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Zero Property of Multiplication - Definition, Examples - What is the Zero Property? 

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Get unlimited access to over 84, lessons. Already registered? Log in here for access. Log in or sign up to add this lesson to a Custom Course. Log in or Sign up. The Zero Property of Multiplication is important to keep in mind, particularly when simplifying algebraic expressions. No matter what other operations are used, how many expressions there are, one multiplier of zero outside of parentheses will make the entire answer zero.

Note that the zero has to be outside of the parentheses. Additionally, if there is an operator after the zero, it must not be subtraction or addition. The Order of Operations tells us that multiplication is performed before subtraction and addition, so those numbers will be added to or subtracted from that zero. While the Order of Operations says that we need to solve what's in the parentheses first, the Zero Property tells us that the answer will be zero no matter what.

We could solve the parentheses and divide one by the other if we really wanted to, but the last operation will give us zero. Again, we have parentheses with a multiplier of zero outside them. Since zero has multiplication operators on both sides, the Zero Property still applies.

Since the numbers in the parentheses are so big and complex, we probably don't want to take the time to do calculations we don't need to do. Regardless of what the solutions of the parentheses are, the answer will be zero. In this example, the zero is listed first with the multiplier on its only side. However, since there's another operator outside the parentheses, we need to take that into account before we can apply the Zero Property.

Working out this problem using the Order of Operations tells us that the solution of the first parentheses zero will still be added to the solution of the second one Therefore, we can use the Zero Property for the first parentheses but not the second.

The answer may seem obvious, but let's work it out anyway. Using the Zero Property of Multiplication, we know that anything times zero equals zero, so our answer is zero.

No new games were added to Avery's library. The goal of 1, is irrelevant since it doesn't contribute to the end result. However, the Zero Property of Multiplication can be used for the original equation without solving for w. Since anything times zero equals zero, we know that 7 must be multiplied by zero in order to equal zero. In this lesson, we covered the Zero Property of Multiplication with examples. This property states that any number multiplied by zero will equal zero.

No matter how many parentheses or algebraic variables are included in the equation, if they are all multiplied by zero, then the answer is zero. You don't let that big, scary number faze you because you know that it does not matter what the other number is. When zero is added, that other number will stay the same. You know your teacher is talking about adding because the word sum indicates adding the two values.

You confidently tell your teacher that the answer is 1, Yesterday, you made five dollars in allowance from doing the laundry. But, your parents did not give you any money for taking out the trash.

How much total money in allowance did you make yesterday? Well, simply add five and zero to get your grand total of five dollars. It's the end of baseball season and you are trying to tally up the amount of runs you had this season.

You had six games. You scored one run during the first game, three during the second game, two during the third game, five during the fourth game, one during the fifth game, and none during the sixth game. How many runs did you score in all? To solve, simply add up the numbers 1, 3, 2, 5, and 1 to get Then add 0 to 12 to get The additive property of zero simply says that adding zero to any number does not change the number.

In other words, x plus zero will always equal x. So if you are asked to add 99, and 0, you know the answer will be 99,! According to the zero product rule, if the product of any number of expressions is 0, then at least one of them must also be zero.

That is to say,. As a result, we solve quadratic equations by first setting them to 0. This polynomial can now be factored into terms. These terms will have a product of zero, so we will use the zero product rule to find the roots of our equation. Let's look at an example of how to use the zero product property:. To find the equation, use the zero product property:.

To begin, set everything to zero as shown below:. Then, factorise the left side as follows:. The only way that you get the product of two quantities, and you get zero, is if one or both of them is equal to zero.

I really wanna reinforce this idea. I'm gonna put a red box around it so that it really gets stuck in your brain, and I want you to think about why that is. Try to come up with two numbers. Try to multiply them so that you get zero, and you're gonna see that one of those numbers is going to need to be zero. So we're gonna use this idea right over here.

Now this might look a little bit different, but you could view two X minus one as our A, and you could view X plus four as our B. So either two X minus one needs to be equal to zero, or X plus four needs to be equal to zero, or both of them needs to be equal to zero.

So I could write that as two X minus one needs to be equal to zero, or X plus four, or X, let me do that orange. Actually, let me do the two X minus one in that yellow color.

So either two X minus one is equal to zero, or X plus four is equal to zero. X plus four is equal to zero, and so let's solve each of these.

If two X minus one could be equal to zero, well, let's see, you could add one to both sides, and we get two X is equal to one. Divide both sides by two, and this just straightforward solving a linear equation. This is interesting 'cause we're gonna have two solutions here, or over here, if we wanna solve for X, we can subtract four from both sides, and we would get X is equal to negative four.

So it's neat.