# Multiplication properties

Mathematics in life is often needed. But it happens that if you knew her well in school, many rules are forgotten. In this article, we recall the properties of multiplication.

## Multiplication and its properties

The action that results in the sum of the same terms is called multiplication. That is, multiplying the number X by the number Y means that you need to determine the sum of Y terms, each of which will be equal to X. The numbers that are multiplied together are called multipliers (factors), the result of multiplication is called the product.

### For example,

548x11 = 548 + 548 + 548 + 548 + 548 + 548 + 548 + 548 + 548 (11 times)

- If natural numbers are involved in multiplication, then the result of such multiplication will always be a positive number.
- If one of several factors is 0 (zero), then the product of these factors will be equal to zero. Conversely, if the result of a product is 0, then one of the factors must be zero.
- In the case when one of these multipliers equals 1 (one), then their product will be equal to the second multiplier.

There are several laws of multiplication.

## First law

He reveals to us the combination property of multiplication.The rule is as follows: to multiply two factors by the third factor, you must multiply the first factor by the product of the second and third factors.

The general form of this formula looks like: (NхХ) хА = Nх (ХхА)

### Examples:

(11x12) x 3 = 11 x (12 x 3) = 396;

(13 x 9) x 11 = 13 x (9 x 11) = 1287.

## Second law

He tells us about the switching property of multiplication. The rule is: when you rearrange the factors, the product remains the same.

General record looks like:

NxXXA = AhXXN = XxNxA.

### Examples:

11 x 13 x 15 = 15 x 13 x 11 = 13 x 11 x 15 = 2145;

10 x 14 x 17 = 17 x 14 x 10 = 14 x 10 x 17 = 2380.

## Law three

This law says about the distribution property of multiplication. The rule is as follows: to multiply a number by the sum of numbers, you must multiply this number by each of the given terms and add the results.

The general entry will be as follows:

Xx (A + N) = XxA + XxN.

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