Converting Mix Numbers to Improper Fractions

Converting between mixed numbers and improper fractions. A mixed number is a number that combines a whole number with a fractional part. If we had a pie cut into four pieces and then three more quarter slices, that would be one and three quarter pies. One and three fourths is an example of a mixed number. An improper fraction is a fraction where the numerator is greater than the denominator. Here, we have seven quarters of a pie. This is seven fourths, which is an improper fraction. If we rearrange the slices, we can now see that seven fourths is the same as one and three quarters. Any mixed number can be converted into an improper fraction or the other way around. Any improper fraction can be converted into a mixed number. But is there a way we can do this conversion without cutting up a bunch of pies? We'll start by converting two and four fifths into an improper fraction. One way to think about this mixed number is that two and four fifths is the same as two plus four fifths, a whole number plus a fraction. So if we could find a way to convert the whole number two into a fraction, we could simply add the fractions. And the easiest way to add two fractions together is if they both have the same denominator. So we need to figure out how many fifths two is. Well, two is the same as two times one, and five fifths is the same as one. This is because if you have five slices of pie and each is one fifth, when you put them together, you have one whole pie. Now, if we change the two to 2/1, we can multiply the two fractions and get ten fifths, which makes two equal to ten fifths. Now, we can add ten fifths by the four fifths from the original mixed number, and we get 14 fifths. A quicker way to do this is to multiply the whole number part of the mixed number by the denominator of the fractional part of the mixed number. This becomes the numerator of the fraction version of the whole number. Then take the denominator of the fractional part of the mixed number and put it into the denominator of the fraction we're going to add to the fractional part of the mixed number. Then we multiply to get ten and add to get 14 fifths. Now we'll convert an improper fraction to a mixed number. The improper fraction is 12 sevenths. To do this conversion, we divide the numerator of the fraction, 12 by the denominator, seven. Seven goes into 121 time with a remainder of five. This becomes the whole number part of our mixed number, and the remainder five becomes the numerator of the fractional part. The denominator of the improper fraction becomes the denominator of the fractional part of the mixed number. So 12 sevenths equals one and five sevenths. In summary, to convert an improper fraction to a mixed number, divide the numerator by the denominator. The result of the division is the whole number part of the mixed number. The remainder becomes the numerator of the fractional part. The denominator of the improper fraction stays the denominator for the fractional part.