1.4 Multiply whole numbers  (Page 2/7)

What happens when you multiply a number by zero? You can see that the product of any number and zero is zero. This is called the Multiplication Property of Zero.

What happens when you multiply a number by one? Multiplying a number by one does not change its value. We call this fact the Identity Property of Multiplication, and $1$ is called the multiplicative identity.

Earlier in this chapter, we learned that the Commutative Property of Addition states that changing the order of addition does not change the sum. We saw that $8+9=17$ is the same as $9+8=17.$

Is this also true for multiplication? Let’s look at a few pairs of factors.

When the order of the factors is reversed, the product does not change. This is called the Commutative Property of Multiplication.

To multiply numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition and subtraction.

We start by multiplying $3$ by $7.$

We write the $1$ in the ones place of the product. We carry the $2$ tens by writing $2$ above the tens place.

Then we multiply the $3$ by the $2,$ and add the $2$ above the tens place to the product. So $3\times 2=6,$ and $6+2=8.$ Write the $8$ in the tens place of the product.

The product is $81.$

When we multiply two numbers with a different number of digits, it’s usually easier to write the smaller number on the bottom. You could write it the other way, too, but this way is easier to work with.