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Fractions & Decimals

Fractions & Decimals

At a Glance - Dividing Decimals

Okay let's be honest, long division with decimals can be very tedious. Also, beyond pre-algebra you probably will rarely, if ever, need to do this without a calculator.

Having said that, long division with decimals is a skill often tested on state and national tests, so it makes sense for you to learn how to do it without a calculator. Using graph paper when practicing is really helpful for keeping track of place values and decimals.

Here are some important vocabulary terms to keep in your pocket throughout this section:

Quotient: the answer to a division problem.

  • In the problem 45 / 5 = 99 is the quotient.

Dividend: the number being divided.

  • In the problem above, 45 is the dividend.

Divisor: the number doing the dividing.

  • In the problem above, 5 is the divisor.

dividend, divisor, quotient

The key to division with decimals is to move the decimal out of the divisor and make up for that move in the dividend. Then follow the steps for long division as usual. The decimal in the quotient will be in the same place as it is in the dividend.

Now, we know that was a lot of math mumbo-jumbo, but the examples below will help to make sense of this.

Look Out: you cannot reverse the order in which you divide two numbers. Make sure that you put the first number (the dividend) inside the division box!

Long Division Example 1

Divide 7.54 / 3

Long Division Example 2

Divide 312.63 / 0.5

Long Division Example 3

Divide 12 / 1.25

Exercise 1

Divide 5.75 / 5.

Exercise 2

Divide 72.08 / 0.5.

Exercise 3

Divide 90 / 1.25.

Exercise 4

Divide 4.5678 / 0.9.

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