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Division with Remainders (Area Models)

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Division with Remainders (Area Models)
CCSS.MATH.CONTENT.4.NBT.B.6

Basics on the topic Division with Remainders (Area Models)

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In This Video on Remainders (Area Model)

Mr. Squeaks and Imani want to share some treasure with their crew. To do this, they want to learn how to solve division problems with remainders using the area model, so they can share equally between their crew and keep the remainder for themselves! In this video, you will learn how to use a area model with division and remainders.

Area Model Division with Remainders

You can use an area model for division with remainders by following some steps. Let’s practice with fifty-nine divided by five.

First, set up an area model with columns matching the number of place values of the dividend. Fifty-nine has two place values, so set up an area model with two columns.

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Next, put the divisor, five, on the left side, and write fifty-nine inside the first column.

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It is usually easier to multiply by tens first, so write a ten above the first column.

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Now multiply ten by the divisor, five, which is fifty. We need to subtract fifty from fifty-nine, which is nine.

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Then, bring the nine over to the next column. This time, think how many times does five go into nine. It goes one time, so write one above the column.

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Next, multiply five by one, which is five, and subtract this from the nine, which leaves us with four.

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Since five cannot go into four, this will be the remainder. We add the ten and one at the top of the columns for the quotient, and add R 4 for the remainder.

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Area Model and Remainders - Review

To do division with area models:

  • Step 1 - Divide the area model to match the number of place values in the dividend.
  • Step 2 - Write the divisor on the left side.
  • Step 3 - Find a multiple of the divisor that is close to, but doesn't go over, the dividend.
  • Step 4 - Subtract the product from the dividend and carry the leftover to the next column.
  • Repeat step 3 and step 4 until you are left with a remainder.
  • Step 5 - Add the numbers above the columns for the quotient, then write followed by the remainder.

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Below you will find a worksheet on dividing with area models and remainders.

Transcript Division with Remainders (Area Models)

Mr. Squeaks and Imani have been on a treasure hunt with their crew. "Alright, me hearties! I shall share the gems and gold equally with you all and any left over is mine!" "Is mine!" Let's help share the treasure equally by learning about division with remainders, area models. Mr. Squeaks has fifty-nine gems to be shared between five crew mates! When using division to find remainders, we can use area models like this. Split the area model into columns to match the number of place values in the dividend. Fifty-nine has two place values, tens and ones, so split the area model into two columns. Then, write the divisor, five, on the left side of the area model. Next, write fifty-nine here. Now think, what number, when multiplied by five, has a product that is close to, but doesn't go over, fifty-nine? It is often easier to multiply by tens first when dividing two-digit numbers with area models. So write ten above the column. Then, multiply the divisor, five, by ten to get the product, fifty. Now, subtract fifty from fifty-nine to get nine, and carry it over to the next column. Now we need to identify how many times five, goes into the leftover value, nine. Five goes into nine only one time, so write one here. Now, multiply five by one, to get five. Then, subtract five from nine to get four. Since five cannot go into four, we add the numbers above the columns to find the quotient. Ten plus one equals eleven. Since there are four leftover, this is the remainder. Write an R to represent remainder, followed by four. Fifty-nine divided by five equals eleven with four remaining meaning the five crew mates will get eleven gems each, with four left for Mr. Squeaks. Now, Mr. Squeaks wants to share three hundred forty-seven coins between three crew mates! What is the first step? Split the area model into three columns, since the dividend has three place values, hundreds, tens, and ones. What happens with the divisor and dividend? Write the divisor, three, on the left side of the area model, and write the dividend inside the first column. Now find a three-digit number, when multiplied by three, has a product that is close to three hundred forty-seven. It is often easier to multiply by hundreds and tens first when dividing three-digit numbers with area models. What could we multiply three by? We could multiply three by one hundred, so write it here. Three times one hundred is three hundred, so subtract three hundred from three hundred forty-seven to get forty-seven. What is the next step? Write forty-seven here. What number, when multiplied by three, has a product close to forty-seven? We could multiply three by ten, so write it here. Three times ten is thirty so subtract thirty from forty-seven to get seventeen. What is the next step? Write seventeen here. What number, when multiplied by three, has a product that is close to seventeen? Five, so write five here. Three times five is fifteen, so subtract fifteen from seventeen, which is two. What is the final step? Add all the numbers above the columns to get one hundred fifteen. Don't forget to represent the remainder by writing R two. Three hundred forty-seven divided by three equals one hundred fifteen with two remaining, meaning the three crew mates will get one hundred fifteen coins each, with two remaining for Mr. Squeaks. While Mr. Squeaks finishes up, let's review! Remember, when dividing using area models first, divide the area model to match the number of place values in the dividend. Second, write the divisor on the left side. Third, find a multiple of the divisor that is close to, but doesn't go over, the dividend. Fourth, subtract the product from the dividend and carry the leftover to the next column. Repeat steps three and four until you are left with a remainder. Add the numbers above the columns for the quotient, then write R followed by the remainder. "Captain Squeaks, what about our treasure!?"