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

Ethan used an area model to help him multiply 248 by 2. Find the answer to 248 × 2 and show how to calculate the answer by adding partial products in columns.

04:26

Video Transcript

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.

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