How to Multiply Mixed Numbers Using Partial Products

TenMarks teaches you how to multiply mixed numbers using partial products.

How to Multiply Mixed Numbers Using Partial Products Multiplication Using Partial Products So our first problem, we need to find 1 1/3 x 1/5. So to do that, I’m going to go ahead and first write it, so 1 1/3 x 1/5. It’s easier for me to see that way. So first thing we need to do is 1 1/3 is the same thing as 1 + 1/3. So I’m just going to rewrite it that way. So (1 + 1/3) x 1/5. Now I’m going to go ahead and use my Distributive Property. I’m going to distribute my 1 and my 1/3. So I’m going to take (1 + 1/3) x 1/5. I’m going to take the 1 and multiply it by 1/5. So I’m going to take (1 x 1/5) + my (1/3 x 1/5). So I’m distributing these numbers right across the equation, so 1/3 x 1/5. So now I just used my Distributive Property. Next what I need to do is I need to find my Partial Product. So to find the Partial product, I need to find the product of 1 x 1/5. So 1 x 1/5 is 1/5. And then, 1/3 x 1/5 is 1/15. Now, I need to go ahead and rewrite this now, so 1/5 + – because we’re adding these two Partial Products, plus 1/15. So I’m going to go ahead and add my two fractions. Now, in order for me to add, my denominators need to be the same, which they are not. So, I can go ahead and change my 5 into a 15 very easily by multiplying by 3, the denominator and the numerator by 3. So I’m going to multiply 1 x 3 and 3 x 5 to get 3/15, which then will allow me to add this. So now, I’m going to take 3/15 + 1/15. So now I can add these because they have the same denominator, and that would be 4/15. So 1 1/3 x 1/5 equals 4/15. Let’s move on to our second problem. And let me give more room here. So in this problem, we need to find 5 1/2 x 2 1/3. So I’m going to go ahead and rewrite this again, 5 1/2 x 2 1/3. So the first thing is, again we have mixed numbers right? And a mixed number is the same thing as 5 + 1/2, so I’m just going to rewrite it as such, times – and I would do the other mixed number, so that would be 2 + 1/3. So now, I can go ahead and use my Distributive Property again. So, I’m going to go ahead and distribute. So I’m going to take 5 x 2, so let’s go down to 5 x 2 +, and then I’m going to take the 5 x 1/3 +, and then I’m going to go ahead and move on to my 1/2, plus the (1/2 x 2) + (1/2 x 1/3). So now, I just distributed them using the Distributive Property. So next, what I need to do is I’m going to go ahead and find my Partial Product. So I’m going to go ahead and find the product. So, I have 5 x 2 – so I do 5 x 2 is 10, plus 5 x 1/3 is 5 1/3, plus 1/2 x 2 is 1, because 2/2 which is 1, plus 1/2 x 1/3 is 1/6. So now I’m going to go ahead and add my Partial Products. So I have 10 + 5/3 + 1 + 1/6. So, I can do my 10 and my 1 as 11 +, and then I have 5/3 + 1/6. And again, I have two denominators that are different. So I have to make sure in order to add these two fractions, my denominators have to be the same. I can easily turn this 3 right, and the denominator, I can easily turn the 3 into a 6 by multiplying by 2. So I’m going to go ahead and I’m just going to multiply the 5 x 2 and the 3 x 2 and get 10/6. So now, I have 11 + 10/6 + 1/6. So when I add these, I get 11 + 11/6, and remember 11 + 11/6 is same thing as the mixed number 11 11/6. So 5 1/2 x 2 1/3 equals 11 11/6. So, some tips to remember. To multiply a mixed number with a fraction or a mixed number, we can use the Partial Product. We also used the Distributive Property, is used to find the Partial Product. So for example, let’s do a quick example down here, one more quick example and we’ll do that in here. So for example, if we had 1 1/2 x 1 1/3, we would – it’s the same thing as (1 + 1/2) x (1 + 1/3). And then you would use the Distributive Property, and that would be (1 x 1) + (1 x 1/3) + (1/2 x 1) + ( 1/2 x 1/3), and then you would find the Partial Products. So the Partial products would be 1 and – (1 x 1/3), (1/2 x 1), so these are your Partial Products. So here, we used the Distributive Property, we distributed them to find our Partial Products. And then the last thing to do would be to find the products and then to add the products to get your result, just like we did up in here. We found our Partial Products and we added them to get our answer.