LESSON: Dividing by Decimals

READ: Divide Decimals by Decimals by Rewriting Divisors

Divide Decimals by Decimals by Rewriting Divisors as Whole Numbers

In our introductory problem, Miles is working on dividing up sand. If you were going to complete this problem yourself, you would need to know how to divide decimals by decimals.

How can we divide a decimal by a decimal?

To divide a decimal by a decimal, we have to rewrite the divisor. Remember that the divisor is the number that is outside of the division box. The dividend is the number that is inside the division box.

Let’s look at an example.

Example

$2.6 \overline{)10.4 \;}$

In this problem, 2.6 is our divisor and 10.4 is our dividend. We have a decimal being divided into a decimal. Whew! This seems pretty complicated. We can make our work simpler by rewriting the divisor as a whole number.

How can we do this?

Think back to the work we did in the last section when we multiplied by a power of ten. When we multiply a decimal by a power of ten we move the decimal point one place to the right.

We can do the same thing with our divisor. We can multiply 2.6 times 10 and make it a whole number. It will be a lot easier to divide by a whole number.

2.6 $\times$ 10 $=$ 26

What about the dividend?

Because we multiplied the divisor by 10, we also need to multiply the dividend by 10. This is the only way that it works to rewrite a divisor.

10.4 $\times$ 10 $=$ 104

Now we have a new problem to work with.

$& \overset{ \qquad 4}{26\overline{ ) 104 \;}}$

Our answer is 4.

What about if we have two decimal places in the divisor?

Example

$.45 \overline{)1.35 \;}$ In this example, we want to make our divisor .45 into a whole number by multiplying it by a power of ten. We can multiply it by 100 to make it a whole number. Then we can do the same thing to the dividend.

Here is our new problem and quotient.

$& \overset{ \qquad 3}{45\overline{ ) 135 \;}}$

Now it is time for you to practice a few. Rewrite each divisor and dividend by multiplying them by a power of ten. Then find the quotient.

$1.2 \overline{)4.8 \;}$
$5.67 \overline{)11.34 \;}$
$6.98 \overline{)13.96 \;}$

Take a minute to check your rewrite and quotient. Is your work accurate?