# Converting Improper Fractions to Mixed Numbers and Decimals

The processes for converting improper fractions to mixed numbers and decimals share the same first step. I’ll demonstrate with a few examples. In this first example we have 34 over 5. The first step is to see how many times the denominator will go into the numerator and see with the remainder is.

So 5 will go into 34 six times with the remainder of 4. So this mixed number equivalent is going to be 6 and 4/5. Now we’ve already got our first step completed, we have the whole number.

So, we take the whole number and put it to the left of the decimal and then we take the fraction down here and we need to convert the fraction to another fraction with the denominator that’s the power of ten, so 10 or 100 or 1000.

In this case we can convert it to the denominator of 10 by multiplying top and bottom by 2. So this is equivalent to 8 over 10. Now we can take the numerator and put it to the right and decimal, so our decimal equivalent is 6.8.

In the second example we have 29 over 4. 4 goes into 29 seven times with the remainder 1. So a mixed number equivalent is 7 and 1/4. Now we take the whole number, put it to the left of the decimal, take the fraction and now we have to convert the fraction to a power of ten in the denominator.

4 won’t go into 10 evenly, but it will go into 100, so will multiply the top and bottom by 25. And that gives us 25/100. So now we can take the numerator and put it to the right of the decimal, 7.25. In this final example we have 63 over 8.

8 goes into 63 seven times with the remainder of 7. So we have 7 and 7/8. Once again we’ll pull down the 7, put it to the left of the decimal, and then convert this fraction to a denominator of a power of ten. Since the denominator is 8 we’re going to have to go with the denominator of 1000.

So, to do that, we’ll multiply top and bottom by 125. This gives us a denominator of 1000 and the numerator of 875. Now we can take the numerator put it to the right of the decimal which gives us a decimal equivalent of 7.875.

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by Mometrix Test Preparation | This Page Last Updated: February 17, 2022