Dividing Decimals

Dividing decimals is very challenging and many teachers allow students to use a calculator whenever it comes up. Still, you should know how to do so on your own and learn how to estimate the answer so you can tell if the calculator's answer is reasonable. Let's begin by reviewing the terminology. If you're looking at:

The x is called the dividend, the y is the divisor, and z is the quotient. You may also see division expressed as a fraction:

$\frac{x}{y}=z$

Dividing decimals step by step

Step 1: The first step is estimating your answer by rounding. This will tell you if your final answer is way off later on.

Step 2: Move the divisor's decimal place n places to the right to make it a whole number. Then, move the decimal place of the dividend an equal number of places to the right to maintain the same relationship, adding zeros if you need to.

Step 3: Next, divide as usual. If the divisor doesn't go into the dividend evenly, multiply the dividend by powers of 10 until you get a remainder of zero or a repeating pattern emerges.

Step 4: Place a decimal point in the quotient directly above where it appears in the dividend, and check your work by comparing your answer to the estimate you made in the first step.

Dividing decimals: A sample problem

$\frac{0.45}{3.6}$

The divisor is greater than the dividend, so we expect an answer of less than one. Since 0.45 is about a tenth of 3.6, we expect an answer around 0.1. That's the estimate we'll use.

Since the divisor isn't a whole number, we're going to move the decimal point one place in both the divisor and the dividend. That means we're looking at:

$\frac{4.5}{36}$

Since 36 is bigger than 4.5, we multiply 4.5 by 100 or ${10}^2$ , to get 450. When we divide 450 by 36 using long division we get an answer of 125 and have a remainder of zero. Finally, since we multiplied one number by 100, and the other by 10, we need to divide the answer we got by 1000 $(100\times 10)$ , giving us a final answer of 0.125. That's pretty close to 0.1, so our initial estimate makes sense.

A shortcut for dividing decimals

Sometimes, it's easier to use mental math to divide decimals than the procedure above. For example:

$\frac{0.42}{70}$

You probably don't know the answer to this offhand, but you do know that $\frac{42}{7}=6$ . If the dividend is decreased by a factor of 10, then the quotient will also decrease by a factor of 10:

$\frac{42}{7}=6$

$\frac{4.2}{7}=0.6$

$\frac{0.42}{7}=0.06$

Similarly, if the divisor is increased by a factor of 10, then the quotient will decrease by a factor of 10:

$\frac{0.42}{70}=0.006$

We've successfully solved the problem!

Dividing decimals practice questions

a. $\frac{0.55}{7.5}$

0.07333333..

b. $\frac{0.34}{9.8}$

0.03469387755

c. $\frac{0.4}{1.2}$

$\frac{0.4}{1.2}=\frac{4}{12}=\frac{1}{3}$

0.333333..

Topics related to the Dividing Decimals

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Operations with Decimals

Decimals an Introduction

Flashcards covering the Dividing Decimals

6th Grade Math Flashcards

Common Core: 6th Grade Math Flashcards

Practice tests covering the Dividing Decimals

MAP 6th Grade Math Practice Tests

6th Grade Math Practice Tests

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