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Dividing with Decimals

Many times students freeze at the sight of a decimal, but there’s no need to do so.
Let me help you put the decimal drama to rest.

Before we begin, let’s review some vocabulary. “40.8” is called the dividend. “8” is the divisor, and the answer to a division problem is called the quotient.

How to do division when there is a . . .

Decimal in the Dividend

1. Place a decimal directly above the existing decimal. That’s it for the decimal drama!
2. Divide as usual. The quotient / answer is below.

Dividing with Decimals in the Divisor and Dividend

Decimals in the divisors are a “no- no.” So to make life easier, follow these steps.

1. Move the decimal to the right until the decimal is behind the number which makes it into a whole number.

2. Make note of how many times the decimal was moved to the right.

In this example, the decimal would move once to change “.8” into “8”

Thus, move the decimal in the dividend to the right the same number of times.
Now the problem reads 405.6 divided by 8.

3. Place a decimal directly above the existing decimal.
4. Divide as usual.
The quotient is 50.7

Another example: 4056 divided by .8

1. Move the decimal in the divisor to make it a whole number.

2. Move the decimal in the dividend the same number of times
But wait a minute! Where is the decimal in the dividend? Do you see it? I don’t!

Oh yeah, all whole numbers have an implied or invisible decimal after the last digit. Therefore the decimal in 4056 is behind the six. Can you see it now? “4056.” Move the decimal once and use a zero as a place holder. Thus, the dividend looks like this, “40560."

3. Now that the new location of the decimal has been found, place another decimal in the quotient area directly above the existing decimal.

4. Divide as usual
The answer / quotient is 5070

Note: To check the accuracy of any division problem, multiply the divisor by the quotient. Add any remainder to the product. For example, to check the last problem we multiply .8 times 5070. The product is 4056.0 which is the original dividend.

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