Multiplication using facts and patterns

So in this problem we need to write the number that makes each sentence true. So we have, 2x3=n, 2x30=m, 2x300=p. So we know that 2x3=6, this is a basic fact of multiplication. So if we add the same number if zeros to one of the factors and to the product, the statement remains true. So if I have 2 times and I take my 3 and add a zero to one of the factors and then I add a zero to my product, the statement remains true, so 2x30=60, equal number of zeros increase on both sides. Same holds true if I take 2x300, so if add two zeros, that would equal and I added two zeros. So the equal number of zeros increased on both sides. So when we add the same number of zeros to one of the factors and to the product the statement remains true. So therefore we get a pattern, 2x3 is 6, 2x30 is 60, ,2x300 is 600. So if we refer back to our original equations and this one 2x3=n, so n=6, 2x30=m, 2x30=60 so m=60 and then 2x300=p, 2x300=600 so p=600.

Now let’s take a look at b, it says multiply 8x500. So we know the basic multiplication fact that 8x5 is 40. Now if we add the same number of zeros to one of the factors and to the product the statement remains true. So if I have 8x5 and I added zero which will make it 50, so I added the zero to one of the factors and then if I add zero to the product, so we started with the product of 40, now I add zero to the product, I have equal number of zeros increased on both sides, so I added one zero to the factor and then one zero to the product, the statement remains true, 8x50 =400.

Please note that if a zero exists in the product we need to keep it in the product as we add the zeros, so if you notice how in 40 we already had a zero in 40 so I kept that zero and I added my extra zero. So if we were to continue with this pattern and now I’m going to take the 5, I’m going to add two zeros it will be 500 = 40 and since I add two zeros, I’m going to add two zeros to my product. So the equal number of zeros were increased on both sides, so 8x500=4000. So if we go back, 8x500=4000.

Some tips to keep in mind, product means multiplication, so anytime you have a product that means multiplication. The product of two and three is simply a way of writing 2x3 where two and three are factors and then 6 is the product. So two and three are factors and 6 called your product. If we add the same number of zeros to one of the factors and to the product the statement remains true. Keep in mind that if a zero already exists in the product we need to keep the zero as we add zeros.