Prealgebra for Two-Year Colleges/Appendix (procedures)/Adding whole numbers with carrying

Addition
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:
 * $$7 + 5 = 12$$ and $$5 + 7 = 12$$


 * $$3 + 2 + 4 = 9$$ and $$4 + 3 + 2 = 9$$

Vertical Addition
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

Add the tens column now.

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

Answers

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

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:
 * $$7 - 5 = 2$$ and $$5 - 7 = -2$$


 * $$3 - 2 - 4 = -3$$ and $$4 - 3 - 2 = -1$$

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

Answers

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