Lucas says that since 40x70 and 60x50 both have factors with a total of two zeros, they will both have products with a total of two zeros. Is this correct? Explain. 40x70=2800 and 60x50=3000. They both have zeros in the answer. Right

They both have two zeros because they're multiples of ten

what happens when you multiply something by 10?

what happens when you multiply something by 100?
by 1000? etc

so look at 60x50 as
6x10 x 5x10
= 6x5x10x10
= 30x100
= 3000

I need help understanding how to explain the total of two zeros

Ah, Lucas and his mathematical musings! Well, my dear friend, let me explain with a dash of humor.

You see, Lucas is like a comedian who tells a joke and expects the punchline to always land perfectly. But in the world of math, things aren't always as predictable as a well-timed punchline.

While it is true that both 40x70 and 60x50 have factors with a total of two zeros, it doesn't necessarily mean that their products will have the same total. Let's break it down, shall we?

When we multiply 40x70, we get 2800. And if we do the math for 60x50, we get 3000. Now, although they both have zeros in the answer, it's important to note that the total number of zeros doesn't necessarily determine their equivalence.

In the case of 40x70, the product has two zeros because one zero comes from the factor 40 and the other zero comes from the factor 70. But in the case of 60x50, it has three zeros because two zeros come from the factor 50 and one zero comes from the factor 60.

So, while Lucas may have thought they'd be the same, like two identical twins, these two products just turned out to be distant cousins. As we learned, having the same total number of zeros doesn't guarantee they'll have the same value.

Remember, mathematics can be a bit mischievous. So, it's important to keep a keen eye out for those zany surprises that numbers like to throw at us. Keep the laughter and the learning alive!

No, Lucas's statement is not correct. The number of zeros in the factors does not determine the number of zeros in the product.

To understand this, let's break down Lucas's argument.

First, he says that since 40x70 and 60x50 both have factors with a total of two zeros, they will both have products with a total of two zeros. This implies that if a number has factors with a certain number of zeros, the product will also have the same number of zeros.

However, the number of zeros in a product is determined by the combined number of factors of 10 in the factors being multiplied. A factor of 10 is created when a number has both factors of 2 and 5.

Let's examine the factors of 40x70. We can write it as (2x2x2x5) x (2x5x7). Here, we have two factors of 2 and two factors of 5. When we multiply these factors together, we get 4x2x5x7=280, which has only one zero.

Now, let's look at the factors of 60x50. It can be written as (2x2x3x5) x (2x5x5). Here, we again have two factors of 2 and two factors of 5. When we multiply these factors, we get 4x3x5x5=300, which has two zeros.

So, as we can see, even though both 40x70 and 60x50 have two zeros as factors, the number of zeros in the product is different. Therefore, Lucas's statement is incorrect.

In general, the number of zeros in a product is determined by the total number of factors of 10 present in the factors being multiplied, not simply the number of zeros in the factors themselves.

𝕀𝕕𝕜 𝕤𝕠𝕣𝕣𝕪 𝕚𝕞 𝕟𝕠 𝕙𝕖𝕝𝕡