# Translations of Encyclopedia about Mathematics

## Multiplication

Multiplication is a shortened version of adding several same values together.

Summation: 6 + 6 + 6 = 18
Multiplication: 6 . 3 = 18

The numbers 6 and 3 are the multipliers and the number 18 is the multiple.

With real numbers, it generally applies that their order does not matter:

6 . 3 = 3 . 6 = 18

You can confirm or test a multiplication by dividing it (refer to next section) in the following manner:

Test: 18 : 3 = 6 or 18 : 6 = 3

If we want to multiply larger numbers without the use of a calculator, we can use the following method:

example: 160 . 23 160

. 23

480

3200

3680

The first two rows contain the given function and the subsequent rows the result of partial multiplication: 3*160 (3*0=0, so we write 0; 3*6=18, so we write 8, carrying over the 1 to the next column; 3*1=3, which gives us 3 and to which we add the 1 we carried over to give us 4) =480.

In the fourth row, the partial multiplication is 2*160 (2*0=0 – although we do not write it in the column to the far right but rather under the 2 we are multiplying against – in the far right column we place a 0). Next column we have 2*6=12, where we write the 2 in the row below and carry the 1 over to the next column. In the next column we have 2*1=2, but to this we add the 1 we carried over to give us 3, placing that in the appropriate column, the fourth from the right. This gives us a final figure of 3,200. Adding these two produced values (480+3,200), we get the final sum 3,680.

Some more examples for your viewing:

1213 *134

12300 4478 * 89

3690 358240

121·3 492 40302

363 16482 398542

Test:

363: 121 = 3 16482 : 123 = 134 398542 : 4478 = 89

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## Basic Arithmetical Functions with Whole Numbers, Decimal Numbers and Fractions

There are four basic arithmetical functions: addition, subtraction, multiplication and division, which are the foundation for more complex arithmetical functions, such as exponentiation, extraction of root and calculating logarithms, which we can use in our daily lives for the most varied of tasks. From the simplest of calculations, 1*1, to calculating interest for a savings account, we constantly apply the rules of mathematics.

For more difficult calculations, we can benefit from the common pocket calculator or computer. For more simple calculations, we might find it faster or easier to make the computation in our heads or to use a pen and paper.

The various arithmetical functions are subject to certain rules which must be adhered to when computing.

All mathematical rules make up a closed system (system of axioms) and, once we allow a mistake to occur in a calculation at the lower level, the error transfers throughout the entire function.

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