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## Properties of multiplications

The operation of **multiply has a number of properties** that we must know in order to facilitate and correctly solve the operations in which it is involved.

### Commutative property:

Comutative ownership means that **the order of the factors does not change the product**. That is to say, it does not matter if we multiply 2 x 3 or 3 x 2, since in both cases, the result will be equal to six.

This property can be applied to multiplications involving a larger number of factors. For example:

3 x 5 x 10 = 5 x 3 x 10 = 10 x 3 x 5 = 10 x 5 x 3 x 3 = 150

As you can see,** any of the above combinations give the same result**Therefore, it is verified that the multiplications satisfy the commutative property.

### Associative property:

The associative property states that the **way of grouping the factors** in a multiplication does not change the result of the multiplication.

For example:

(3 x 2) x 5 = 3 (2 x 5)

If we solve the parentheses we have that:

6 x 5 = 3 x 10

And finally, we arrive at the result that both multiplications give us a value of 30 even though we have solved the operations with different multiplication groupings. Again, it is verified that the associative property is satisfied.

### Distributive property:

To** multiply a number by a sum**If the sum of the multiplications of that number by each of the addends is the result. Example:

2 x (4 + 6) = 2 x 4 + 2 x 6

Let's see if we get the same result from both equalities:

2 x 10 = 8 + 12

Indeed, we see that the equality is fulfilled and therefore, it is verified that the multiplications also enjoy the distributive property.

## Rule of signs in multiplications

As with divisions, multiplication also involves a number of different **sign rules to be complied with** to know what sign the result of the operation will have.

Below is a summary of the possible combinations when multiplying two numbers:

- + x + = +
- - x - = +
- + x - = -
- - x + = -

You can use the associative property that we have seen above for **to know the sign that a multiplication with more factors will have**.

For example, let's see the sign that the multiplication will have:

-2 x 3 x (-6) = (-2 x 3) x (-6)

The first parenthesis will give us a negative number, which multiplied by another negative number, will give us a positive result:

(-6) x (-6) = 36

## Multiplication tables

Below you will find a list of all the **multiplication tables 1 to 9** for you to learn or refresh your memory in case you have forgotten any of them.

On each page you will find a multiplication table from 0 to 100 of each number for you to download or print, tricks to memorize them and a song for children to learn to multiply.

### Table 1

**Multiplying by one is the easiest** that there is because when we multiply by the unit, we obtain as a result the number by which we multiply. Easy, isn't it? 1 x 1257 = 1257. Very simple.

### Table of 2

When multiplying by two, we must think that** the result will give us an even number which will be exactly double** of the number by which we multiply.

Don't miss our section dedicated to the multiplication table of the number 2.

### Table of 3

In the case of the multiplication table of the number three, **there is no trick to it** We are not known to involve the use of our fingers, something that would give us away to the rest of the world who sees us performing operations in this unorthodox way.

Luckily, we have compiled for you a lot of material related to the three so that **learn to multiply by it** in a simple and fast way.

### Table of 4

Number four is one of those that** nor does it provide us with any tricks** to learn to multiply by it. In this situation, the only thing left to do is to learn the multiplication table by four and make use of the material that you will find in the link that we have left a few words above.

### Table of 5

The multiplication table of five is easy to learn, and there are tricks to make it even easier. Although these secrets to multiplying by five you will find them in its dedicated sectionwe anticipate that **there is a pattern that is always repeated** you multiply a number by 5.

### Table of 6

Did you know that when you multiply six by another even number, the result ends up with the same number as the even number? We teach you this trick and others in the page dedicated to the table of 6as follows **you will learn to multiply by this number** thanks to all the material we have compiled for you in it.

### Table of 7

The multiplication table of 7 is one of the most difficult to learn. There are no tricks to memorize it easily so we will have to learn it by heart.

In the table page 7 you will find material to make it easier for you to remember how to multiply by this number. With a little practice, you will surely be able to solve these operations with ease.

### Table of 8

**Writing the multiplication table of 8 is very easy** with the trick that you will discover in this page. When you see it, you will know how to write the table from 8 to 10 without needing to know the results of the operations. Sounds good, doesn't it?

As in the rest of the numbers we have seen so far, you will also find the relevant table so you can print it and a song dedicated to children who are learning how to multiply at school or at home.

### Table of 9

To conclude, number nine gives us another trick very similar to the table of 8 to write the result of multiplications in a matter of seconds. Don't miss it and** learn to be the fastest at multiplying by 9.**

## Printable multiplication table

Finally, here you have another multiplication table that collects the **results from 1×1 to 15×15**.

All you have to do is **find where row and column intersect** of the numbers you want to multiply together and you will find the result of the operation.

X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 26 | 28 | 30 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 | 39 | 42 | 45 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 | 52 | 56 | 60 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 | 65 | 70 | 75 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 | 78 | 84 | 90 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 | 91 | 98 | 105 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 | 104 | 112 | 120 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 | 117 | 126 | 135 |

10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 | 130 | 140 | 150 |

11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 | 143 | 154 | 165 |

12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 | 156 | 168 | 180 |

13 | 13 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | 117 | 130 | 143 | 156 | 169 | 182 | 195 |

14 | 14 | 28 | 42 | 56 | 70 | 84 | 98 | 112 | 126 | 140 | 154 | 168 | 182 | 196 | 210 |

15 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 |