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Long Division with Two Digits
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Introduction

In this lesson, you will learn to use the division algorithm with larger numbers.

Previously, you learned how to do long division when dividing by a one-digit number or divisor. You use the same division steps when the number being divided by (the divisor) has multiple digits.


This video illustrates the lesson material below. Watching the video is optional.


Practicing Long Division with Two Digits

This example demonstrates how to use the division algorithm with bigger numbers. Use the steps for division:

  1. Put the number being divided (the dividend) under the box and the other number (the divisor) to the left of the box.
  2. Starting on the left, determine how many times the divisor can go into the first digit of the dividend.
  3. Write that number above the digit and subtract the product of that number and the divisor from the dividend.
  4. Repeat steps 2 and 3, moving to the right.

Example 1
\(5986\div82\)

Begin by drawing the division symbol. Put 5986 underneath it, and 82 to the left of the symbol:
\begin {align*}
\require{enclose}82\enclose{longdiv}{5986}
\end {align*}

Starting on the left, look at the first value in the dividend, or the number being divided. In this case, 5. How many times can 82 go into 5? The answer is zero. Because it is zero, move to the next number. How many times does 82 go into 59. Again, the answer is zero. Move another digit to the right. How many times does 82 go into 598?

With problems like these, it is not always easy to know the answer. You may need to guess or estimate. Start with 7. \(82\times7=574\). 574 is close to 598 while still being less than 598. The 7 will go above the 8 because it is the last digit we have used so far.

Subtract, \(598-574=24\). Carry down the number in the next column to the right, which is 6. Now you are working with 246.

The image shows 7 x 82 = 574. Then 574 being subtracted from 598 which equals to 24, the number 6 from 5986 is brought down.

Figure 1

How many times does 82 go into 246?

To help you guess, you can choose to think of this problem in terms of the multiplication facts you know. If we only consider the tens column of the divisor for a minute, in this case 8, and the first two digits of the dividend, we might recognize that 8 goes into 24. \(8\times3=24\).

Start with 3. \(82\times3=246\). The 3 will go above the 6 because it is the last digit we have used so far. Subtract 246.

The equation shows that since the answer is zero, there are no remaining leftovers to bring down. This shows that the correct answer is 73.

Figure 2

Since the answer is 0, that means there are no leftover or remaining parts. The correct answer is 73.

Remember: It’s okay to guess and have to erase as you work through this process. With more practice, you’ll become better at it, and it will go faster. It will also be easier and faster if you have your multiplication facts memorized, so keep working on those!


Things to Remember


  • Make sure to bring down the numbers for remaining place values while completing the division equation.
  • Memorizing the multiplication facts will make division easier.
  • Division can involve a lot of trial and error. It's okay if it takes a few tries to figure out which number is part of the correct answer.

Practice Problems

Evaluate the following expressions:
  1. \(152 \div 8 = ?\) (
    Solution
    x
    Solution: 19
    Details:
    To determine how many times 8 goes into 152, first look at the 1 in 152. You can’t make 8 with 1, or in other words, there aren’t enough pieces in 1 to have a set of 8. Next, look at the digits 1 and 5 together, and ask yourself how many times would 8 go into 15, or how many sets of 8 can you get with 15 pieces? The answer is 1 time or 1 set of 8.

    Place the 1 in the answer location above the 5.

    In this image the number 8 and the number 152 are written on the same imaginary horizontal line but they are separated by the division symbol. This symbol is a short vertical line and a long horizontal line that come together as though they are making the top left corner of a rectangular box. The short vertical line is what separates the 8 from the number 152. Above the 5 in 152 and above the horizontal line of the division symbol is the number 1.

    Next, multiply \(8 \times 1\) and put the solution of 8 below the 5. Place the 8 below the 15 and subtract \(15 − 8\). The remainder is 7. Place the 7 below the 5 and 8.

    This is the same as the previous image except now there is a new number 8 below the number 5 and a subtraction symbol to the left of this number 8. Below it is a new horizontal line and the number 7 written in the same imaginary column as the previous 5 and 8.

    The next step is to bring down the 2 in 152 and place it next to the 7 in the remainder. Now there is 72 in this area.

    This image is the same as the previous except there is an arrow pointing down from the 2 in the number 152. There is also a 2 written below the subtraction line, to the right of the 7, within the same vertical column as the 2 in 152. This means the new number below the subtraction line and the number to be divided next is the number 72.

    You are still dividing the original problem, but you are doing it in parts.

    The next step is to determine how many times will 8 go into 72 and the answer is 9 because \(8 \times 9 = 72\).

    Place the 9 in the answer area above the 2 in 152.

    This image is the same as the previous except there is a 9 above the division symbol, in the same imaginary vertical column as the 2 in 152.

    Since \(8 \times 9\) is 72, place 72 below the 72 and subtract. There’s 0 remaining. You can stop dividing once you reach a remainder of 0.

    This image is the same as the previous except there is a 72 written directly below the previous 72. There is also a subtraction symbol to the left of the new 72 and a horizontal line directly below. Under this horizontal line is written zero zero indicating that 2 subtract 2 is zero and 7 subtract 7 is zero.

    The answer to 152 divided by 8 is 19.

    This image is the same as the previous one except the number 19 above the division symbol is surrounded by a square indicating that our final answer is 19.
    )
  2. \(1620 \div 20 = ?\) (
    Solution
    x
    Solution: 81
    Details:
    To determine how many times 20 goes into 1620, first test the 1. There are zero sets of 20 in 1. Next, look at the digits 1 and 6, and ask yourself how many times would 20 go into 16? Again, there are zero sets of 20 in 16, so it goes into 16 zero times. Next, look at the digits 1, 6, and 2 together and ask yourself how many times would 20 go into 162? The answer is \({\color{Red}{\text{about }} 8 {\text{ times}}}\).

    In this image the number 20 and the number 1620 are written on the same imaginary horizontal line but they are separated by the division symbol. This symbol is a short vertical line and a long horizontal line that come together as though they are making the top left corner of a rectangular box. The short vertical line is what separates the 20 from the number 1620. Above the 2 in 1620 and above the horizontal line of the division symbol is the number 8.

    Multiply \(8 \times 20\) to find it equals 160. Place the 160 below the 162 and subtract. There is a remainder of 2.

    This is the same as the previous image except now there is the number 160 written directly below the numbers 1 6 and 2 of the number 1620. There is also a horizontal line directly below the 160 a subtraction symbol to the left and the number 2 written below the new horizontal line. This two is in the same column as the 2 of 1620 and the 0 of 160.

    Now bring down the 0 from the top, to make 20.

    This is the same as the previous image except now there is an arrow pointing down from the 0 in the number 1620. It is pointing to a new 0 written to the right of the number 2, under the horizontal line from the previous step creating the number 20 under the line. Note that the new 0 is in the same imaginary column as the original 0 in 1620.

    Repeat the process again by asking yourself how many times does 20 go into 20. The answer is \({\color{Red}1 {\text{ time}}}\). You know that \(20 \times 1 = 20\). Place the 1 in the answer location above the 0 in 1620 and multiply \(1 \times 20 = 20\). Place the 20 below the other 20 and subtract. There is 0 left over and no other digits to bring down, so you can stop the division process.

    This is the same as the previous image except now there is a number 1 written just to the right of the 8 in the solution area above the division symbol. This 1 is in the same imaginary column as the 0 in 1620. There is also the number 20 written directly below the 20 from the previous step. They are stacked with the twos in the same column and the zeros in the same column. There is a subtraction symbol to the left and a new horizontal line drawn below the new 20. Below the line is written 0 and 0 in each imaginary column.

    The answer to the original question of how many times 20 goes into 1620 is \({\color{Red}81 {\text{ times}}}\).

    This image is the same as the previous except there is a box around the number 81 in the solution area above the division symbol.
    )
  3. \(2349 \div 87 = ?\) (
    Video Solution
    x
    )
  4. \(3003 \div 39 = ?\) (
    Solution
    x
    Solution:
    77
    )
  5. \(14363 \div 53 = ?\) (
    Video Solution
    x
    Solution: 271
    Details:

    (Long Division #5 (03:15 mins) | Transcript)
    )
  6. \(45696 \div 64 = ?\) (
    Solution
    x
    Solution:
    714
    )

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