Lesson Video: Multiplying Three-Digit Numbers by One-Digit Numbers: Adding Partial Products Mathematics • 4th Grade

In this video, we will learn how to multiply three-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication.

11:40

Video Transcript

Multiplying Three-Digit Numbers by One-Digit Numbers: Adding Partial Products

In this video, we’re going to learn how to multiply three-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication.

In this example, we have to multiply a three-digit number, the number 135, by a one-digit number, the number three. We know that three-digit numbers have a hundreds, tens, and ones digit. So, to help us multiply 135 by three, we could partition the number or break it apart into its hundreds, tens, and ones, and then we can multiply each part by three. If 100 plus 30 plus five is 135, then to find 135 times three, we would need to multiply each part by three.

We could use an area model to help us multiply each of our three parts. We need to multiply three by 100 and three by 30 and three by five. Let’s start by multiplying the ones in 135 by three. Three times five ones is 15. Next, we need to multiply the tens part of our number by three. What is three times 30? We know that three times three is nine. So, three times 30 is 10 times greater than nine, which is 90. And finally, we can multiply the hundreds part of the number 135 by three. Three multiplied by 100 is 300. Now, what we need to do is add our partial products together: 300 plus 90 plus 15. The total of our ones is five, the total of our tens is 10, and we’ve got a total of four 100s. Three times 135 equals 405.

Let’s recap what we’ve learned about multiplying three-digit numbers by one-digit numbers using partial products. The first thing we did was to partition or break apart our three-digit number into its hundreds part, tens part, and ones part. Next, we drew an area model, which shows our three-digit number written in expanded form. Then we used the distributive property to multiply each of the parts. Then all we had to do was add our three partial products. Three times 135 is 405. Let’s practice what we’ve learned and answer some questions where we need to multiply a three-digit number by a one-digit number using partial products.

Ethan used an area model to help him multiply 248 by two. Find the answer to 248 multiplied by two and show how to calculate the answer by adding partial products in columns.

In this question, Ethan is trying to multiply a three-digit number, the number 248, by a one-digit number, the number two, and he’s using an area model to help him multiply. He’s broken the number 248 up into its parts. In other words, he’s written it in expanded form. The hundreds part of 248 is worth 200, the tens part is worth 40, and the ones part is worth eight. 200 plus 40 plus eight equals 248.

Next, Ethan can multiply each part by two. The ones product is 16 because eight multiplied by two is 16. The tens product is 80 because two times 40 equals 80, and the hundreds product is 400. Two times 200 equals 400. We have to find the answer to 248 multiplied by two and show how to calculate the answer by adding partial products in columns. So, we have to work out which of these five calculations is correct. We know by looking at Ethan’s area model that the ones product is 16, and each of our possible answers show 16 as its ones product.

So, we need to keep working through the calculations. Let’s keep going and Look at the tens product. We know because of Ethan’s area model that two times 40 is 80. We can rule out this possible answer because the tens product is 40. It looks like they’ve confused the hundreds and the tens digit, multiplied two 10s by two instead of four 10s by two. Let’s look at our second possible answer. Tens product is 80, so this could be the correct answer.

This could also be the correct answer. But we know that the product of 40 and two is not eight; it’s 80. Eight is the product of four times two not 40 times two, so we can rule this one out. And it looks like there’s been some confusion with the hundreds and the tens digits in this answer. Two 10s multiplied by two is 40, but the product of four 10s or 40 times two is 80.

Let’s check the hundreds parts of the calculation. We know from Ethan’s area model that the product of two multiplied by 200 is 400. Both of our calculations have the correct number of hundreds, but they both have different answers. So, let’s complete the final step of the calculation by adding the partial products. Six plus zero plus zero is six. One 10 plus eight 10s gives us a total of nine 10s.

We found the mistake: 16 plus 80 plus 400 is 496, not 486. This is the correct way to find the answer to 248 multiplied by two by calculating partial products and then adding the partial products in columns.

Use partial products to calculate 124 times four.

In this question, the calculation has been set out for us. We’re multiplying our three-digit number, 124, by four. And we can see from the red arrow that we have to multiply the ones part of 124 first. What is four multiplied by four? 16. Next, we have to calculate two 10s or 20 multiplied by four. 20 times four is 80. So, we’ve got our ones product and now our tens product. Finally, we need to find the hundreds product. The one in 124 is worth 100, so we need to multiply 100 by four, which is 400.

Now, all we have to do is add together our three partial products. We’ve got a total of six ones, nine 10s, and four 100s. 124 multiplied by four is 496. We used partial products to calculate the answer.

Find the product. 213 multiplied by two.

In this question, we have to multiply our three-digit number, 213, by a one-digit number, the number two. First, we need to find the ones product. And we know the ones digit in 213 is three, so we have to multiply two by three, which is six. Next, we need to find the tens product. 213 has one 10, so we need to multiply two by 10. So, our product is 20. And finally, we need to find the hundreds product. The hundreds digit in 213 is two, worth 200. So, we’re multiplying two by 200. Two times 200 is 400.

Now, what we need to do is add our three partial products. We’ve got six in the ones column, a total of two in the tens column, and a total of four in the hundreds column. The product of 213 multiplied by two is 426.

What have we learned in this video? We have learned how to multiply three-digit numbers by one-digit numbers by calculating partial products and using expanded column multiplication.

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