# Converting Mixed Numbers to Decimals and Improper Fractions

**The methods for converting a mixed number to a fraction and a decimal are very different from one another.** I’m going to demonstrate how to convert to a fraction on all three of these examples first. Here we have 4 and 2/5. Now, to convert this to a fraction.

We have to take the denominator and multiply by a whole 5 times 4, and then add the numerator, 2. We have 5 times 4 is 20, plus 2 is 22. Now, we take that and that’s a new numerator, and we retain the same denominator, 5. **This is the fractional form of that mix number.**

Moving on to this one, we have 2 we’ll multiply it by 7 to get 14, and then we’ll add 1 to get 15. We retain the same denominator once again, 15/2. Finally, this one we have 4 times 3 is 12, and we’ll add this 3 to get 15. We have 15, and once again retaining the same denominator before, we have 15/4.

The method for converting to a decimal is to take the whole part of the number, in this case 4, add a decimal point, and then take the fractional part 2/5, and modify this fraction so that it retains its value but has a denominator of 100. To do this, we have to multiply the top and bottom by 20, 20/20.

2 times 20 is 40, 5 times 20 is 100. Once we have a denominator of 100, we can take the numerator and put it to the right of the decimal, 40. This number is 4.40. In this case we have 7, put a decimal point past it, and we have 1/2. To convert 1/2 to denominator of 100 we multiply by 50/50 and we get 50/100.

We can take this 50 and put it to the right of the decimal, we have 7.50. The third example we have a 3 and we have 3/4. To get 3/4 to have the denominator of 100 we multiply by 25 /25 and we get 75/100. Then we can put 75 to the right of the decimal, 3.75.