Think you’ll never be able to master long division? Think about the acronym DMSB, which stands for Divide, Multiply, Subtract, Bring down. But isn’t it easier to remember: Dad, Mother, Sister, Brother or Does McDonalds Serve Burgers? Both of these phrases can help you remember the steps of a long division problem. Dad corresponds with divide; mother corresponds with multiply, and so on. If you can remember the four steps, you are half way to learning how to do one of these problems.
Also, knowing your multiplication tables will make these problems easier. You can always use a multiplication table until you can memorize your facts.
Step One: Divide
Let's say your problem is 358/20. The first step is to divide. Remember 20 in this problem is called the divisor, and 358 is the dividend. The answer you write above the division symbol is called the quotient.
So, how many times will 20 go into 358? That is too large of a problem to undertake, and so you break up the division problem into smaller steps. The first problem you would work in this example is: How many times can you divide 20 into 35? The answer is 1. So, you put a 1 above the 5 on the quotient line. You have now divided.
Step Two: Multiply
The next step is multiply. You are going to multiply your answer from step one and your divisor. In this example, you are multiplying 1 x 20, which equals 20. You write this 20 underneath the 35 (which is the first part of the dividend, 358 from step one).
Step Three: Subtract
Next you are going to subtract. You will work the problem 35 – 20. The answer in this example is 15.
Step Four: Bring Down
The last step in the long division process is to bring down. This means you are bringing down the next number from the dividend that hasn't been used yet in the first small division problem. In this example, the number you are bringing down is 8. You are bringing it down and writing it next to the 15, which was the answer you got when you subtracted. Now, you have a new number 158 (which is also the new dividend. Your divisor is still 20.).
Starting All Over Again
Now, you are going to do the long division steps again with a new problem: 158/20. You will divide, multiply, subtract, and bring down.
Divide: how many times does 20 go into 158? The answer is 7 times. Write the 7 on the quotient line above the 8 and next to where you wrote the 1. Now on the quotient line, you have 18.
Multiply: Multiply the new answer you have from dividing, which is 7, with the divisor 20. You get 140. Write this underneath the 158.
Subtract: Subtract the two numbers: 158-140= 18.
Bring down: There is nothing left to bring down. Check to make sure the 18, the answer you got when you subtracted, is less than the divisor. In this case, the divisor is 20, so 18 is less. This means the problem was done correctly and there is a remainder of 18.
Next to the quotient of 17 write R18 for remainder of 18.
Putting it all together
Let’s put all the steps together to work one more problem. How about: 954/32?
Divide: The first problem you would work is: 95/32. The answer would be 2. This 2 should be written above the 5 on the quotient line.
Multiply: Next, you multiply the divisor and the quotient, which is 32 x 2 = 64.
Subtract: Write the 64 below 95. This problem would be 95 – 64 = 31.
Bring down: Bring down the 4 from 954. Bring it down next to the 31 you figured in the step above to make 314.
Divide: The new problem you are working is 314/32. How many times does 32 divide into 314? The answer is 9. Write 9 on the quotient line above the 4 and to the right of 2. So, you have the answer, quotient, of 29.
Multiply: Multiply 9 x 32, which equals 288. Write 288 below 314 at the bottom of the problem.
Subtract: You are now subtracting 314 – 288. This equals: 26
Bring down: There is nothing left to bring down from the original dividend of 954, so the problem is completed.
Your answer is 29 R 26. (29 with a remainder of 26)
Long Division Made Easy
You probably don’t want to hear this, but practice is the secret to remembering all the steps! You have to get used to the four steps, and remember that you may have to do them multiple times in one problem.
- Lesson Plans Page: http://www.lessonplanspage.com/mathlongdivisionwithacronymidea45-htm
- Smockity Frocks: http://www.smockityfrocks.com/2009/03/teaching-long-division.html