1. Created by Paula Cantera Elk Neck Elementary

2. When using this algorithm, you will first calculate partial differences, subtracting from left to right, one place-value column at a time. Next, you will add all the partial differences to find the total difference.

3. Let’s review some vocabulary: minuend subtrahend difference 456 - 342 114

4. When first starting to use this algorithm, it may help to write the minuend and subtrahend out in expanded form before you begin. This step can be eliminated as you become more comfortable with the algorithm. ***HELPFUL HINT***

5. Let’s give one a try!

6. Let’s write the minuend and subtrahend in expanded form. 496 - 231 400 + 90 + 6 200 + 30 + 1

7. Remember--- subtract from left to right, one place-value at a time. 496 - 231 400+ 90+ 6 20 0 + 30 + 1

8. 496 - 231 400+ 90+ 6 20 0 + 30 + 1 Subtract the hundreds. (400 -200) 20 0

9. 496 - 231 400+ 90+ 6 20 0 + 30 + 1 Subtract the hundreds.(400 -200) 20 0 Subtract the tens. (90- 30) 60

10. 496 - 231 400+ 90+ 6 20 0 + 30 + 1 Subtract the hundreds.(400 -200) 20 0 Subtract the tens.(90- 30) 60 Subtract the ones. (6- 1) 5

11. 496 - 231 400+ 90+ 6 20 0 + 30 + 1 Subtract the hundreds.(400 -200) 20 0 Subtract the tens.(90- 30) 60 Subtract the ones. (6- 1) 5+ Now, add the partial sums. (200+60+5) 265

12. Let’s try another one! A little bit harder this time!

13. 7,513 - 2,442 + 500+ 10+ 3 + 400+ 40+ 2 Subtract the thousands. (7,000 -2000) 5,000 7,000 2,000

14. 7,513 - 2,442 + 500+ 10+ 3 + 400+ 40+ 2 Subtract the thousands. (7,000 - 2000) 5,000 7,000 2,000 Subtract the hundreds. (500 - 400) 100

15. 7,513 - 2,442 + 500+ 10+ 3 + 400+ 40+ 2 Subtract the thousands. (7,000 - 2000) 5,000 7,000 2,000 Subtract the hundreds. - 30 - 400) 100 (500 - 40)(10 Subtract the tens. Note the negative symbol!! Since you normally would regroup in this instance, you will record the partial difference as a negative number and subtract it rather than add it when adding up your partial differences.

16. 7,513 - 2,442 + 500+ 10+ 3 + 400+ 40+ 2 Subtract the thousands. (7,000 - 2000) 5,000 7,000 2,000 Subtract the hundreds. - 30 - 400) 100 (500 - 40)(10 Subtract the tens. Subtract the ones. (3- 2) 1

17. 7,513 - 2,442 + 500+ 10+ 3 + 400+ 40+ 2 Subtract the thousands. (7,000 - 2000) 5,000 7,000 2,000 Subtract the hundreds. - 30 - 400) 100 (500 - 40)(10 Subtract the tens. Subtract the ones.(3- 2) 1 + 5,071 Now, add the partial sums. (5,000 + 100 - 30+ 1) * Remember the negative symbol

18. Partial differences are much easier to work with and you will feel empowered when you discover that, with practice, you just might be able to use this algorithm to subtract numbers mentally!

19. Give the Partial-Differences Algorithm a try. You might find that it makes subtraction of mult-digit numbers easier for you!