乘以1

(Video) Multiplication Properties of 0 and 1

by mathman1024

Here's a video by mathman1024 explaining the multiplication property of zero and the multiplication property of one.

$\large{\text{Summary}}$

The Multiplication Property of One (also known as the Multiplicative Identity) states: $$a\cdot1=a$$ This means that any number times one will just stay that number. Multiplying by $1$ doesn't change anything.

For example, $$1(-959)=-959$$

The commutative property of multiplication says the $1$ can be on the left or the right. As an example,

$$-959(1) = -959$$

This means exactly the same thing as the previous equation!

Numbers stay the same when you multiply them by $1$

When you multiply a number by $1$, that number stays the same. That is because when you multiply, you're essentially saying that you want to add a number to itself a bunch of times.

For example, in the expression $2 \times 5$, we're basically just adding $2$ to itself five times. Take a look at the number line below to get a visualization of how that works:

If we had the equation $2 \times 1$, we would stop after we added $2$ once:

We could also interpret $2 \times 1$ as adding $1$ to itself twice, but if you look at the image you can see that that just gets us the same answer:

No matter what, if you multiply $2$ by $1$, the answer is still $2$. The same goes for any other real number—if you multiply something by $1$, it will stay the same.

Identity Property of Multiplication

The Identity Property of Multiplication states that if you multiply any number by $1,$ the result will be that number.

Think about it: if you multiply a number by $1,$ it will retain its identity...it will stay the same! Thus we call $1$ the multiplicative identity.

Examples:

$$\begin{align} 1 \cdot 4 &=4\\ 123 \cdot 1 &= 123\\ (x+y+z) \cdot 1 &= x+y+z \end{align}$$

As a bonus, we can multiply the $1$ first or second. This is because multiplication is commutative.

Bonus

Interested in mathematical properties? Check out some other cool properties, like the reflexive, symmetric, and transitive properties!