created by paula cantera elk neck elementary. when using this algorithm, you will first calculate...
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![Page 1: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/1.jpg)
Created by Paula Cantera
Elk Neck Elementary
![Page 2: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/2.jpg)
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 differencesto find the total difference.
![Page 3: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/3.jpg)
Let’s review some vocabulary:
minuend
subtrahend
difference
456- 342
114
![Page 4: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/4.jpg)
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***
![Page 5: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/5.jpg)
Let’s give one a try!
![Page 6: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/6.jpg)
Let’s write the minuend and subtrahend in expanded form.
496- 231
400 + 90 + 6
200 + 30 + 1
![Page 7: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/7.jpg)
Remember--- subtract from left to right, one place-value at a time.
496- 231
400 + 90 + 6
200 + 30 + 1
![Page 8: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/8.jpg)
496- 231
400 + 90 + 6
200 + 30 + 1
Subtract the hundreds. (400 -200) 200
![Page 9: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/9.jpg)
496- 231
400 + 90 + 6
200 + 30 + 1
Subtract the hundreds. (400 -200) 200Subtract the tens. (90 - 30) 60
![Page 10: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/10.jpg)
496- 231
400 + 90 + 6
200 + 30 + 1
Subtract the hundreds. (400 -200) 200Subtract the tens. (90 - 30) 60Subtract the ones. (6 - 1) 5
![Page 11: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/11.jpg)
496- 231
400 + 90 + 6
200 + 30 + 1
Subtract the hundreds. (400 -200) 200Subtract the tens. (90 - 30) 60Subtract the ones. (6 - 1) 5+
Now, add the partial sums. (200+60+5)
265
![Page 12: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/12.jpg)
Let’s try another one!
A little bit harder this time!
![Page 13: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/13.jpg)
7,513
- 2,442+ 500 + 10+ 3
+ 400 + 40+ 2
Subtract the thousands.(7,000 -2000) 5,000
7,000
2,000
![Page 14: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/14.jpg)
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
![Page 15: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/15.jpg)
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)(10Subtract 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 whenadding up your partial differences.
![Page 16: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/16.jpg)
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)(10Subtract the tens.
Subtract the ones. (3 - 2) 1
![Page 17: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/17.jpg)
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)(10Subtract the tens.
Subtract the ones. (3 - 2) 1+5,071Now, add the partial sums.
(5,000 + 100 - 30+ 1)* Remember the negative symbol
![Page 18: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/18.jpg)
Partial differences are much easier to work with and you willfeel empowered when you discover that, with practice,you just might be able to use this algorithm to subtract numbersmentally!
![Page 19: Created by Paula Cantera Elk Neck Elementary. When using this algorithm, you will first calculate partial differences, subtracting from left to right,](https://reader036.vdocuments.us/reader036/viewer/2022083005/56649f265503460f94c3ca8c/html5/thumbnails/19.jpg)
Give the Partial-DifferencesAlgorithm a try.
You might find that it makessubtraction of mult-digit numberseasier for you!