Types of Subtraction

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Types of Subtraction
Click on the underlined link you wish to follow.

• U.S. Traditional Subtraction
• Trade- First Subtraction
• Counting-Up Subtraction
• European Subtraction
• Left-to-Right Subtraction
• Partial-Differences Subtraction

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U. S. Traditional
Start on the Right Side 5,
3 4 2 1. When the top number in
a column is larger than - 2 7
9 6 the bottom number, you need
to borrow 1 unit 6 from the
place value to the left. 2. Subtract
that column. 5, 3 4 2 3.
Continue on to the next column. - 2
7 9 6 2, 5 9
6
1
12
13
4
1
3
Trade- First

• This algorithm is like the U.S. traditional form.
  
• Check all columns and trade as needed so that the
  top number in each place is as large or larger
  than the bottom number.
• Work right to left when trading. (you can go left
  to right but the first way is more efficient.
• Subtract column by column in any order.
• Drawing vertical lines between columns can be
  helpful.

• 9, 0 6 2
• 4, 7 4 8
• 8 10 5 12
• 9, 0 6 2
• - 4, 7 3 8
• 4, 3 2 4

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Counting- Up
Solve 932- 356 by counting up. 3 5
6 4 Count to the nearest
10 3 6 0 4 0
Count to the nearest 100 4 0 0
5 0 0 Count to the largest possible
100 9 0 0 3 2
Count to the largest number Then add 4
So . . . 4 0 9 3 2
5 0 0 - 3 5 6
3 2 5 7 6
5 7 6

• This method is similar to what cashiers do when
  they give change.
• Keep a running total of the amounts counted up
  and then totals all of the count-up amounts to
  find the differences.
• This method is good for mental math. It helps to
  start with larger place values.

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European Subtraction
6 2 3 - 3 4 5
13 6 2 3 -
3 14 5 14 1 4 5
8 12 13 14
10 40 50 6 2 3
- 1 3 14 5 13 100 300 400
2 7 8

• This method increases the bottom number in the
  next column to the left. It is also used in many
  other countries in the world today.
• Steps
• Increase the bottom number in the next column on
  the left.
• Make a small mark next to the number in that
  place value this compensates for adding 10 to
  the number in the column on the right.
• The mark changes the 40 to 40 10 or 50
• Continue this process to the next column

6-4 2
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Left-to-Right Subtraction
Start at the left and subtract column by
column. Subtract the 100s Subtract the
10s Subtract the 1s

• 932- 356
• 9 3 2
• 3 0 0
• 6 3 2
• - 5 0
• 5 8 2
• 6
• 5 7 6

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Partial- Differences
Steps 1. Find a partial difference for each
place value. 2. Record them and then add them to
find the total difference. 3. The only area of
confusion may be when the partial difference is
negative- make sure the student understands
negative numbers.
9 3 2 - 3 5 6 Subtract 100s
900 300 6 0 0 Subtract 10s 30 50
- 2 0 Subtract 1s 2 6
- 4 Add the partial differences 5 7
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