# Prealgebra for Two-Year Colleges/Appendix (procedures)/Subtracting whole numbers with borrowing

Addition operations are denoted by the + sign and the - (-)= +. The addition operator (plus sign) will take any two numbers, called addends, as operands to work on. The result is called the sum of the two numbers.

The operation of addition is commutative. This means that the addition of two numbers will give the same sum regardless of the order in which the numbers are added.

Example:

• ${\displaystyle 7+5=12}$ and ${\displaystyle 5+7=12}$
• ${\displaystyle 3+2+4=9}$ and ${\displaystyle 4+3+2=9}$

To add vertically, stack the numbers on top.

``` 52
19
----------------
```

Now add the numbers in the first or right column. If you get a number with tens in it, put what's in the tens place on the tens place in the problem. You should have:

``` 1
52
19
----------------
1
```

``` 1
52
19
----------------
71
```

Repeat in a similar fashion for each additional column (hundreds, thousands, etc.)until you finish the problem.

### Exercises

In Exercises 1–25, find the sum.

• 1. ${\displaystyle 5+3}$
• 2. ${\displaystyle 8+7}$
• 3. ${\displaystyle 9+2}$
• 4. ${\displaystyle 6+3}$
• 5. ${\displaystyle 1+4}$
• 6. ${\displaystyle 2+17}$
• 7. ${\displaystyle 12+11}$
• 8. ${\displaystyle 53+8}$
• 9. ${\displaystyle 41+9}$
• 10. ${\displaystyle 84+12}$
• 11. ${\displaystyle 16+17}$
• 12. ${\displaystyle 7,576+5,345}$
• 13. ${\displaystyle 2,345+3,245}$
• 14. ${\displaystyle 8,952+9,423}$
• 15. ${\displaystyle 2,783+2,389}$
• 16. ${\displaystyle 189,583+1,574,822}$
• 17. ${\displaystyle 1.5+2.7}$
• 18. ${\displaystyle 5.4+3.9}$
• 19. ${\displaystyle 8.3+9.2}$
• 20. ${\displaystyle 2.23+4.89}$
• 21. ${\displaystyle 534.4+34.675}$
• 22. ${\displaystyle 348.904+23,498.2}$
• 23. ${\displaystyle 1.673+48,210.38}$
• 24. ${\displaystyle 10.4823+94.29478}$
• 25. ${\displaystyle 128.52+2,070.24}$

• 1. ${\displaystyle 8}$
• 2. ${\displaystyle 15}$
• 3. ${\displaystyle 11}$
• 4. ${\displaystyle 9}$
• 5. ${\displaystyle 5}$
• 6. ${\displaystyle 19}$
• 7. ${\displaystyle 23}$
• 8. ${\displaystyle 61}$
• 9. ${\displaystyle 50}$
• 10. ${\displaystyle 96}$
• 11. ${\displaystyle 33}$
• 12. ${\displaystyle 12,921}$
• 13. ${\displaystyle 5,590}$
• 14. ${\displaystyle 18,375}$
• 15. ${\displaystyle 5,172}$
• 16. ${\displaystyle 1,764,405}$
• 17. ${\displaystyle 4.2}$
• 18. ${\displaystyle 9.3}$
• 19. ${\displaystyle 17.5}$
• 20. ${\displaystyle 7.12}$
• 21. ${\displaystyle 569.075}$
• 22. ${\displaystyle 23,847.104}$
• 23. ${\displaystyle 48,212.053}$
• 24. ${\displaystyle 104.77708}$
• 25. ${\displaystyle 2,198.76}$

## Subtraction

Subtraction, as you probably also have seen, uses the minus (-) sign. The generic subtraction operator will take any two numbers as operands. The result is called the difference of the two numbers.

Subtraction is not a commutative operation. Changing the order of the operands will likely give a different (not the same) result.

Example:

• ${\displaystyle 7-5=2}$ and ${\displaystyle 5-7=-2}$
• ${\displaystyle 3-2-4=-3}$ and ${\displaystyle 4-3-2=-1}$

### Exercises

In Exercises 26–50, find the difference.

• 26. ${\displaystyle 5-3}$
• 27. ${\displaystyle 8-7}$
• 28. ${\displaystyle 9-2}$
• 29. ${\displaystyle 6-3}$
• 30. ${\displaystyle 1-4}$
• 31. ${\displaystyle 2-17}$
• 32. ${\displaystyle 12-11}$
• 33. ${\displaystyle 53-8}$
• 34. ${\displaystyle 41-9}$
• 35. ${\displaystyle 84-12}$
• 36. ${\displaystyle 16-17}$
• 37. ${\displaystyle 7,576-5,345}$
• 38. ${\displaystyle 2,345-3,245}$
• 39. ${\displaystyle 8,952-9,423}$
• 40. ${\displaystyle 2,783-2,389}$
• 41. ${\displaystyle 1,574,822-189,583}$
• 42. ${\displaystyle 2.7-1.5}$
• 43. ${\displaystyle 5.4-3.9}$
• 44. ${\displaystyle 8.3-9.2}$
• 45. ${\displaystyle 2.23-4.89}$
• 46. ${\displaystyle 10.38-1.673}$
• 47. ${\displaystyle 534.4-34.675}$
• 48. ${\displaystyle 348.904-23,498.2}$
• 49. ${\displaystyle 10.4823-94.29478}$
• 50. ${\displaystyle 2,070.24-128.52}$

• 26. ${\displaystyle 2}$
• 27. ${\displaystyle 1}$
• 28. ${\displaystyle 7}$
• 29. ${\displaystyle 3}$
• 30. ${\displaystyle -3}$
• 31. ${\displaystyle -15}$
• 32. ${\displaystyle 1}$
• 33. ${\displaystyle 45}$
• 34. ${\displaystyle 32}$
• 35. ${\displaystyle 72}$
• 36. ${\displaystyle -1}$
• 37. ${\displaystyle 2,231}$
• 38. ${\displaystyle -900}$
• 39. ${\displaystyle -471}$
• 40. ${\displaystyle 394}$
• 41. ${\displaystyle 1,385,239}$
• 42. ${\displaystyle 1.2}$
• 43. ${\displaystyle 1.5}$
• 44. ${\displaystyle -0.9}$
• 45. ${\displaystyle -2.66}$
• 46. ${\displaystyle 8.707}$
• 47. ${\displaystyle 499.725}$
• 48. ${\displaystyle -23,149.296}$
• 49. ${\displaystyle -83.81248}$
• 50. ${\displaystyle 1,941.72}$