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Division with Decimal Results
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The videos in this lesson will teach you how to do division with multiple digits. This process is applicable for numbers that divide evenly, and those with decimal answers. The videos in this lesson demonstrate one way to do division. If you are familiar with another algorithm or pattern, you are welcome to use it. The important thing is to understand what you are doing and why so you can apply it to real-world situations.

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.

The following video will walk through these steps in a couple of examples.

Dividing by single whole number

Video Source (07:23 mins) | Transcript

The same process of division is used, even when we get a decimal answer. Remember, we can always add 0’s after the decimal place on a number (for example: 2 = 2.0 = 2.00). The following video will show how to divide with decimals.

Division algorithm (Answers with decimals)

Video Source (02:54 mins) | Transcript

Repeating decimals

Video Source (05:57 mins) | Transcript

Once again, you may find yourself going slowly through this process. That’s alright. To help yourself speed up, try studying and memorizing your 1-digit multiplication facts. Knowing these will help you as you follow the division steps.

Additional Resources

Practice Problems

Evaluate the following expression:
  1. \(77 ÷ 2 = ?\) (
    Solution
    x
    Solution: \(38.5\)
    Details:
    Start by dividing in parts. First, divide 7 by 2.
    This image shows a division symbol of a vertical line and a horizontal line coming together as though they are making the top left corner of a rectangle. Inside this imaginary rectangle is the number 77. To the left of the vertical line and on the same horizontal plane as the 77 is the number 2. This means 77 is being divided by the 2.

    Place your answer above the line and directly above the 7. The answer will be 3, because 2 goes into 7 about 3 times.
    This image is the same as the previous one except now there is a 3 above the division symbol horizontal line and in the same column as the leftmost 7 in the number 77. In this case this means the 3 is in the tens place just as the leftmost seven is in the tens place in 77.

    Place the result of \(2 \times 3\) below the 7 and subtract.
    This image is the same as the previous one except now there is a 6 in the tens column below the leftmost 7 in 77. There is also a subtraction symbol to the left of the 6. A horizontal line is below the 6 indicating we will put our new number below that line.

    The difference between 7 and 6 is 1. Place the answer directly below the 6.
    This image is the same as the previous one except now there is a 1 below the subtraction horizontal line directly below the 6. This is the solution of 7-subtract-six from the previous image.

    Next step is to bring down the next number. Bring the second 7 down and place it next to the 1. Now divide 17 by 2.
    This image is the same as the previous image except now there is a downward arrow from the rightmost 7 in 77 and a 7 is written to the right of the 1. This makes the new number below the subtraction line 17.

    Divide 17 by 2. The answer is about 8.
    This image is the same as the previous image except now, above the division symbol, to the right of the three is a number 8. This indicates that 2 goes into 17 eight times.

    Place the 16, the results of \(8 \times 2\), below the 17 and subtract.
    This image is the same as the previous image except now there is a 16 directly below the 17, a new subtraction symbol to the left of the 16, and a new horizontal line below it as well.

    The difference between 17 and 16 is 1. Place the 1 below the 6.
    This image is the same as the previous one except now there is a 1 directly below the 7 and 6 in 17 and 16 respectively. This 1 is also below the newest horizontal line.

    At this point, there’s a remainder. Add a decimal and a zero after the 77.
    This image is the same as the previous one except now there is a decimal point and a zero written to the right of the 77. This makes it seventy-seven-point-zero. An arrow is used to draw attention to this new part of the number.

    Continue, by bringing the new zero down.
    This image is the same as the previous one except now there is a downward arrow from the 0 in seventy-seven-point-zero. It points to a zero to the right of the 1 below the most recent horizontal line. This makes the newest number we will be dividing a 10.

    Now divide 10 by 2 which is 5 and place it next to the 8 above our new 0 in the solution.
    This image is the same as the previous one except now there is a 5 above the division symbol and to the right of the 8. This makes the number above the division symbol three-eight-five from left to right.

    Place the results of \(2 \times 5\) below the 10 and subtract. The difference between 10 and 10 is zero. When we reach 0 we stop dividing.
    This image is the same as the previous one except that below the 10 at the bottom of our problem there is another 10. They are written directly one over the other. There is also a subtraction symbol to the left and a new horizontal line below the new 10. Below this horizontal line is zero-zero. This is because the solution to 10 subtract 10 is zero.

    Place the decimal point between 38 and 5. Notice that the decimal point in the answer is placed directly above the decimal point in \(77.0\).
    This image is the same as the previous one except there is a decimal point in the number above the division symbol. The decimal point is between the 8 and the 5. There is an arrow pointing it out. This makes the solution to the division problem thirty-eight-point-five.

    The answer is \(38.5\)
    )
  2. \(339 ÷ 4 = ?\) (
    Solution
    x
    Solution: \(84.75\)
    Details:
    Start by dividing 33 by 4.
    This image shows a division symbol of a vertical line and a horizontal line coming together as though they are making the top left corner of a rectangle. Inside this imaginary rectangle is the number 339. To the left of the vertical line and on the same horizontal plane as the 339 is the number 4. This means 339 is being divided by the 4.

    The number 4 goes into 33 about 8 times.
    This image is the same as the previous one except now there is an 8 above the division symbol horizontal line and in the same column as the rightmost 3 in the number 339. In this case this means the 8 is in the tens place just as the rightmost three is in the tens place in 339.

    Place the product (answer) of \(8 \times 4 = 32\) below 33 and subtract.
    This image is the same as the previous one except now there is a 33 below the 33 in 339. There is also a subtraction symbol to the left of the 32. A horizontal line is below the 32 indicating we will put our new number below that line.

    There is a remainder of 1 remainder. Place it below the line and bring down the 9.
    This image is the same as the previous one except now there is a 1 below the subtraction horizontal line directly below the 32. This is the solution of 33-subtract-32 from the previous image.

    Divide 19 by 4.
    This image is the same as the previous image except now there is a downward arrow from the 9 in 339 and a 9 is written to the right of the 1. This makes the new number below the subtraction line 19.

    Four goes into 19 about 4 times, because of \(4 \times 4 = 16\). Place the new 4 next to the 8 in the answer.
    This image is the same as the previous image except now, above the division symbol, to the right of the 8 is a number 4. This indicates that 4 goes into 19 four times.

    Place 16, the product of \(4 \times 4\), below the 19 and subtract.
    This image is the same as the previous image except now there is a 16 directly below the 19, a new subtraction symbol to the left of the 16, and a new horizontal line below it as well.

    The difference between 19 and 16 is 3. Place the 3 below the right-most column.
    This image is the same as the previous one except now there is a 3 directly below the 9 and 6 in 19 and 16 respectively. This 3 is also below the newest horizontal line.

    Next, add a decimal point after the 9 in the dividend (339) and include two zeros.
    This image is the same as the previous one except now there is a decimal point and two zeros written to the right of the 339. This makes it three-hundred-thirty-nine-point-zero. An arrow is used to draw attention to this new part of the number.

    Continue the same pattern. Bring the next number down. In this case, the zero. Divide 30 by 4.
    This image is the same as the previous one except now there is a downward arrow from the 0 in 339.00. It points to a zero to the right of the 3 below the most recent horizontal line. This makes the newest number we will be dividing a 30.

    4 goes into 30 about 7 times.
    This image is the same as the previous one except now there is a 7 above the division symbol and to the right of the 84. This makes the number above the division symbol eight-four-seven from left to right.

    Place 28, the product of \(4 \times 7\), below the 30 and subtract.
    This image is the same as the previous one except that below the 30 at the bottom of our problem there is 28. They are written directly one over the other. There is also a subtraction symbol to the left and a new horizontal line below the new 30.

    The difference between 30 and 28 is 2. Place the 2 below the line. Notice we had to do some regrouping in order to do this subtraction.
    This image is the same as the previous one, except that the 3 in 30 is crossed out and under it is written 2. The 0 is 30 is also crossed out and under it is written a 10. There is a new horizontal line on the bottom, below it is written 2. This indicates that 2 is the result when 28 is subtracted from 30.

    Continue by bringing the last 0 down, next to the 2. Divide 20 by 4.
    This image is the same as the previous one, except that the second zero in 339.00 is brought down below the bottom horizontal line, right next to the number 2. The new number under the bottom horizontal line is 20.

    The number 4 goes into 20 exactly 5 times, because 4 × 5 is 20. Subtract to get a zero remainder.
    This image is the same as the previous one, except that there's a 5 written on the top right next to 7. Now the top line consists of the numbers 8, 4, 7, and 5.

    This image is the same as the previous one, except that there's another 20 written below the 20, with a subtraction sign to its right. There's a new horizontal line on the bottom, below which two zeros are written, indicating that 20 subtracted from 20 equals zero.

    The last step is to place the decimal point in our answer. Place the decimal point between 84 and 75 lined up with the decimal point in the dividend, \(339.00\).
    This image is the same as the previous one, except that a decimal point is placed on the top line between numbers 4 and 7. This makes the final answer eighty-four-point-seventy-five.

    Our final answer: \(84.75\)
    )
  3. \(21 ÷ 8 = ?\) (
    Video Solution
    x
    Solution: \(2.63\), when rounded to the nearest hundredth.
    Details:

    (Video Source | Transcript)
    )
  4. \(37 ÷ 3 = ?\) (
    Solution
    x
    Solution: \(12.33\), when rounded to the nearest hundredth.
    )
  5. \(559 ÷ 6 = ?\) (
    Video Solution
    x
    Solution: \(93.17\), when rounded to the nearest hundredth.
    Details:

    (Video Source | Transcript)
    )
  6. \(258 ÷ 7 = ?\) (
    Solution
    x
    Solution: \(36.86\), when rounded to the nearest hundredth.
    )

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