How to Do Long Division

Long division is the process of solving a division problem by hand, on paper. While some schools, like those in Australia have dropped the requirement to use it, others, such as those in the UK, still consider it a basic element of primary math.^[1]Here's how to do it, whatever your reason for needing to know.

EditSteps

1. 1
   Start with an example. For instance, if there are six mushrooms in a 250 gram pack, how much does each mushroom weigh? In this case, we must divide 250 by 6.
   
   
   
2. 2
   Set up the equation. Place the dividend (number being divided) under the tableau, the divisor (number doing the division) to the left outside, and the quotient (answer) will eventually go on top.
   
   
   
3. 3
   Ask yourself how many times the divisor goes into the first digit of the dividend without exceeding it. In this case, you'd ask how many times 6 goes into 2. The answer is zero, so write that directly above the 2.
   
   
   
4. 4
   Ask yourself how many times the divisor goes into the first two digits of the dividend without exceeding it. If your answer to the previous step was 0 (which it is in the example), then expand the number by one digit. In this case, we'd ask how many times 6 can go into 25.
   
   
   
   • Work in terms of whole numbers. If you pull out a calculator, you'll discover that 6 goes into 25 a total of 4.167 times. That's not the correct answer for doing long division by hand. Instead, we want 4.
5. 5
   Put the number of times the divisor goes into the dividend above the tableau. For the example, place 4 above the 5, since we're putting it into 25.
   
   
   
6. 6
   Put the result of the divisor multiplied by the digit you just put into the quotient beneath the dividend. For the example, 6 times 4 is 24. After you've added 4 to the quotient (above the tableau), put 24 under 25.
   
   
   
7. 7
   Subtract the number you got in Step 6 from the dividend. For the example, we'll subtract 24 from 25. (Note that you won't subtract 24 from 250. The reason for this is that you are only working with the first 2 digits of 250 for right now.)
   
   
   
8. 8
   Bring down the next digit of the dividend, and add it to your result from Step 7. Your answer from Step 7 should have been one. Because 6 can't go into 1 without exceeding it, you need to bring down another digit. In this case, you'll grab the 0 from 250 and add it to 1, making it 10 (which 6 can go into).
   
   
   
9. 9
   Repeat the process with your new number. Figure out how many times 6 can go into 10. Add that number (1) to the quotient above the tableau. Then multiply 6 by 1, and subtract the result from 10. You should end up with 4.
   
   
   
10. 10
    Add a decimal point. At this point in the example, we need to add a decimal point to both the quotient and the dividend. Since 250 is a whole number, every digit after the decimal will be 0, making it 250.000.
    
    
    
11. 11
    Repeat the same process as above with your new number. Figure out how many times 6 can go into 40. Add that number (6) to the quotient above the tableau (past the decimal point). Then multiply 6 by 6, and subtract the result from 40. You should end up with 4 again.
    
    
    
12. 12
    Know when to stop. In the case of the example, you could keep getting 4 out of 40-36 forever, and add 6's to your quotient indefinitely. Instead of doing this, stop the problem and round the quotient. Because 6 is greater than 5, you would round up to 41.67.
    
    
    
13. 13
    Add the unit back to your answer. Because the example asked how much each mushroom in a 250-gram pack of 6 weighs, you'll need to put your answer into grams. Therefore, your final answer is 41.67 grams.
    
    
    

EditTips

• Start with simple calculations.
• Look for everyday practical examples. This is helpful in making the methodology stick, because you can relate it to real life utility.
• If you have time, it's a good idea to do calculations on paper first, then check with a calculator or computer. Remember that machines sometimes get the answers wrong for various reasons. If there is an error, then do a third check using logarithms. It is also good for your brain health to do mental workouts and not rely on machines all the time.
• A way to remember the steps to long division is: Does McDonald's Sell Cheese Burgers. D for divide the number. M for multiply. S for subtract. C for checking to see if the product of the multiplication problem is less than the divisor. And B for bring down if there's anything from the dividend.

EditThings You'll Need

• Paper
• Pen or pencil/Led pencil
• Eraser