Dividing Decimals

Dividing decimals is another crucial math function that you need to master before moving on to theoretical manipulations. Dividing, like multiplying, has many steps that require practice to master.

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Necessary Skills

Depending on the problem, you may need the following skills.

Steps for Dividing Decimals

There are multiple division methods, but this post is all about long decimal division. Before beginning, let’s get you caught up on terms. The dividend is the leftmost number in a division problem, and it goes inside the “hut” on the problem. The number to the right of it is the divisor, which sits outside the division hut. The answer to the problem is the quotient.

It’s vital that you remember to keep columns lined up while dividing decimals. You have to manipulate decimal positions, and it is only possible with neat columns. If there is a decimal in the divisor, you need to move it right until it is out of the problem. Then you move the decimal in the dividend the same number of places.

Once you have moved the decimal, you should float it up to the top line. Make sure you maintain the position when you do this. Then you can ignore the decimal for the rest of the problem. Assuming you kept the position right, your quotient will be accurate.

Now that you have the problem set up, you can begin. You’re going to ask yourself how many times the divisor goes into the leftmost number in the dividend. You’ll write how many times the divisor goes in up top over that digit of the dividend.

Then you’ll multiply the divisor by the number you just wrote down. That answer you will write under the digit you were using in the dividend. Then you will subtract the two, writing the answer underneath. At this point, you drag the next digit in the dividend down to that answer.

Then you ask how many times the divisor goes into the answer at the bottom of the problem. You’ll repeat this process as long as there are digits in the dividend, taking care to always write in the correct column on the quotient line up top.

You may find that the number you are trying to fit the divisor in is smaller than the divisor. That does not work. Instead, write a zero above that number on the quotient line. Then bring the next digit in the dividend into the problem.

Sometimes, numbers do not divide evenly. If you find you’ve run out of digits, but the bottom of the problem is not a 0, you need to add 0s to the end of the dividend. You can then continue division until you bottom number is 0 or until you can round to the place specified in the problem.

Example Problems for Dividing Decimals

Let’s look at some problems to clear it up. Remember, it’s vital you keep your decimal division problems as neat and lined up as possible.

For the first problem, let’s do 4.8 divided by 2. In this case, 4.8 is the dividend and 2 is the divisor. We’ll start by asking how many times 2 goes into 4. That 2 gets written above the 4 in the dividend. The 2 times the divisor is 4, and when we subtract it from the number in the dividend, we get to write a 0 underneath. Then we drag down the 8, ask ourselves how many times 2 goes into 8, and write the resulting 4 in the quotient line. From there 4 times the divisor 2 is 8, and when we subtract that 8 from the 8, we get 0. The final answer is 2.4.

Dividing Decimals Example 1

For our next, let’s do 243 (dividend) divided by .3 (divisor). That means we need to move the decimal in the .3 one spot to the right, add a .0 to the 243, and move that to the right as well. Once we have it set up, we realize 3 does not go into the 2, so we must consider how many times 3 goes into 24. The answer is 8, which we write above the 4. After subtracting and writing the resulting 0 at the bottom of the problem, we bring down the 3. The divisor 3 will go into that 1 time, which we write on the quotient line. That 3 minus 3 is 0.  Since 3 will not go in that last 0, the final answer is 810.

Dividing decimals example 2

For our last example, let’s do 14.3 (dividend) divided by 5 (divisor). The 5 does not go into the 1, so we ask how many times 5 goes into 14. The answer, 2, goes onto the quotient line above the 4. Then 2 times 5 is 10, so we subtract that from 14 and write the 4 from that operation at the bottom of the problem. Since 5 doesn’t go into 4, we bring the 3 down to make 43. The divisor does go into that 8 times, which goes on the quotient line. Then we do 5 times 8, which is 40, and take that from 43. Then we add another 0 to the dividend, bring that down, and ask how many times 5 goes into 30. That makes our final answer 2.86.

Decimal Division example 3