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Lesson 7: Subtracting with regrouping within 1000

# Worked example: Subtracting 3-digit numbers (regrouping from 0)

Sal has to borrow from a 0 to subtract 301-164. Created by Sal Khan.

## Want to join the conversation?

• Is there any other methods other than regrouping?
• There is a Vedic method that involves writing bars (or vinculums) on digits to indicate "negative" digits, as we subtract in each column. Then, for each string of bar digits, we use complements (subtract digits from 9 except the last digit from 10, within the string of bar digits) and also decrease the digit immediately to the left of the string by one, to convert the answer to normal digits.

Example: Suppose we want to subtract 912 - 749. Remember that a bar digit occurs when the bottom digit in a column is greater than the top digit.

Hundreds column: 9-7 = 2.

Tens column: When we do 1-4, we end up short by 3. So we use the "negative" digit 3bar.

Ones column: When we do 2-9, we end up short by 7. So we use the "negative" digit 7bar.

Thus we get 2 3bar 7bar, but this has to be converted to a normal number. For the bar digits from left to right, 9-3=6 and 10-7=3. We must also decrease the hundreds digits 2 by one, to get 1. The final answer is 163.

Note: in some subtraction problems, the differences might be 0's in some of the columns. This method is more clear if any string of 0's that occur immediately to the left of a string of bar digits are also treated as bar digits.

Example: Suppose we want to do 93418 - 53442.

From left to right, the differences in the columns are 4, 0, 0, 3bar, 6.
Let's write this as 4 0bar 0bar 3bar 6.

When we use complements, we get the normal digits 9-0=9, 9-0=9, 10-3=7 to replace the string of three bar digits. We must also decrease the digit 4 immediately to the left of this string by one, to get 3. The final answer is 39,976.
• I have a problem. How do you subtract 1000-392?
• Step 1: Subtract 1000 by 300. Since the hundred's place equals 0, something less than 3, you borrow from the thousand's place (or basically, subtract 10 by 3). This gives you 700.
Step 2: Subtract 700 by 90. Since the ten's place equals 0, something less than 9, you will again need to borrow from next higher place value. The 7 in the hundred's place is reduced to 6, while 10 minus 9 equals 1. You put the 1 into the ten's place, and for now gives you 610.
Step 3: Subtract 610 by 2. Since the one's place equals 0, something less 2, you once again will need to borrow from a next higher place value. Reduce the 1 in the ten's place by 1, and subtract 10 by 2 which equals 8. Put the 8 into the one's place, you will have 608 as the solution.
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