How to Add and Subtract Decimals
To add and subtract decimal numbers without a calculator, both numbers must have the same number of decimal places. This is because the decimal points must line up in the solution grid to add or subtract the decimal numbers.
If it turns out one number has a greater number of decimal places than the other, simply add zeros to the end of the number with fewest decimal places until it has the same number of decimal places as the other.
For example, suppose we are attempting to add the following two decimal numbers:
Since the first number has 2 more decimal places than the second number, we need to add 2 zeros to the end of the second number (12.34 becomes 12.3400). That way the decimal points (indicated by a red vertical line) will line up in the solution grid, like this:
This also ensures that the sum of the two numbers will have the same number of decimal places as the number with the most number of decimal places.
How to Add Negative Numbers
If one or more of the numbers in the addition problem is negative, the steps for adding the numbers depends on whether or not the signs of the two numbers are the same.
If the signs are the same:
Simply add the absolute values of the two numbers and give the sum the same sign as the two numbers.
Add the absolute value of -7 (|-7| = 7) to the absolute value of -2 (|-2| = 2) to get 9, and give the sum the sign of the two numbers, which in this case is a negative sign.
| 7 | |||
| + | 2 | ||
| = | - | 9 | |
| Column | A | B | |
If the signs are not the same:
Using their absolute values, subtract the smaller of two numbers from the larger of the two numbers and give the sum the sign of the number with the largest absolute value.
Subtract the absolute value of the smaller number (|2| = 2) from the absolute value of the larger number -7 (|-7| = 7) to get 5, and give the result the sign of the number with the largest absolute value, which in this case is a negative sign.
| 7 | |||
| - | 2 | ||
| = | - | 5 | |
| Column | A | B | |
How to Subtract Negative Numbers
If the problem is subtraction, change the subtraction to addition and change the sign of the last number to its opposite. Then follow the steps for adding negative numbers.
Change (-7) - (2) to (-7) + (-2) and follow the rules for addition.
Since the signs are now the same, add the absolute value of -7 (|-7| = 7) to the absolute value of -2 (|-2| = 2) to get 9, and give the sum the sign of the two numbers, which in this case is a negative sign.
| 7 | |||
| + | 2 | ||
| = | - | 9 | |
| Column | A | B | |
Change (-7) - (-2) to (-7) + (2) and follow the rules for addition.
Since the signs are no longer the same, subtract the absolute value of the smaller number (|2| = 2) from the absolute value of the larger number -7 (|-7| = 7) to get 5, and give the result the sign of the number with the largest absolute value, which in this case is a negative sign.
| 7 | |||
| - | 2 | ||
| = | - | 5 | |
| Column | A | B | |
If you're not sure how to perform long addition or subtraction, the calculator on this page shows its work and includes the solution steps for each calculated result.