WHOLE NUMBER SUBTRACTION

Concept: Use subtraction to find the difference between two numbers or amounts. The answer to a subtraction equation is called the difference. Follow these steps to subtract whole numbers.

Steps for Subtraction of Whole Numbers

Step 1 | Write the larger number above the smaller number. Arrange the number being subtracted so the digits are aligned in columns from right to left.
Step 2 | Start with the column furthest to the right (called the “ones” column). Subtract the bottom number from the top number in the ones column, placing the result underneath the Results Line. Working from right to left, subtract the numbers in each column keeping the numbers in each column lined up,.
Step 3 | When a digit from the bottom number is greater than the digit above it, you must borrow from the top number on the left.
Step 4 | Check your answer by adding the result (called the difference) to the smaller number above it. The sum should equal the top number in the original problem.

Example 1 Subtract 21 from 64

Step 1 | Write the larger number (64) above the smaller number (21). Arrange the number being subtracted (21) so that digits are aligned in columns from right to left. | 6 4 2 1
Step 2 | Start with the column furthest to the right (called the ones column). Subtract the bottom number from the top number in the ones column, (4 – 1), placing the result (3) underneath the Results Line. | 6 4 – 2 1 3
| Since you work from right to left, subtracting the numbers in each column as you go, you must now subtract the numbers in the tens column (6 – 2), placing the result (4) underneath the Results Line. Be sure to keep all the numbers in each column lined up. | 6 4 – 2 1 43
Step 3 | When a digit in the bottom number is greater than the digit above it, you must borrow from the top number on the left.. Step 3 does not apply in this equation. |
| Our answer is: 6 4 – 2 1 = 43 |
Step 4 | Check your answer by adding result (called the difference, 43) to the smaller number above it. (21). The sum should equal the top number (64) in the original problem. | 43 +21 64

Example 2 Subtract 2438 from 5025

Step 1 | Write the larger number (5025) above the smaller number (2438). Arrange the number being subtracted (2438) so that digits are aligned in columns from right to left. | 5 0 2 5 2 4 3 8
Step 2 | Start with the column furthest to the right (called the ones column). Subtract the bottom number from the top number in the ones column, (5 – 8). Oops! Note that you can not subtract 8 from 5, because 8 is greater than 5. Therefore, you need to borrow. | 5 0 2 5 – 2 4 3 8
Step 3 | When a digit in the bottom number is greater than the digit above it, you must borrow from the top number on the left. Since you cannot subtract 8 from 5, because 8 is greater than 5, you need to borrow 1 from the tens column in 5025. That drops the value in the tens column from 2 to 1, and raises the value in the ones column from 5 to 15. Write these new values above the original values. | 1 15 5 0 2 5 – 2 4 3 8
| Now complete the subtraction in the ones column: 15 – 8 = 7. | 1 15 5 0 2 5 – 2 4 3 8 7
| Since you work from right to left, subtracting the numbers in each column as you go, you must now subtract the tens column: (1 – 3). Oops! Again you must borrow from the column to the left, since 3 is greater than 1. The value of the digit in the hundreds column of 5025 is 0. We can not borrow anything from 0. For that reason you must now borrow from the thousands column. | 1 15 5 0 2 5 – 2 4 3 8 7
| The value of the digit in the thousands column will now go from 5 to 4, and the value of the digit in the hundreds column of 5025 will now become 10. | 4 10 1 15 5 0 2 5 – 2 4 3 8 7
| Next, borrow from the hundreds column. The value in the hundreds column goes from 10 to 9. The value in the tens column goes from 1 to 11. | 9 11 4 10 1 15 5 0 2 5 – 2 4 3 8 7
| Complete the subtraction in the tens column: 11 – 3 = 8. | 9 11 4 10 1 15 5 0 2 5 – 2 4 3 8 8 7
| Now, move to the hundreds column. Complete the subtraction in the hundreds column: 9 – 4 = 5 | 9 11 4 10 1 15 5 0 2 5 – 2 4 3 8 5 8 7
| Finally, move to the thousands column. Complete the subtraction in the thousands column: 4 – 2 = 2. | 9 11 4 10 1 15 5 0 2 5 – 2 4 3 8 2 5 8 7
| Our answer is: 5 0 2 5 – 2 4 3 8 = 2587 | 9 11 4 10 1 15 5 0 2 5 – 2 4 3 8 2 5 8 7
Step 4 | Check your answer by adding the result, 2587 (called the difference) to the smaller number above it, 2438. The sum, 5025, should equal the top number in the original problem. | 1 1 1 2 5 8 7 + 2 4 3 8 5 0 2 5