    4. [latex]4\,957 - 821 =[/latex]
    5. [latex]94\,658 - 12\,307 =[/latex]
    6. [latex]89\,653 - 27\,450 =[/latex]

1.3: Practice Answers

  1. Find the differences.
    1. 24
    2. 34
    3. 12
    4. 26
    5. 54
    6. 14

     

  2. Find the differences.
    1. 511
    2. 237
    3. 197
    4. 343
    5. 521
    6. 156

     

  3. Find the differences.
    1. 8304
    2. 624
    3. 2411
    4. 33523
    5. 25158
    6. 45320

     

  4. Subtract these numbers.
    1. 24
    2. 711
    3. 727
    4. 4136
    5. 82351
    6. 62203

Attribution

This chapter has been adapted from Topic B: Subtraction of Larger Numbers in Adult Literacy Fundamental Mathematics: Book 2 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard, which is under a CC BY 4.0 license.

License

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Intermediate PreAlgebra: Building Success Copyright © 2024 by Kim Tamblyn, TRU Open Press is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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