WHOLE NUMBERS – ROUNDING WITH SUBTRACTION

There are two steps to solving these problems. First, round the numbers. Then subtract.

Concept for Rounding: Use rounding to make difficult calculations easier to perform, especially when you do not need exact numbers in your calculations.

Steps for Rounding

Step 1 | Find the digit you want to round to. Call it the target digit.
Step 2 | Look at the digit to the right of the target digit.
Step 3 | If the digit to the right of the target digit is 5 or more, add 1 to the target digit. If the digit to the right of the target digit is less than 5, do not change the target digit.
Step 4 | In either case, change all digits to the right of the target digit to zeros.

Example of Rounding Round 31,338,180 to the nearest hundred

Step 1 | Find the digit you want to round to. Call it the target digit. In this case we are targeting the hundreds digit which is a 1 in 31,338,180. | 31,338,1 80
Step 2 | Look at the digit to the right of the target digit. That digit is an 8. | 31,338,1 8 0
Step 3 | If the digit to the right of the target digit is a 5 or more, add 1 to the target digit. 8 is more than 5, so we will add 1 to the target digit. Our target digit is now a 2. (If the digit to the right of the target digit had been less than a 5, we would not have changed the target digit.) | 31,338,2 8 0
Step 4 | In either case, change all digits to the right of the target digit to zeros. 31,338,180 rounded to the nearest hundred is 31,338,200. | 31,338,2 00

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

Steps for Subtraction

Step 1 | Write the larger number above the smaller number. Arrange the number being subtracted (the smaller number) so that digits with the same place value are lined up.
Step 2 | Start with the ones column Subtract the numbers in the ones column, placing the result underneath the line in the ones column. Work from right to left, subtracting the numbers in each column.
Step 3 | When a digit in the bottom number is greater than the digit above it, you must borrow from the top number in the column to the left.
Step 4 | Check your answer by adding the difference to the bottom number of the original problem. The sum should equal the top number in the original problem.

Example of Subtraction 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 with the same place value are lined up. | 5 0 2 5 2 4 3 8
Step 2 | Start with the ones column. Subtract the numbers in the ones column, placing the result underneath the line in the ones column. Oops! Note that you cannot 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 column to the left. Since you can not 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. Place 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 87
| 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 8 587
| 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 2587
| 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 2587
Step 4 | Check your answer by adding the difference (2587) and the number which you subtracted (2438). The sum (5025) should equal the top number in the original problem. | 1 1 1 2587 + 2438 5025