### Video Transcript

Multiplying by One and Zero

In this video, we will learn how to
multiply whole numbers by zero and one.

Let’s start by thinking about what
happens when we multiply a number by one. This model shows six egg cups. And each egg cup contains one
egg. And we can say that six times one
equals one. What do you notice about this
number sentence? Well, we started with the number
six, and the product is six. When we multiplied six by one, the
product or the result is six. So we could say that when we
multiply a number by one, the product or the result we get is that number. Let’s test this statement by
investigating what happens when we multiply different numbers by one.

In this multiplication table,
Sophia colored all the multiples of one green. Use the table to finish the
following sentence. When you multiply any number by
one, the product is zero, one, or the same number.

In this question, we have to
investigate what happens when you multiply any number by one. Is the product zero, one, or the
same number? And we’re given this multiplication
table to help. Sophia’s colored all the multiples
of one green. So we can see that the product of
one times one is one. Two times one is two. Three times one or one times three
is three. Four times one is four. And five times one is five.

What did you notice? When we multiplied one by one, the
product is one. When we multiplied two by one, the
product is two. Three multiplied by one is
three. Four multiplied by one is four. And five multiplied by one is
five. So when we multiply any number by
one, the product is the same number.

We call this rule the identity
property of multiplication. When you multiply a number by one,
the product is the same number. Let’s investigate what happens when
you multiply a number by zero.

When we multiply, we can think
about equal groups of dots. Four groups of two dots equals
eight dots; four times two equals eight. How many dots would there be if you
drew zero groups with eight dots in each group? Find the missing number: Zero times
eight equals what.

This is a two-part question. In the first part, we have to think
about how many dots there would be if we had zero groups with eight dots in each
group. When we’re multiplying, we can
think about equal groups of dots to help. This model shows four groups of
two. And four times two is eight. This model shows four groups. If we draw no groups or zero
groups, there would be no dots. If there are no groups, there are
no dots, which means that zero multiplied by eight equals zero. If four groups of two dots equals
eight dots and four multiplied by two equals eight, then no groups with eight dots
equals zero and zero multiplied by eight equals zero.

We call this the zero property of
multiplication. When you multiply a number by zero,
the product is zero.

Matthew started with 12 stars in
three groups of four. Three groups of four. Three times four equals 12. Remove one group at a time. Find the missing numbers. Two groups of four, two times four
equals what. One group of four, one times four
equals what. Zero groups of four, zero times
four equals what.

Matthew started with 12 stars in
three groups of four. We have to remove one group of four
at a time to find the missing numbers. We know that three times four is
12. So to find two groups of four, we
just need to take away one group of four. What is four less than 12? Two times four is eight. Four less than 12 is eight.

If we take away another four, we
will have one group of four, which is four. One group of four or one times four
is four. And to find zero times four, we
just need to take away another group of four. Four take away four is zero. Zero times four equals zero.

Matthew started with 12 stars in
three groups of four. And he removed one group at a
time. Two groups of four or two times
four equals eight. One group of four or one times four
equals four. And zero groups of four equal
zero.

So what have we learned in this
video? We’ve learned that when we multiply
a number by one, the product is that number. We call this the identity property
of multiplication. We also learned that when we
multiply a number by zero, the product is zero. And we call this the zero property
of multiplication.