Why does multiplying by 0 equal 0?

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In summary, when dealing with the zero-factor algebraic property, it is important to remember that multiplying 0 by any number will always result in 0. This is because of the properties of numbers such as 0 + a = a, 0 + 0 = 0, and a - a = 0. It may be helpful to think of multiplication as repeated addition, where adding 100 zero times will result in 0, but adding 100 one time will result in 100. It is important to break through the barrier of thinking that "none" and "at least one" are conceptually different in order to fully understand this property.
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symbolipoint said:
This is far too natural to be confusing. Remember that multiplication is repeated addition. If you add 100, ZERO times, you have ZERO. If you want 100 as result, then you must add 100 ONE time.

Hi all.
Just saw this post and wanted to follow up with a question that will address this point: the issue is in the order, if you think about it. What if one sees the issue as not adding 100 zeros, but as adding 100 zero times (read this carefully, as it confuses people even if I speak it in person). Basically the statement that if you have 100 already and you don't add anything to it (as you add 100 zero times, thus add nothing or anything really). So the order of numbers comes to play, in a way, and so when let's say 8*5 is the same as 5*8, when it come to zero it's not interchangeable (or at least one can argue that perception may be argued). It is partially a language issue, I def agree with that. But it also seems to be the issue of view point and perception of the order in the world.
I’m not a mathematician by trade at all but whole zero concept always got to me. I should say that I was always somewhat bright when it came to math and I liked to think deeply about it when I was in high school. Comes from having a grandfather physicist I guess and ironically this issue was actually seeded in me by the same grandfather (though I think he only wanted to mass with me at the time and make me think). In reality I understand that the concept works and all, but it still bugs me that in practical applications there is certain way of perceiving multiplication by zero that does create some confusion.
In any event, if someone looking for some helpful links, I found these very straight forward:
http://mathforum.org/library/drmath/view/61435.html
http://www.math.utah.edu/~pa/math/0by0.html
 
<h2>1. Why does multiplying by 0 equal 0?</h2><p>When we multiply any number by 0, the result is always 0. This is because the concept of multiplication is essentially repeated addition. For example, 3 x 4 means adding 3, 4 times (3 + 3 + 3 + 3 = 12). However, when we multiply by 0, we are essentially adding 0, which has no value. Therefore, the result is always 0.</p><h2>2. Is there a mathematical proof for why multiplying by 0 equals 0?</h2><p>Yes, there is a mathematical proof for this concept. It is based on the properties of multiplication, specifically the zero property. This property states that any number multiplied by 0 is equal to 0. Therefore, when we multiply by 0, we are simply following this property, resulting in a product of 0.</p><h2>3. Can you provide an example to illustrate why multiplying by 0 equals 0?</h2><p>Sure, let's take the equation 5 x 0. We can rewrite this as 0 + 0 + 0 + 0 + 0, which is essentially adding 0, 5 times. However, since 0 has no value, the result is still 0. This can be applied to any number multiplied by 0, resulting in a product of 0.</p><h2>4. Is multiplying by 0 the same as dividing by 0?</h2><p>No, multiplying by 0 and dividing by 0 are two different mathematical operations with different rules and outcomes. When we multiply by 0, the result is always 0. However, when we divide by 0, it is undefined and has no solution. In fact, dividing by 0 is considered an invalid operation in mathematics.</p><h2>5. Are there any real-life applications of multiplying by 0?</h2><p>Yes, there are several real-life applications of multiplying by 0. For example, when we have a group of objects and we want to find out how many objects are in 0 groups, the answer would be 0. This concept is also used in computer programming, where multiplying by 0 is a common operation to clear or reset a variable.</p>

Related to Why does multiplying by 0 equal 0?

1. Why does multiplying by 0 equal 0?

When we multiply any number by 0, the result is always 0. This is because the concept of multiplication is essentially repeated addition. For example, 3 x 4 means adding 3, 4 times (3 + 3 + 3 + 3 = 12). However, when we multiply by 0, we are essentially adding 0, which has no value. Therefore, the result is always 0.

2. Is there a mathematical proof for why multiplying by 0 equals 0?

Yes, there is a mathematical proof for this concept. It is based on the properties of multiplication, specifically the zero property. This property states that any number multiplied by 0 is equal to 0. Therefore, when we multiply by 0, we are simply following this property, resulting in a product of 0.

3. Can you provide an example to illustrate why multiplying by 0 equals 0?

Sure, let's take the equation 5 x 0. We can rewrite this as 0 + 0 + 0 + 0 + 0, which is essentially adding 0, 5 times. However, since 0 has no value, the result is still 0. This can be applied to any number multiplied by 0, resulting in a product of 0.

4. Is multiplying by 0 the same as dividing by 0?

No, multiplying by 0 and dividing by 0 are two different mathematical operations with different rules and outcomes. When we multiply by 0, the result is always 0. However, when we divide by 0, it is undefined and has no solution. In fact, dividing by 0 is considered an invalid operation in mathematics.

5. Are there any real-life applications of multiplying by 0?

Yes, there are several real-life applications of multiplying by 0. For example, when we have a group of objects and we want to find out how many objects are in 0 groups, the answer would be 0. This concept is also used in computer programming, where multiplying by 0 is a common operation to clear or reset a variable.

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