PARTIAL-DIFFERENCES ALGORITHM

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PARTIAL-DIFFERENCES ALGORITHM FOR SUBTRACTION
Created by Paula Cantera Elk Neck Elementary
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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.
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Lets review some vocabulary
456 - 342
minuend
subtrahend
114
difference
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HELPFUL HINT
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.
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Lets give one a try!
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Lets write the minuend and subtrahend in
expanded form.
496
400 90 6
- 231
200 30 1
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Remember--- subtract from left to right, one
place-value at a time.
496
400
90
6
- 231
1
200
30
8
496
400
90
6
- 231
1
200
30
-200)
200
Subtract the hundreds.
(400
9
496
400
90
6
- 231
1
200
30
-200)
200
Subtract the hundreds.
(400
60
(90
- 30)
Subtract the tens.
10
496
400
90
6
- 231
1
200
30
-200)
200
Subtract the hundreds.
(400
60
Subtract the tens.
(90
- 30)
5
(6
- 1)
Subtract the ones.
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496
400
90
6
- 231
1
200
30
-200)
200
Subtract the hundreds.
(400
60
Subtract the tens.
(90
- 30)
5

(6
- 1)
Subtract the ones.
265
Now, add the partial sums. (200605)
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Lets try another one!
A little bit harder this time!
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7,513
500
10
3
7,000
- 2,442
400
40
2
2,000
-2000)
5,000
Subtract the thousands.
(7,000
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(500
7,513
500
10
3
7,000
- 2,442
400
40
2
2,000
- 2000)
5,000
(7,000
Subtract the thousands.
100
- 400)
Subtract the hundreds.
15
- 30
7,513
500
10
3
7,000
- 2,442
400
40
2
2,000
- 2000)
5,000
(7,000
Subtract the thousands.
100
- 400)
(500
Subtract the hundreds.
- 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.
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- 30
7,513
500
10
3
7,000
- 2,442
400
40
2
2,000
- 2000)
5,000
(7,000
Subtract the thousands.
100
- 400)
(500
Subtract the hundreds.
- 40)
(10
Subtract the tens.
1
Subtract the ones.
(3
- 2)
17
- 30
7,513
500
10
3
7,000
- 2,442
400
40
2
2,000
- 2000)
5,000
(7,000
Subtract the thousands.
100
- 400)
(500
Subtract the hundreds.
- 40)
(10
Subtract the tens.

1
Subtract the ones.
(3
- 2)
5,071
Now, add the partial sums. (5,000 100 - 30
1) Remember the negative symbol
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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!
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Give the Partial-Differences Algorithm a try.
You might find that it makes subtraction of
mult-digit numbers easier for you!