Created by Paula Cantera

Elk Neck Elementary

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.

Let’s review some vocabulary:

minuend

subtrahend

difference

456- 342

114

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***

Let’s give one a try!

Let’s write the minuend and subtrahend in expanded form.

496- 231

400 + 90 + 6

200 + 30 + 1

Remember--- subtract from left to right, one place-value at a time.

496- 231

400 + 90 + 6

200 + 30 + 1

496- 231

400 + 90 + 6

200 + 30 + 1

Subtract the hundreds. (400 -200) 200

496- 231

400 + 90 + 6

200 + 30 + 1

Subtract the hundreds. (400 -200) 200Subtract the tens. (90 - 30) 60

496- 231

400 + 90 + 6

200 + 30 + 1

Subtract the hundreds. (400 -200) 200Subtract the tens. (90 - 30) 60Subtract the ones. (6 - 1) 5

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

Let’s try another one!

A little bit harder this time!

7,513

- 2,442+ 500 + 10+ 3

+ 400 + 40+ 2

Subtract the thousands.(7,000 -2000) 5,000

7,000

2,000

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

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.

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

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

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!

Give the Partial-DifferencesAlgorithm a try.

You might find that it makessubtraction of mult-digit numberseasier for you!