The document discusses various properties and methods of multiplication. It defines factors and products, and covers the associative, commutative, and distributive properties. It also discusses finding multiples of a number, and methods for multiplying numbers by 1, 2, or 3 digits as well as powers of ten.

1. The terms of the multiplication are the factors
and the product.
Factor
Product

3. Properties of the multiplication
Associative property:
When three or more numbers are multiplied, the product is the
same regardless of the grouping of the factors.
Conmutative property:
When two numbers are multiplied together, the product is the
same regardless of the order of the multiplicands.

4. Distributive property:
The sum of two numbers times a third number is equal to the
sum of each addend times the third number.
Identity property:
The product of any number and one is that number.

5. Multiples of a number
The multiples of a number are all the products that we get
when we multiply the number times each natural number.
Example:
The bus to Cali leaves the bus station every 3 hours. The first
bus leaves at 6:00 am. Let´s find the multiples of 3 in order to
know what are the hours in which the bus leaves the station.

6. M3: {0,3,6,9,…………..18,21,24}
The bus leaves the bus station at:
6:00 am
9:00 am
12:00 pm
3:00 pm
6:00 pm
9:00 pm
Multiples of 3: {0,3,6,9,12,15,18,21}

7. Multiplication by one digit
In order to multiply a number by one digit factor we first
multiply , the ones, then the tens, the hundreds and so
on.
Let´s multiply 403 x 2.
First step
403
x
2
6
Second step
Ones
x
403
2
06
tens

8. Third step
403
x
2
1,094
Hundreds

9. Multiplication by two digits
In order to multiply a 2 digit factor, we multiply the number by the
ones, then by the tens and finally we add the products
Let´s multiply 412 x 13.
Step 1 : multiply the number in the ones place which is 3 by 412.
Ones
1,236

10. Step 2: Because the place value of number 1 in the
Tens is 10 you write a zero 0.
Tens
+
1, 236
4, 120
5,356
Step 3: Multiply 1 by 412 and write the product to the left of
the 0.
Step 4: Add the products and find the total.

11. Multiplication by 3 digits
Let´s multiply 413 x 321.
413
8260
1 2 3, 9 0 0
1 3 2, 5 7 3

12. Multiplication by 10, 100 and 1,000
In order to multiply a number by 10, 100 and 1,000 in an
abbreviated way you write the number followed by 1, 2 or
3 ceros respectively.
Example 1: You write the number then you add one zero.

13. Example 2: To multiply by 100 you write the number and
you add two zeros (0 0).
Example 3: To multiply by 1,000 you write the number
and you add three zeros (0 0 0).