Subtraction Lesson

Once we have memorized all of the single-digit subtraction facts, we are ready to subtract with multi-digit whole numbers. In most cases, we will perform multi-digit subtraction using a vertical format. This process is known as vertical subtraction. Vertical Subtraction will allow us to simplify a multi-digit subtraction problem into a series of smaller single-digit subtraction problems.

Vertical Subtraction - Multi-Digit Subtraction without Regrouping (Borrowing)

• Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.
• Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number
• Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.
• Place the result directly below the horizontal line
• Repeat the subtraction process in each column moving left until there are no more columns to subtract

Example 1: Find the difference.
59 - 27

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.
2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.

4. Place the result directly below the horizontal line

5. Repeat the subtraction process in each column moving left until there are no more columns to subtract

59 - 27 = 32
Example 2: Find the difference.
996 - 584

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.
2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.

4. Place the result directly below the horizontal line

5. Repeat the subtraction process in each column moving left until there are no more columns to subtract

996 - 584 = 412

Vertical Subtraction - Multi-Digit Subtraction with Regrouping (Borrowing)

In many cases, the lower digit of a column is larger than the upper digit. When this occurs, we utilize a procedure known as borrowing. Borrowing is just a way to re-write our number such that the subtraction in a particular column is possible. Let's think about a simple example.
Example 3: Find the difference.
71 - 35

1. Arrange the numbers vertically and by place value, the minuend will be on top and the subtrahend will be on the bottom. Remember, subtraction is not commutative, so the order does matter here.
2. Draw a horizontal line underneath the bottom number and place a "-" to the left of the bottom number

3. Subtract the digits in the rightmost column, this will contain the ones' place digit for each number. We subtract the bottom number away from the top number.
   • In this case, the subtraction in the ones' column provides an issue. We can't subtract 1 - 5 since 1 is not large enough to take 5 away. When this occurs, we can borrow from the next digit left. 71 = 7 tens + 1 ones. If we borrow 1 ten or 10 ones from the 7, we could rewrite the number 71 as:
     6 tens + 11 ones. This would allow us to subtract in the ones' column since 11 is larger than 5.

• Now we can subtract 11 - 5

4. Place the result directly below the horizontal line

5. Repeat the subtraction process in each column moving left until there are no more columns to subtract

71 - 35 = 36

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