1.4: Subtraction With Borrowing

When you subtract, the digit you are taking away may be larger than the top digit in that same column. You must borrow from the column on the left.

First, let’s look at two examples using the place value shapes.

Example A

[latex]243-128[/latex]

 

2 hundreds, 4 tens and 3 ones
Figure 1.4.1

Step 1: 3 ones − 8 ones cannot be done

Borrow one ten and rename it as ten ones.

Add the ten ones to the three ones.

 

2 hundreds 4 tens and 13 ones
Figure 1.4.2

Now you can subtract:

[latex]13 \text{ ones }- 8 \text{ ones }= 5 \text{ ones}[/latex]

Step 2: Subtract the tens.

[latex]3 \text{ tens }- 2 \text{ tens }= 1 \text{ ten}[/latex]

Step 3: Subtract the hundreds.

[latex]2 \text{ hundreds }- 1 \text{ hundred }= 1 \text{ hundred}[/latex]

Here is the question using numerals:

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{13}{\cancel{3}} \\ -&1\,\,2\,\,8 \\ \hline &1\,\,1\,\,5 \\\end{array}[/latex]

Example B

[latex]350-124[/latex]

 

3 hundreds and 5 tens
Figure 1.4.3

Step 1: 0 ones − 4 ones cannot be done

Borrow one ten and rename it as ten ones.

 

3 hundreds 4 tens and 10 ones
Figure 1.4.4

[latex]10 \text{ ones }-4 \text{ ones }= 6 \text{ ones}[/latex]

Step 2:

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

Step 3:

[latex]3 \text{ hundreds }- 1 \text{ hundred }= 2 \text{ hundreds}[/latex]

This is how the question looks using numerals:

[latex]\require{cancel}\begin{array}[t]{rr}&3\overset{4}{\cancel{5}}\overset{10}{\cancel{0}} \\ -&1\,\,2\,\,4 \\ \hline &2\,\,2\,\,6 \\\end{array}[/latex]

Exercise 1

You may need to borrow 1 ten and rename it as 10 ones to do these subtractions.

Examples:

[latex]\begin{array}[t]{rr}&53\\-&16\\ \hline &37 \end{array} \ \begin{array}[t]{rr}&82\\-&45\\ \hline&37 \end{array}[/latex]

 

  1. [latex]\begin{array}[t]{rr}&37\\-&9\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&28\\-&4\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&63\\-&7\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&54\\-&5\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&25\\-&7\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&84\\-&6\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&45\\-&15\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&40\\-&38\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&45\\-&20\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&70\\-&21\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&645\\-&26\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&258\\-&14\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&786\\-&47\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&895\\-&29\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&747\\-&109\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&642\\-&420\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&438\\-&215\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&953\\-&838\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&532\\-&314\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&795\\-&238\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&956\\-&348\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&574\\-&218\\ \hline \\ \end{array}[/latex]

Exercise 1 Answers

  1. 28
  2. 24
  3. 56
  4. 49
  5. 18
  6. 78
  7. 30
  8. 2
  9. 25
  10. 49
  11. 619
  12. 244
  13. 739
  14. 866
  15. 638
  16. 222
  17. 223
  18. 115
  19. 218
  20. 557
  21. 608
  22. 356

To check your subtraction, add the answer (the difference) to the number you took away. If your subtracting was correct, the result of the adding will equal the number you started with in the subtraction question.

Example C

Difference:

[latex]\begin{array}[t]{r}726\\-317\\ \hline 409\end{array}[/latex]

Check: 409 to 317

[latex]\begin{array}[t]{r} 409\\+317\\ \hline 726\end{array}[/latex]

Exercise 2

You may need to borrow 1 ten and rename it as 10 ones to do these subtractions. Use the method for checking your answer beside each question.

Example:     [latex]\begin{array}[t]{rr}&42\\-&5\\ \hline &37 \end{array}[/latex] Check: [latex]\begin{array}[t]{rr}&37\\+&5\\ \hline &42 \end{array}[/latex]

 

  1. [latex]\begin{array}[t]{rr}&83\\-&6\\ \hline \\ \end{array}[/latex] Check:
  2. [latex]\begin{array}[t]{rr}&91\\-&7\\ \hline \\ \end{array}[/latex] Check:
  3. [latex]\begin{array}[t]{rr}&70\\-&4\\ \hline \\ \end{array}[/latex] check:
  4. [latex]\begin{array}[t]{rr}&64\\-&37\\ \hline \\ \end{array}[/latex] Check:
  5. [latex]\begin{array}[t]{rr}&32\\-&16\\ \hline \\ \end{array}[/latex] Check:
  6. [latex]\begin{array}[t]{rr}&65\\-&16\\ \hline \\ \end{array}[/latex] Check:
  7. [latex]\begin{array}[t]{rr}&98\\-&39\\ \hline \\ \end{array}[/latex] Check:
  8. [latex]\begin{array}[t]{rr}&775\\-&49\\ \hline \\ \end{array}[/latex] check:
  9. [latex]\begin{array}[t]{rr}&974\\-&26\\ \hline \\ \end{array}[/latex] Check:
  10. [latex]\begin{array}[t]{rr}&483\\-&75\\ \hline \\ \end{array}[/latex] Check:
  11. [latex]\begin{array}[t]{rr}&896\\-&57\\ \hline \\ \end{array}[/latex] Check:
  12. [latex]\begin{array}[t]{rr}&785\\-&627\\ \hline \\ \end{array}[/latex] Check:
  13. [latex]\begin{array}[t]{rr}&961\\-&543\\ \hline \\ \end{array}[/latex] Check:
  14. [latex]\begin{array}[t]{rr}&941\\-&319\\ \hline \\ \end{array}[/latex] Check:
  15. [latex]\begin{array}[t]{rr}&850\\-&434\\ \hline \\ \end{array}[/latex] Check:

Exercise 2 Answers

  1. 77
  2. 84
  3. 66
  4. 27
  5. 16
  6. 49
  7. 59
  8. 726
  9. 948
  10. 408
  11. 839
  12. 158
  13. 418
  14. 622
  15. 416

Use this same method of borrowing when you subtract the hundreds, thousands, ten thousands, and so on. Look at the place value shapes as you work through these examples.

Example D

[latex]225-162[/latex]

 

2 hundreds 2 tens and 5 ones
Figure 1.4.5

Step 1:

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

Step 2: 2 tens − 6 tens (can’t be done)

Borrow one hundred and rename it as 10 tens.

Add the 10 tens to the 2 tens.

 

1 hundred, 12 tens and 3 ones left
Figure 1.4.6

[latex]12 \text{ tens }- 6 \text{ tens }= 6 \text{ tens}[/latex]

 Step 3:

[latex]1 \text{ hundred }– 1 \text{ hundred }= 0 \text{ hundreds}[/latex]

Note: The 0 in the hundreds is not needed in the answer (063) because it is the first digit and does not have to hold the place.

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{1}{\cancel{2}}\overset{12}{\cancel{2}}5 \\ -&1\,\,6\,\,2 \\ \hline &6\,\,3 \\\end{array}[/latex]

Example E

[latex]331-145[/latex]

Step 1: 1 one − 5 ones (can’t be done)

Borrow 1 ten and rename it as 10 ones, which you add onto the 1 one.

 

3 hundreds 3 tens and 1 one
Figure 1.4.7

[latex]11 \text{ ones }- 5 \text{ ones }= 6 \text{ ones}[/latex]

Step 2: 2 tens − 4 tens (can’t be done)

Borrow one hundred and rename it as 10 tens, which you add onto the 2 tens.

 

3 hundreds 2 tens and 11 ones
Figure 1.4.8

Step 3:

[latex]2 \text{ hundreds }- 1 \text{ hundred }= 1 \text{ hundred}[/latex]

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{2}{\cancel{3}}\overset{\overset{12}{\cancel{2}}}{\cancel{3}}\overset{11}{\cancel{1}} \\ -&1\,\,4\,\,5\, \\ \hline &1\,\,8\,\,6\, \\\end{array}[/latex]

Check:

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{1}{1}\overset{1}{8}6 \\ +&145 \\ \hline &331 \\\end{array}[/latex]

Exercise 3

Subtract the following.

Examples:

[latex]\begin{array}[t]{rr}& 286\\-&138\\ \hline& 148 \end{array} \ \begin{array}[t]{rr}& 481\\-&225 \\ \hline& 256 \end{array}[/latex]

 

  1. [latex]\begin{array}[t]{rr}& 390\\-&135\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 390\\-&135\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 734\\-&582\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 281\\-&175\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 925\\-&68\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 260\\-&154\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 379\\-&235\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 532\\-&290\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 82\\-&79\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 262\\-&39\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}& 427\\-&183\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}& 452\\-&173\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}& 692\\-&473\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}& 634\\-&273\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}& 465\\-&374\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}& 785\\-&147\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}& 937\\-&258\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}& 946\\-&463\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}& 734\\-&208\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}& 563\\-&154\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}& 782\\-&254\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}& 621\\-&442\\ \hline \\ \end{array}[/latex]

Exercise 3 Answers

  1. 255
  2. 152
  3. 152
  4. 106
  5. 857
  6. 106
  7. 144
  8. 242
  9. 3
  10. 223
  11. 244
  12. 279
  13. 219
  14. 361
  15. 91
  16. 638
  17. 679
  18. 483
  19. 526
  20. 409
  21. 528
  22. 179

Exercise 4

Subtract the following.

  1. [latex]\begin{array}[t]{rr}&776\\-&382\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&426\\-&327\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&957\\-&234\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 845\\-&416\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&967\\-&173\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&406\\-&257\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&857\\-&143\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&757\\-&129\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&567\\-&182\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&952\\-&278\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&863\\-&389\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&689\\-&434\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&754\\-&526\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&572\\-&493\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&714\\-&588\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&795\\-&497\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&390\\-&256\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&745\\-&649\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&639\\-&484\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&811\\-&173\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&678\\-&290\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&740\\-&272\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}&983\\-&876\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}&839\\-&653\\ \hline \\ \end{array}[/latex]

Exercise 4 Answers

  1. 394
  2. 109
  3. 723
  4. 429
  5. 794
  6. 149
  7. 714
  8. 628
  9. 385
  10. 674
  11. 474
  12. 255
  13. 228
  14. 79
  15. 126
  16. 298
  17. 134
  18. 96
  19. 155
  20. 638
  21. 388
  22. 468
  23. 107
  24. 186

Now, work through this example, where you must also rename one thousand as ten hundreds to do the subtraction.

Example F

[latex]3\,245-1\,678[/latex]

Step 1: Subtract the ones.

[latex]\require{cancel}\begin{array}[t]{rr}&3\,\,2\overset{3}{\cancel{4}}\overset{15}{\cancel{5}} \\ +&1\,\,6\,\,7\,\,8\, \\ \hline &7\, \\\end{array}[/latex]

Step 2: Subtract the tens.

[latex]\require{cancel}\begin{array}[t]{rr}&3\overset{1}{\cancel{2}}\overset{\overset{13}{\cancel{3}}}{\cancel{4}}\overset{15}{\cancel{5}} \\ +&1\,\,6\,\,7\,\,8\, \\ \hline &6\,\,7\, \\\end{array}[/latex]

Step 3: Subtract the hundreds.

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{2}{\cancel{3}}\overset{\overset{11}{\cancel{1}}}{\cancel{2}}\overset{\overset{13}{\cancel{3}}}{\cancel{4}}\overset{15}{\cancel{5}} \\ -&1\,\,6\,\,7\,\,8\, \\ \hline &5\,\,6\,\,7\, \\ \end{array}[/latex]

Step 4: Subtract the thousands.

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{2}{\cancel{3}}\overset{\overset{11}{\cancel{1}}}{\cancel{2}}\overset{\overset{13}{\cancel{3}}}{\cancel{4}}\overset{15}{\cancel{5}} \\ -&1\,\,6\,\,7\,\,8\, \\ \hline &1\,\,5\,\,6\,\,7\, \\ \end{array}[/latex]

Check:

[latex]\require{cancel}\begin{array}[t]{rr}&\overset{1}{1}\,\overset{1}{5}\overset{1}{6}7 \\ +&1\,678 \\ \hline &3\,245\\ \end{array}[/latex]

Exercise 5

Find the differences.

  1. [latex]\begin{array}[t]{rr}&4\, 295\\-& 724\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}&8\, 281 \\-& 470\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}&5\, 564 \\-& 644\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}&6\, 382\\-& 882\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}&8\, 513 \\-& 829\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}&3\, 527 \\-& 758\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}&3\, 154\\-& 205\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}&2\, 640 \\-& 834\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}&7\, 355 \\-& 4\, 038\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}&5\, 189 \\-& 2\, 348\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}&4\, 289 \\-& 2\, 534\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}&6\, 753\\-& 1\, 942\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}&8\, 684\\-& 2\, 916\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}&7\, 459 \\-& 3\, 927\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}&8\, 360\\-& 6\, 376\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}&9\, 418 \\-& 4\, 739\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}&75\, 762\\-& 9\, 351\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}&72\, 641\\-& 8\, 736\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}&16\, 793\\-& 7\, 325\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}&12\, 533\\-& 9\, 362\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}&72\, 209\\-& 9\, 786\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}&34\, 092 \\-& 4\, 538\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}&42\, 126 \\-& 24\, 762\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}&52\, 750 \\-& 14\, 789\\ \hline \\ \end{array}[/latex]

Exercise 5 Answers

  1. 3571
  2. 7811
  3. 4920
  4. 5500
  5. 7684
  6. 2769
  7. 2949
  8. 1806
  9. 3317
  10. 2841
  11. 1755
  12. 4811
  13. 5768
  14. 3532
  15. 1984
  16. 4679
  17. 66411
  18. 63905
  19. 9468
  20. 3171
  21. 62423
  22. 29554
  23. 17364
  24. 37961

Exercise 6

Find the differences.

Example:     [latex]\begin{array}[t]{rr}& 4\,262 \\-& 2\, 738 \\ \hline& 1\, 524 \end{array}[/latex]

 

  1. [latex]\begin{array}[t]{rr}& 3 \,236 \\-& 1\, 594\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 4\, 697 \\-& 3\, 268\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 8 \,321 \\-& 4\, 543\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 2\, 831 \\-& 289\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 5\, 623 \\-& 3\, 352\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 8 \,428 \\-& 6\, 309\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 9 \,629\\-& 7\, 258\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 5 \,230\\-& 2 \,456\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 3 \,682 \\-& 963\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 29\, 285 \\-& 18\, 357\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}& 43\, 325 \\-& 3\, 187\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}& 81\, 328 \\-& 22\, 595\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}& 58\, 234 \\-& 23\, 678\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}& 28\, 243\\-& 9 \,578\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}& 3\, 245 \\-& 1\, 678\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}& 6\, 254 \\-& 1 \,733\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}& 5\, 214 \\-& 1 \,783\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}& 23\, 244 \\-& 15\, 534\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}& 16\, 121 \\-& 12\, 768\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}& 53\, 507 \\-& 14 \,421\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}& 31\, 582 \\-& 14 \,413\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}& 71\, 629 \\-& 12 \,350\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}& 44\, 610 \\-& 13 \,071\\ \hline \\ \end{array}[/latex]

Exercise 6 Answers

  1. 1642
  2. 1429
  3. 3778
  4. 2542
  5. 2271
  6. 2119
  7. 2371
  8. 2774
  9. 2719
  10. 10928
  11. 40138
  12. 58733
  13. 34556
  14. 18665
  15. 1567
  16. 4521
  17. 3431
  18. 7710
  19. 3353
  20. 39086
  21. 17169
  22. 59279
  23. 31539

Zeroes in Subtracting

You will have subtraction questions with a zero in the place you want to borrow from. You have to do a double borrowing.

Look carefully at the following example.

Example G

[latex]2\,405-368[/latex]

Step 1: 5 ones – 8 ones (can’t be done)

Borrow one ten – whoops – no tens!

Borrow one hundred and rename it as 10 tens…

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{10}{\cancel{0}}5 \\ -&3\,\,6\,\,8 \\ \hline \\ \end{array}[/latex]

Step 2: Borrow a ten.

[latex]15 \text{ ones }- 8 \text{ ones }= 7 \text{ ones}[/latex]

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{10}{\cancel{0}}\overset{15}{\cancel{5}} \\ -&3\,\,6\,\,8 \\ \hline &7 \\ \end{array}[/latex]

Step 2:

[latex]9 \text{ tens }- 6 \text{ tens }= 3 \text{ tens}[/latex]

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{\overset{9}{\cancel{10}}}{\cancel{0}}\overset{15}{\cancel{5}} \\ -&3\,\,6\,\,8 \\ \hline &3\,\,7 \\ \end{array}[/latex]

Step 3:

[latex]3 \text{ hundreds }- 3 \text{ hundreds }= 0 \text{ hundreds}[/latex]

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{\overset{9}{\cancel{10}}}{\cancel{0}}\overset{15}{\cancel{5}} \\ -&3\,\,6\,\,8 \\ \hline &0\,\,3\,\,7 \\ \end{array}[/latex]

Step 4: 2 thousands − no thousands = 2 thousands

[latex]\require{cancel}\begin{array}[t]{rr}&2\overset{3}{\cancel{4}}\overset{\overset{9}{\cancel{10}}}{\cancel{0}}\overset{15}{\cancel{5}} \\ -&3\,\,6\,\,8 \\ \hline &2\,\,0\,\,3\,\,7 \\ \end{array}[/latex]

Exercise 7

Find the differences.

  1. [latex]\begin{array}[t]{rr}& 102\\-&23\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 508\\-&39\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 804\\-&37\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 607\\-&48\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 406\\-&178\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 302\\-&218\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 203\\-&157\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 601\\-&296\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 2\, 075\\-&436\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 3\, 076\\-&594\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}& 4\, 037\\-&289\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}& 6\, 032\\-&764\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}& 4\, 057 \\-& 2\, 049\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}& 6\, 035 \\-& 2\, 634\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}& 9\, 025 \\-& 4\, 603\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}& 5\, 075 \\-& 2\, 364\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}& 50\, 398\\-& 4\, 247\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}& 40\, 683 \\-& 3 \,162\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}& 50\, 216 \\-& 5 \,183\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}& 60\, 831 \\-& 7\, 081\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}& 40\, 465 \\-& 21\, 528\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}& 30 \,429 \\-& 14\, 953\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}& 70\, 543 \\-& 37\, 835\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}& 80\, 106 \\-& 47\, 297\\ \hline \\ \end{array}[/latex]

Exercise 7 Answers

  1. 79
  2. 469
  3. 767
  4. 559
  5. 228
  6. 84
  7. 46
  8. 305
  9. 1639
  10. 2482
  11. 3748
  12. 5268
  13. 2008
  14. 3401
  15. 4422
  16. 2711
  17. 46151
  18. 37521
  19. 45033
  20. 53750
  21. 18937
  22. 15476
  23. 32708
  24. 32809

Exercise 8

Find the differences.

  1. [latex]\begin{array}[t]{rr}& 400\\-&197\\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 307\\-&138\\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 800\\-&475\\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 608\\-&439\\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 307\\-&168\\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 200\\-&99\\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 400\\-&43\\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 208\\-&126\\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 3\, 000\\-& 2\, 678\\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 7\, 205 \\-& 2\, 306\\ \hline \\ \end{array}[/latex]
  11. [latex]\begin{array}[t]{rr}& 2\, 048 \\-& 281\\ \hline \\ \end{array}[/latex]
  12. [latex]\begin{array}[t]{rr}& 6\, 005\\-& 2 \,368\\ \hline \\ \end{array}[/latex]
  13. [latex]\begin{array}[t]{rr}& 5\, 000 \\-& 3 \,468\\ \hline \\ \end{array}[/latex]
  14. [latex]\begin{array}[t]{rr}& 4 \,006 \\-& 2 \,179\\ \hline \\ \end{array}[/latex]
  15. [latex]\begin{array}[t]{rr}& 3 \,007 \\-& 1 \,930\\ \hline \\ \end{array}[/latex]
  16. [latex]\begin{array}[t]{rr}& 2 \,007 \\-& 237\\ \hline \\ \end{array}[/latex]
  17. [latex]\begin{array}[t]{rr}& 43\, 004 \\-& 2 \,873\\ \hline \\ \end{array}[/latex]
  18. [latex]\begin{array}[t]{rr}& 20\, 038 \\-& 9 \,156\\ \hline \\ \end{array}[/latex]
  19. [latex]\begin{array}[t]{rr}& 60 \,125 \\-& 8 \,421\\ \hline \\ \end{array}[/latex]
  20. [latex]\begin{array}[t]{rr}& 40 \,063 \\-& 2 \,734\\ \hline \\ \end{array}[/latex]
  21. [latex]\begin{array}[t]{rr}& 70 \,059 \\-& 38 \,423\\ \hline \\ \end{array}[/latex]
  22. [latex]\begin{array}[t]{rr}& 80 \,062 \\-& 35 \,087\\ \hline \\ \end{array}[/latex]
  23. [latex]\begin{array}[t]{rr}& 90 \,035 \\-& 68 \,746\\ \hline \\ \end{array}[/latex]
  24. [latex]\begin{array}[t]{rr}& 60 \,063 \\-& 55 \,895\\ \hline \\ \end{array}[/latex]

Exercise 8 Answers

  1. 203
  2. 169
  3. 325
  4. 169
  5. 139
  6. 101
  7. 357
  8. 82
  9. 322
  10. 4899
  11. 1767
  12. 3637
  13. 1532
  14. 1827
  15. 1077
  16. 1770
  17. 40131
  18. 10882
  19. 51704
  20. 37329
  21. 31636
  22. 44975
  23. 21289
  24. 4168

If a subtraction question has 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.

Example H: 5 625 − 2 468

[latex]5\,625-2\,468[/latex]

[latex]\require{cancel}\begin{array}[t]{rr}&5\overset{5}{\cancel{6}}\overset{\overset{11}{\cancel{1}}}{\cancel{2}}\overset{15}{\cancel{5}} \\ -&2\,\,4\,\,6\,\,8\, \\ \hline &3\,\,1\,\,5\,\,7\, \\ \end{array}[/latex]

Exercise 9

Rewrite each question in columns and find the difference.

  1. [latex]\begin{array}[t]{rr}& 5\, 042 \\-& 3\, 185 \\ \hline \\ \end{array}[/latex]
  2. [latex]\begin{array}[t]{rr}& 8 \,042 \\-&6 \,368 \\ \hline \\ \end{array}[/latex]
  3. [latex]\begin{array}[t]{rr}& 2 \,630 \\-&95 \\ \hline \\ \end{array}[/latex]
  4. [latex]\begin{array}[t]{rr}& 1 \,201 \\-&159 \\ \hline \\ \end{array}[/latex]
  5. [latex]\begin{array}[t]{rr}& 34 \,582\\-& 6\, 121 \\ \hline \\ \end{array}[/latex]
  6. [latex]\begin{array}[t]{rr}& 44 \,610\\-& 4\, 527 \\ \hline \\ \end{array}[/latex]
  7. [latex]\begin{array}[t]{rr}& 54 \,507 \\-& 13\, 421 \\ \hline \\ \end{array}[/latex]
  8. [latex]\begin{array}[t]{rr}& 7 \,050 \\-& 2 \,144 \\ \hline \\ \end{array}[/latex]
  9. [latex]\begin{array}[t]{rr}& 71 \,629 \\-& 12 \,350 \\ \hline \\ \end{array}[/latex]
  10. [latex]\begin{array}[t]{rr}& 64 \,182 \\-& 28 \,934 \\ \hline \\ \end{array}[/latex]

Exercise 9 Answers

  1. 1857
  2. 1674
  3. 2535
  4. 1042
  5. 28461
  6. 40083
  7. 41086
  8. 4906
  9. 59279
  10. 35248

1.4: Practice Questions

  1. Find the differences. Check your answers using addition.
    1. [latex]\begin{array}[t]{rr}& 71\\-&32\\ \hline \\ \end{array}[/latex]
    2. [latex]\begin{array}[t]{rr}& 704\\-&325\\ \hline \\ \end{array}[/latex]
    3. [latex]\begin{array}[t]{rr}& 400\\-&208\\ \hline \\ \end{array}[/latex]
    4. [latex]\begin{array}[t]{rr}& 8\,923\\-& 3\, 061\\ \hline \\ \end{array}[/latex]
    5. [latex]\begin{array}[t]{rr}& 5\, 211\\-& 4 \,390\\ \hline \\ \end{array}[/latex]
    6. [latex]\begin{array}[t]{rr}& 8 \,204 \\-& 3 \,461\\ \hline \\ \end{array}[/latex]
    7. [latex]\begin{array}[t]{rr}& 9 \,074 \\-& 5 \,482\\ \hline \\ \end{array}[/latex]
    8. [latex]\begin{array}[t]{rr}& 8 \,092 \\-& 6 \,578\\ \hline \\ \end{array}[/latex]
    9. [latex]\begin{array}[t]{rr}& 49\, 053\\-& 8\, 954\\ \hline \\ \end{array}[/latex]
    10. [latex]\begin{array}[t]{rr}& 86 \,502 \\-& 6 \,590\\ \hline \\ \end{array}[/latex]
    11. [latex]\begin{array}[t]{rr}& 47 \,293 \\-& 26\, 349\\ \hline \\ \end{array}[/latex]
    12. [latex]\begin{array}[t]{rr}& 73 \,050 \\-& 27\, 455\\ \hline \\ \end{array}[/latex]

     

  2. Subtract.
    1. [latex]5\,302 - 3\,981 =[/latex]
    2. [latex]7\,043 - 95 =[/latex]
    3. [latex]6\,000 - 989 =[/latex]

1.4: Practice Answers

  1. Find the differences.
    1. 39
    2. 379
    3. 192
    4. 5 862
    5. 821
    6. 4743
    7. 3562
    8. 1514
    9. 40099
    10. 79912
    11. 20944
    12. 45595

     

  2. Subtract.
    1. 1321
    2. 6948
    3. 5011

Attribution

All figures in this chapter are from Topic D: Subtraction with Borrowing in Adult Literacy Fundamental Mathematics: Book 2 – 2nd Edition by Tagami & Girard (2022), via BCcampus.

This chapter has been adapted from Topic D: Subtraction with Borrowing in Adult Literacy Fundamental Mathematics: Book 2 – 2nd Edition (BCcampus) by Wendy Tagami and Liz Girard (2022), which is under a CC BY 4.0 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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