Partial product method

So in this problem we need to multiply, write each partial product, then add the partial products. So let's take a look at 174 x 9. To multiply a three digit number such as 174 by one digit number such as 9, using the partial products method, we split the three digit number into three parts.

Multiply all of the parts separately by the one digit number and then add the three products. So let’s show you what we’re talking about here. So we have 174, so we’re going to split. So to multiply 174 by 9, we’re going to split 174 into three parts. So the three parts would be, 100 + 70 + 4, so we have split 174 into three parts.

So now we’re going to multiply each part of 174 by 9. So here is our place values, so we have our thousands, our one hundreds, our tens and our ones. So now we have 174 right, so 174, we have one hundreds, seven tens and four ones and we’ll multiply that by nine.

So now, let’s go ahead and multiply. So first we’re going to multiply our hundreds. So we’re going to take one, we have one in our hundreds, so we’re going to take 100 x 9 and that will give us, 100 x 9 is 900. Then we’re going to multiply our tens. So we have seven tens, so that means we have 70 x 9 and 70 x 9 give us 630. Then we have four ones, so we’re going to take 4 x 9, and four 4 x 9 is 36.

Now after we have multiplied each separate part, we’re going to go ahead and then add the three partial products. So 0 + 0 + 6 is 6, 3 + 3 is 6, 9 + 6 is 15. So by adding the three partial products we get the product of the two numbers. So 174 x 9 is 1566.

Let’s take a look at another problem. 34 x 26. So to multiply a two digit number by another two digit number using the partial product method, we split both the numbers into two products. So to multiply 34 x 26, we need to split 34 into two parts and we need to split 26 into two parts. So 34 can be split as 30 + 4 and 26 can be split as 20 + 6. Now we’re going to multiply each part of 26 by each part of 34.

So to do that let’s set it up. So have our hundred spot, our tens place, and our ones place and we’re multiplying 26, so it’s two 20 which is two tens right and then six ones and then three tens and four ones. So we’re going to multiply these. So now when we multiply, we’re going to look at out tens first. So we’re multiplying three tens which is 30 times two tens which is 20. So when we multiply 30 x 20, we get 600.

Next we’re going to multiply our three tens with our ones. So if you noticed we multiplied the two tens and the three tens and now we’re going to multiply the three tens and the three ones. So I’m going to take three tens which is 30 and multiply it by my isix ones which is six, and 30 x 6 is 180.

Next we’re going to multiply our four ones and we have to multiply it with our two tens. So we’re going to take our four ones and multiply it with the two tens. So four times our two tens is 20, so 4 x 20 is 80, then we multiply the four with the six, our four ones and six ones. So four ones is four time six ones is six and 4 x 6 is 24.

Now that we have multiplied each part and we found the partial products, we need to add all our partial products up. So when we add them up, we get four ones, 18 tens and we carry our one and then we get seven plus that carry over one, so we have eight. So by adding the four partial products, we get the product of two numbers. So 34 x26 is 884.

Okay remember that in the partial product method we need to keep track of the place values of each digit. So to multiply remember a two digit number by another two digit number using the partial product method, we split both numbers into two parts and then we multiply both parts. When we multiply a three digit number by one digit number, we split the three digit number into three parts then we multiply all the parts separately by the one digit number and then we add all three products. Remember to add all the partial products to get your final product.