Familiar with the tricks for dividing fractions and decimals? Homework Unlocked is here to help. Homework Unlocked offers homework help to parents so you can help your kids excel in math. Here, Homework Unlocked explains dividing decimals by simplifying fractions.

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## Dividing Decimals by Simplifying Fractions

This last method has the fewest number of steps. For this method:

- Stack the decimals
- Multiply them by a multiple of 10 to remove the decimal
- Simplify.

Like most math problems this is much easier to explain with examples so let’s go over a few.

**Example 1. Divide 0.7 by 0.2**

Step 1. Stack the problem into a fraction. Remember the number we are dividing (the dividend) is the numerator, and the number we are dividing by (the divisor) is the denominator.

0.7 ÷ 0.2 =

Step 2. Multiply the denominator and numerator by a multiple of 10 to remove the decimals. Remember that whatever you multiply the denominator by you must also multiply the numerator by so you don’t change the value of the fraction.

In this example, we only have to move the decimal over 1 place to make 0.7 and 0.2 whole numbers, in other words you have to multiply the numerator and denominator by 10.

Step 3. Simplify and Solve

this fraction is already simplified so we are all finished!

0.7 ÷ 0.2 = =

**Example 2. Divide 0.82 by 0.4**

Step 1. Stack the problem into a fraction

0.82 ÷ 0.4 =

Step 2. Multiply the denominator and numerator by a multiple of 10 to remove the decimal.

To make 0.82 a whole number we have to move the decimal over two places, in other words, you have to multiply by 100.

To make 0.4 a whole number we only have to move the decimal over one place so you only have to multiply by 10.

Remember, we have to multiply the denominator and the numerator by the same number so let’s choose the larger number, in this case 100.

Step 3. Simplify and Solve

When asks to simplify, first check to see if the denominator fits evenly into the numerator. If not, find the largest common factor of the denominator and numerator.

40 does not fit evenly into 82 so were have to find the largest common factor. In this case 2.

To simplify divide the numerator and denominator by 2

and we’re done!

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