1A Formulas with Adding and Subtracting Whole Numbers

Look at the following formula. The first formula (P = L + W + L + W) is one we use to calculate the perimeter of a rectangle. “L” represents the length and “W” represents the width of the rectangle. For example could you calculate how many feet of fencing we will need to fence a horse pasture that is 345 feet by 461 feet? Plugging into the formula we get the following 345 + 461 + 345 + 461, but can you work this out and actually get the correct answer? A recurrent problem in science, algebra and statistics classes is that students can plug into a formula, but cannot get the correct answer due to poor arithmetic skills. In my experience of teaching, most students who fail my algebra class cannot add, subtract, multiply or divide the numbers correctly in order to get the correct answer. Hence we need to practice our arithmetic.

In this section we are looking at reviewing adding and subtracting and the concepts of carrying and borrowing. Review your addition and subtraction facts. You should be able to add numbers like 8+9 and 7+5 quickly. You should also be able to subtract 13-8 and 17-11 quickly.

Example: Add the following: 368 + 79. Remember, we need to line up the place values. 368 means 300 + 60 + 8 and 79 means 70 + 9. Adding the correct place values is critical. Whenever the sum in a place value is 10 or more we carry (re-group) to the next place value. 8+9 = 17 = 10+7 so we put the 7 and carry 1 ten to the tens place. Adding 1+6+7 = 14 tens = 1 hundred + 4 tens, so we put the 4 in the tens place and carry the 1 to the hundreds place. 1+3 = 4 hundreds. So our answer is 447.

$$\begin{array}{l}368\\ \underset{\_}{+79}\\ 447\end{array}$$

Do the following examples with your instructor. Pay close attention to carrying correctly.

Subtract the following: 513 – 268. Remember 513 means 500 + 10 + 3. We want to take away 200, take away 60 and take away 8. Problem is how do you subtract 8 from 3 or 60 from 10? The answer is borrowing and regrouping. Any time you borrow, you can add 10 to the next place value. For example if I borrow 1 hundred, I can add 10 tens to the tens place. Borrowing 1 ten, allows us to add 10 ones to the ones place. So 500 + 10 +3 becomes 400 + 100 +13. Now we subtract. 13-8 = 5. 10 tens – 6 tens = 4 tens = 40. 4 hundreds – 2 hundreds = 2 hundreds. So the answer is 245.

$$\begin{array}{l}513\\ \underset{\_}{-268}\\ 245\end{array}$$

Subtract the following 3000 – 1386. Subtracting from numbers with a lot of zeros can be a particular challenge. An easy way to do this is to think of 3000 as 300 tens. If we borrow 1 ten from 300, we are left with 299 tens. We can now add 10 to the ones place and subtract.

$$\begin{array}{rcccc}& 2& 9& 9& 10\\ & 3& 0& 0& 0\\ -& 1& 3& 8& 6\\ & 1& 6& 1& 4\end{array}$$

Do the following examples with your instructor. Pay close attention to borrowing correctly.

Practice Problems Section 1A

Perform the indicated operation for #1-42.

1. 29 + 41

   Check answer

   70

2. 16 + 39

3. 78 + 44

   Check answer

   122

4. 671 + 9

5. 302 + 58

   Check answer

   360

6. 77 + 125

7. 358 + 412

   Check answer

   770

8. 47 + 183

9. 138 + 216

   Check answer

   354

10. 4671 + 399

11. 387 + 417

    Check answer

    804

12. 985 + 977

13. 379 + 948

    Check answer

    1,327

14. 579 + 321 + 851

15. 73 + 24 + 59 + 31

    Check answer

    187

16. 997 + 842

17. 49 + 38 + 87

    Check answer

    174

18. 68,994 + 47,872

19. 6,752 + 796

    Check answer

    7,548

20. 387 + 4,529

21. 945 + 967 + 899

    Check answer

    2,811

22. 568 + 47,648

23. 785 + 721 + 357

    Check answer

    1,863

24. 95 + 29 + 56 + 33

25. 897 – 342

    Check answer

    555

26. 682 – 384

27. 1,523 – 964

    Check answer

    559

28. 2301 – 1298

29. 13,572 – 8,614

    Check answer

    4,958

30. 5,621 – 3,814

31. 700 – 246

    Check answer

    454

32. 3,000 – 875

33. 40,000 – 12,796

    Check answer

    27,204

34. 703 – 447

35. 612 – 184

    Check answer

    428

36. 1,431 – 675

37. 2101 – 1493

    Check answer

    608

38. 20,135 – 8,769

39. 3,721 – 873

    Check answer

    2,848

40. 400 – 273

41. 7,000 – 1,536

    Check answer

    5,464

42. 30,000 – 9,714

43. Profit = revenue (R) – costs (C). If a company has a revenue of $12,003 this month and their costs were $3,862, what is their profit?

    Check answer

    $8,141

44. Profit = revenue (R) – costs (C). If a company has a revenue of $85,000 this month and their costs were $24,300, what is their profit?

45. Let’s use the perimeter formula from earlier P = L + W + L + W to calculate how many feet of crown molding we must purchase for a room that is 21 feet by 15 feet?

    Check answer

    72 ft

46. Let’s use the perimeter formula from earlier P = L + W + L + W to calculate how many meters of fencing we must purchase to go around a rectangular area that is 472 meters by 326 meters.

47. Two of the tallest buildings in NY are the Empire State Building and the Chrysler Building. The Empire State Building is 1454 feet tall, while the Chrysler Building is 1046 feet tall. What is the difference between the heights of these two famous buildings?

    Check answer

    408 ft

48. Using approximate heights rounded to whole feet, the Eiffel Tower in Paris, France formerly measured 1063 feet including its antenna, and the Statue of Liberty in NY, USA measures 305 feet from the ground to the tip of its torch. Using these heights, how much taller was the Eiffel Tower than the Statue of Liberty?

49. Jeremy works as a taxi driver. On Monday, he made $148. On Tuesday he made $207. On Wednesday he made $264. How much total money did he make for the 3 days of work?

    Check answer

    $619

50. Leah sells jewelry at a booth in the mall. On Friday she sold $729 worth of jewelry. On Saturday she sold $1032 and on Sunday she sold $561. Find her total sales for the three-day period.

51. Elena has $2574 in her checking account. Elena paid her $1045 rent and her $376 car payment. How much money is now left in her checking account?

    Check answer

    $1,153

52. Tyler has $873 in his checking account. His work paid him $1379 which he deposited in his account. He then paid his water bill of $87 and his electric bill of $147. How much money does he have left in his checking account?

Adapted from Preparing for Algebra and Statistics, Third Edition, by Matt Teachout. License: CC BY 4.0. Copyright and sources.