Subtracting whole numbers horizontally and vertically by regrouping

Example

Subtract: $7,452,140 - 5,731,671$

Solution

1. Subtract ones. $0 - 1$. It is not sufficient. Take 1 group of tens from 4 tens, and regroup it to get 10 ones. Add ones: $10 + 0 = 10$. Now subtract ones: $10 - 1 = 9$. Write 9 in the ones place. Remember, 1 ten was regrouped into 10 ones. Thus, 3 tens remained in the tens place.

2. Subtract tens. $3 - 7$. It is not sufficient. Take 1 group of hundreds from 1 hundred and regroup it to get 10 tens. Add tens: $10 + 3 = 13$. Now subtract tens: $13 - 7 = 6$. Write 6 in the tens place. Remember, 1 hundred was regrouped into 10 tens. Thus, 0 hundreds remained in the hundreds place.

3. Subtract hundreds. $0 - 6$. It is not sufficient. Take 1 group of thousands from 2 thousands and regroup it to get 10 hundreds. Add hundreds: $10 + 0 = 10$. Now subtract hundreds: $10 - 6 = 4$. Write 4 in the hundreds place. Remember, 1 thousand was regrouped into 10 hundreds. Thus, 1 thousand remained in the thousands place.

4. Subtract thousands. $1 - 1 = 0$. Write 0 in the thousands place.

5. Subtract ten thousands. $5 - 3 = 2$. Write 2 in the ten thousands place.

6. Subtract hundred thousands. $4 - 7$. It is not sufficient. Take 1 million from 7 millions and regroup it into 10 hundred thousands. Add hundred thousands: $10 + 4 = 14$. Now subtract hundred thousands: $14 - 7 = 7$. Write 7 in the hundred thousands place. Remember, 6 millions remained after taking 1 million from 7 millions.

7. Subtract millions. $6 - 5 = 1$. Write 1 in the millions place.

Therefore, $7,452,140 - 5,731,671 = 1,720,469$.