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How to Divide Big Numbers with Long Division

To divide larger numbers, use long division. Unlike the other Big Four operations, long division moves from left to right. For each digit in the dividend (the number you’re dividing), you complete a cycle of division, multiplication, and subtraction.

In some problems, the number at the very bottom of the problem isn’t a 0. In these cases, the answer has a remainder, which is a leftover piece that needs to be accounted for. In those cases, you write r followed by whatever number is left over.

Sample questions

  1. Divide 956 / 4.

    239. Start off by writing the problem like this:

    image0.jpg

    To begin, ask how many times 4 goes into 9 — that is, what’s 9 / 4? The answer is 2 (with a little left over), so write 2 directly above the 9. Now multiply 2 x 4 to get 8, place the product directly below the 9, and draw a line beneath it:

    image1.jpg

    Subtract 9 – 8 to get 1. (Note: After you subtract, the result should be less than the divisor (in this problem, the divisor is 4). Then bring down the next number (5) to make the new number 15.

    image2.jpg

    These steps are one complete cycle. To complete the problem, you just need to repeat them. Now ask how many times 4 goes into 15 — that is, what’s 15 / 4? The answer is 3 (with a little left over). So write the 3 above the 5, and then multiply 3 x 4 to get 12. Write the product under 15.

    image3.jpg

    Subtract 15 – 12 to get 3. Then bring down the next number (6) to make the new number 36.

    image4.jpg

    Another cycle is complete, so begin the next cycle by asking how many times 4 goes into 36 — that is, what’s 36 / 4? The answer this time is 9. Write down 9 above the 6, multiply 9 x 4, and place this below the 36.

    image5.jpg

    Now subtract 36 – 36 = 0. Because you have no more numbers to bring down, you’re finished, and the answer (that is, the quotient) is the very top number of the problem:

    image6.jpg
  2. Divide 3,042 / 5.

    608 r 2. Start off by writing the problem like this:

    image7.jpg

    To begin, ask how many times 5 goes into 3. The answer is 0 — because 5 doesn’t go into 3 — so write a 0 above the 3. Now you need to ask the same question using the first two digits of the divisor: How many times does 5 go into 30 — that is, what’s 30 / 5? The answer is 6, so place the 6 over the 0. Here’s how to complete the first cycle:

    image8.jpg

    Next, ask how many times 5 goes into 4. The answer is 0 — because 5 doesn’t go into 4 — so write a 0 above the 4. Now bring down the next number (2), to make the number 42:

    image9.jpg

    Ask how many times 5 goes into 42 — that is, what’s 42 / 5? The answer is 8 (with a little bit left over), so complete the cycle as follows:

    image10.jpg

    Because you have no more numbers to bring down, you’re finished. The answer (quotient) is at the top of the problem (you can drop the leading 0), and the remainder is at the bottom of the problem. So 3,042 / 5 = 608 with a remainder of 2. To save space, write this answer as 608 r 2.

Practice questions

  1. Divide 741 / 3.

  2. Evaluate 3,245 / 5.

  3. Figure out 91,390 / 8.

  4. Find 792,541 / 9.

The following are the answers to the practice questions:

  1. 247

    image11.jpg
  2. 649

    image12.jpg
  3. 11,423 r 6

    image13.jpg
  4. 88,060 r 1

    image14.jpg
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