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Math for Kids23 chapters | 325 lessons

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Instructor:
*Laura Pennington*

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

This lesson will explain the extra steps we need to take to divide a whole number by a decimal. We will also go over why those extra steps work and we will look at some examples of carrying out this process.

Most of us know how to divide a whole number by a whole number. There are many different algorithms that can be used to see how many times a divisor fits into a dividend when both the numbers are whole, but what do we do if the divisor is a decimal. In other words, how do we divide a whole number by a decimal? This is what we are going to explore and learn how to do.

Thankfully, to divide a whole number by a decimal, we just add a couple of steps to the process of dividing whole numbers, and these steps are not very difficult. They are as follows.

- Count how many places we need to move the decimal to the right in the divisor to create a whole number.
- Move the decimal this many places to the right in both the divisor and the dividend. This will require adding zeros to the end of the dividend.
- You now have a division problem of two whole numbers and you can carry out the division using the algorithm that you are most comfortable with.

For example, suppose we wanted to divide the whole number 84 by the decimal 1.2. We would first count how many places we need to move the decimal to the right in 1.2 to get a whole number. This would be one place because if we move the decimal one place to the right, we get the whole number 12.

The next step is to move the decimal one place to the right in both 84 and 1.2 to get 840 and 12. We now have 840 divided by 12, which is a division problem of whole numbers. We can carry out this division using the algorithm of our choice to get 70.

The steps we take to divide a whole number by a decimal are as follows.

- Count how many places we need to move the decimal to the right in the divisor to create a whole number.
- Move the decimal this many places to the right in both the divisor and the dividend. This will require adding zeros to the end of the dividend.
- You now have a division problem of two whole numbers and you can carry out the division using the algorithm that you are most comfortable with.

This may leave you wondering why we can just move the decimal in this way. Wouldn't that change the problem? Thankfully, no, and we're going to see why. Let's look again at our example of 84 divided by 1.2 to illustrate why this process works.

In our example, we are dividing the whole number 84 by the decimal number 1.2. This can be illustrated in the following image.

When we look at the decimal problem as a fraction 84 / 1.2 as shown in the image, we know that we can multiply both the numerator and denominator by the same number without changing the value of the fraction.

We saw that the first step is to count the number of places we need to move the decimal to the right in 1.2 to create a whole number, which is one. The next step is to move the decimal this many places to the right in both 84 and 1.2 to get 840 and 12.

Counting the number of decimal places we need to move to the right in 1.2 to get a whole number corresponds to finding what power of 10 we need to multiply 1.2 by in order to get a whole number. We said one place, and 1.2 x 10 1 = 1.2 x 10 = 12.

Moving the decimal one place to the right in both 84 and 1.2 actually corresponds to multiplying both 1.2 and 84 by 10, and as we said, when we think of the division problem as a fraction 84 / 1.2, this corresponds to multiplying both the numerator and denominator by 10, which doesn't change the value of the fraction. We see that this is why we are able to move the decimal in this way without changing the value of the division problem.

In general, counting the number of places we need to move the decimal corresponds to finding the power of 10 that we need to multiply both the dividend and divisor by, and moving the decimal in both numbers corresponds to carrying out that multiplication.

Dividing whole numbers by decimals can show up anywhere in the world around us. For instance, suppose you ran a total of 29 miles in 7.25 days, and you want to know on average how many miles per day that is. To figure this out, you would divide 29 by 7.25, a whole number by a decimal.

First, you count the number of places you need to move the decimal to the right in 7.25 to get a whole number, which is two, because if we move the decimal two places to the right in 7.25, we get 725. The next step is to move the decimal two places to the right in both 29 and 7.25 to get 2900 and 725. Now we have the division problem 2900/725, which we can carry out using the method of our choice to get 4.

We see that you ran an average of 4 miles per day. Good job!

These types of division problems show up often in the real world, so it is nice to know that they only require a couple of easy extra steps to solve the problem.

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Math for Kids23 chapters | 325 lessons

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