# Translations of Encyclopedia about Mathematics

## Subtraction

Subtraction is the opposite of addition and determines the difference between two numbers, such as:

6 – 4 = 2

The number fist listed (in our case 6) is the minuend, which is the number we are subtracting from. The second number (in our case 4) is called the subtrahend and the result of the subtraction gives us what we refer to as the difference. If we would like to verify or confirm our subtraction, all we need to do is reverse the function and add the subtrahend to the difference, such as:

Test: 4 + 2 = 6

If there are a greater number of subtrahends, we subtract them one by one from the subtrahend.

3518 – 516 – 302 – 152 = 2548

Which is achieved in the following manner:

3518 – 516 = 3002
3002 – 302 = 2700
2700 – 152 = 2548

Another option is to add together the various subtrahends and subtract them all from the minuend at once. In this case, brackets can be used because they would define which numbers we want to add together first.

The rule of brackets is as follows: the function shown in the brackets must be computed first. In our example, we would first have to add together the numbers 516, 302 and 152, subtracting their sum afterwards from the number 3518.

3518 – (516 + 302 + 152) = 2548
3518 – 970 = 2548

If we would like to subtract larger numbers without the use of a calculator, we can do so in the following manner:

 516 - 137 carry over 11 = 379

We calculate the difference between the numbers in each column by starting from the far right column. In our case, the number 7 in the subtrahend is greater than the number 6 above it in the minuend. This gives us a negative value, so we borrow a 10 from the left column to give us a number of 16 instead of 6, giving us 16 – 7 = 9. We write down our result of 9 in the far right column and note our borrowed 10 under the relevant column. Now we are subtracting 1 – 3 – 1. In this case, once again, we have to borrow from the column to the left to give us 11 – 3 – 1, which gives us 7. We write this amount below and continue our equation, this time subtracting 5 – 1 – 1 to give us 3. Another example:

 87796 - 33333 - 15001 - 12 carry over 1 = 39450

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