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How to do long division with decimals in 5th grade?

Published in Decimal Division 3 mins read

Long division with decimals is very similar to regular long division! The key is to deal with the decimal point correctly. Here's how:

Steps for Long Division with Decimals:

  1. Set up the problem: Write the problem as you normally would for long division. The number you are dividing into (the dividend) goes inside the "house," and the number you are dividing by (the divisor) goes outside.

  2. Make the divisor a whole number: If the divisor (the number outside the "house") has a decimal, move the decimal point to the right until it becomes a whole number.

  3. Move the decimal in the dividend: Move the decimal point in the dividend (the number inside the "house") the same number of places to the right as you did in the divisor. You might need to add zeros to the end of the dividend to do this.

  4. Bring the decimal up: Place the decimal point directly above the decimal point in the dividend, in the answer space.

  5. Divide as usual: Perform long division as you normally would, ignoring the decimal point (since you've already taken care of it!).

  6. Continue dividing (add zeros if needed): If you have a remainder and want to continue dividing to get a more precise answer, add zeros to the end of the dividend (inside the "house") and continue dividing.

Example:

Let's say we want to divide 26.25 by 5.

  1. Set up:

         ______
    5 | 26.25
  2. Make the divisor a whole number: Our divisor (5) is already a whole number, so we don't need to do anything.

  3. Move the decimal in the dividend: We don't need to move the decimal because the divisor is already a whole number.

  4. Bring the decimal up:

         ______.
    5 | 26.25
  5. Divide as usual:

    • 5 goes into 2 zero times.
    • 5 goes into 26 five times (5 x 5 = 25). Write 5 above the 6.
    • Subtract 25 from 26, which gives you 1.
    • Bring down the 2. You now have 12.
    • 5 goes into 12 two times (5 x 2 = 10). Write 2 above the 2 after the decimal.
    • Subtract 10 from 12, which gives you 2.
    • Bring down the 5. You now have 25.
    • 5 goes into 25 five times (5 x 5 = 25). Write 5 above the 5 after the decimal.
    • Subtract 25 from 25, which gives you 0.
         5.25
    5 | 26.25
        -25
        ----
         1 2
         -1 0
         ----
           25
           -25
           ----
            0

So, 26.25 divided by 5 is 5.25

Another Example (with a decimal in the divisor):

Let's divide 29.4 by 5.25.

  1. Set up:

         ______
    5.25| 29.4
  2. Make the divisor a whole number: Move the decimal two places to the right in 5.25 to make it 525.

  3. Move the decimal in the dividend: Move the decimal two places to the right in 29.4. We need to add a zero: 29.4 becomes 2940.

         ______
    525| 2940.
  4. Bring the decimal up:

         ______.
    525| 2940.
  5. Divide as usual: 525 goes into 2940 five times.

        5.
    525| 2940.
       -2625
       ------
        315
  1. Continue dividing (add zeros if needed): Add a zero to the dividend to get 3150. 525 goes into 3150 six times.
        5.6
    525| 2940.0
       -2625
       ------
        315 0
        -315 0
        ------
           0

Therefore, 29.4 divided by 5.25 is 5.6

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