How to Use Area Models to Divide Two-Digit Numbers By One-digit Numbers

A Step-by-step Guide to Using Area Models to Divide Two-Digit Numbers by One-digit Numbers

Here’s a step-by-step guide to using area models for this purpose.
Let’s say we want to divide 72 by 9.

Step 1: Draw a Rectangle to Represent the Dividend

The first step is to draw a rectangle. This rectangle will represent the total value you’re working with or the dividend. In this case, that’s 72.

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Step 2: Label the Rectangle

Label the rectangle with the total value (72). This helps to visualize that the entire rectangle is equal to the dividend.

Step 3: Determine the Divisor and Start to Partition the Rectangle

The divisor is the number you’re dividing by. In this case, it’s 9. Start to partition (divide) your rectangle into parts that represent the divisor. For instance, since our divisor is 9, we could try partitioning our rectangle into parts of 9.

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Step 4: Continue Partitioning the Rectangle Until You’ve Reached the Total Value

Continue partitioning your rectangle into groups of 9 until you’ve reached the total value of 72. You should end up with 8 equal sections, each representing a value of 9.

Step 5: Count the Number of Sections

The number of sections you have is your answer or quotient. Count up all the sections you have – in this case, you should have 8 sections. So, 72 divided by 9 equals 8.

This is a simplified method and works best when the dividend is a multiple of the divisor. If the dividend isn’t a multiple of the divisor, you’ll end up with a remainder, which can be represented as an additional, smaller section of the rectangle.

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Three More Area Model Division Examples

Draw a rectangle and write the divisor on its left side. Then split the inside into boxes, each holding a part of the dividend that the divisor goes into evenly. The numbers you write along the top are the partial quotients.

Example 1: 84 ÷ 6

Split 84 into 60 and 24. Box one: 60 ÷ 6 = 10. Box two: 24 ÷ 6 = 4. Add the tops: 10 + 4 = 14. Check: 6 × 14 = 84.

Example 2: 96 ÷ 4

Split 96 into 80 and 16. 80 ÷ 4 = 20 and 16 ÷ 4 = 4, so 96 ÷ 4 = 24. Check: 4 × 24 = 96.

Example 3: 95 ÷ 4, with a remainder

Split 95 into 80, 12 and 3. 80 ÷ 4 = 20 and 12 ÷ 4 = 3. The last 3 is too small to share among 4, so it stays as the remainder. The answer is 23 R3. Check: 4 × 23 + 3 = 95.

Picking Friendly Numbers for the Boxes

• Start with the largest multiple of ten you can, such as 60 for 84 ÷ 6. Tens are easy to divide.
• Use facts you know by heart for the second box, like 24 ÷ 6.
• You can use more boxes if that helps. 84 ÷ 6 also works as 30 + 30 + 24, giving 5 + 5 + 4 = 14.
• If what is left is smaller than the divisor, you are done. That leftover is the remainder.
• Always multiply back to check. The divisor times the quotient, plus any remainder, should equal the dividend.

Frequently Asked Questions

How do you do area model division?

Draw a rectangle, write the divisor on its side, and split the dividend into parts the divisor goes into evenly. Divide each part and add the partial quotients along the top. For 96 ÷ 4, split 96 into 80 + 16. Since 80 ÷ 4 = 20 and 16 ÷ 4 = 4, the quotient is 20 + 4 = 24. Check it: 4 × 24 = 96.

How do you use an area model divided into two regions?

Split the rectangle into two boxes whose areas add to the dividend and are both multiples of the divisor. Usually one box is a multiple of ten times the divisor. For 78 ÷ 6, use 60 and 18. Then 60 ÷ 6 = 10 and 18 ÷ 6 = 3, so the two side lengths add to 13, and 78 ÷ 6 = 13.

How do you do area model division with 2-digit divisors?

The steps stay the same; the friendly numbers just change. Write the 2-digit divisor on the side and pick chunks that are easy multiples of it, like 10 times or 5 times. For 156 ÷ 12, split 156 into 120 + 36. Since 120 ÷ 12 = 10 and 36 ÷ 12 = 3, the answer is 13, and 12 × 13 = 156.

Is the area model for division taught in 5th grade?

Yes. Students usually start area model division in 4th grade with one-digit divisors, as in 72 ÷ 9, and Common Core standard 4.NBT.B.6 names rectangular arrays and area models as strategies. In 5th grade, standard 5.NBT.B.6 extends the same idea to dividends up to four digits and two-digit divisors, so the boxes simply get bigger.

How do you divide two-digit numbers by a one-digit number?

Break the two-digit number into a tens-friendly part and a leftover part the divisor also fits into. For 85 ÷ 5, split 85 into 50 + 35. Then 50 ÷ 5 = 10 and 35 ÷ 5 = 7, so 85 ÷ 5 = 17. Drawing these two parts as boxes in a rectangle shows why the partial answers add up to the quotient.