Multiplication

The terms of the multiplication are the factors and the product.

3 x 7 = 21

Factor Product

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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.

3 x 4 = 4 x 3

(8 x 3) x 4 = 8 x (3 x 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 x (4 + 3) = (5 x 4) + (5 x 3)

8 x 1 = 8

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.

M3: {0,3,6,9,…………..18,21,24}

The bus leaves the bus station at:

6:00 am9:00 am12:00 pm3:00 pm6:00 pm9:00 pm

Multiples of 3: {0,3,6,9,12,15,18,21}

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 Second step 403 Ones 403 x 2 x 2 tens 6 06

Third step

403 Hundreds x 2

1,094

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

412X 13

Step 2: Because the place value of number 1 in theTens 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.

412X 13

Multiplication by 3 digits

Let´s multiply 413 x 321.

4 1 3 8 2 6 0 1 2 3, 9 0 0

1 3 2, 5 7 3

413 x 321

Multiplication by 10, 100 and 1,000

In order to multiply a number by 10, 100 and 1,000 in anabbreviated way you write the number followed by 1, 2 or3 ceros respectively.

Example 1: You write the number then you add one zero.

34 x 10 = 340

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).

129 x 100 = 12,900

78 x 1,000 = 78,000