Converting Mixed Numbers to Improper Fractions | Converting Improper Fractions to Mixed Numbers

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to convert an improper fraction to a mixed number and how to convert a mixed number to an improper fraction now when converting between these keep in mind that they are always going to be equivalent for example if we convert a mixed number to an improper fraction both the mixed number and improper fraction are equivalent they are just in different forms depending on the situation or type of problem sometimes we want to have improper fractions and sometimes we want to have mixed numbers so we need to be able to convert between them let's jump into our examples starting with number one where we have 11 thirds this is an improper fraction the numerator the top number is greater than the denominator the bottom number this means we have a value greater than one whole let's change this to a mixed number we do this by dividing we divide the numerator by the denominator so 11 divided by 3. now once you have this down you'll be able to do it without writing it out but for this one let me write out the problem so we have 11 divided by three so how many whole groups of three out of eleven well three that gets us to nine that's going to be the whole number portion of our mixed number so three whole groups of three out of eleven three times three is nine and we end up with a remainder of two we did not hit 11 exactly so that remainder is going to be our numerator and then we use the original denominator of 3 for the denominator of our fractional part of the mixed number always check to see if you can simplify the fractional part of a mixed number two-thirds is in simplest form so we are done let's move on to number two where we have 46 tenths so again we need to divide 46 the numerator divided by 10 the denominator let's write this one out as well so we have 46 divided by 10. so we need to think how many whole groups of 10 do we have in 46 well 4 that gets us to 40. 4 whole groups of 10 so that's our whole number for our mixed number now we do not hit 46 exactly we have a remainder something left over so 4 times 10 is 40. let's subtract and we get 6. so a remainder of 6 that remainder is our numerator and we use our original denominator of 10 for our mixed number as well now the fractional part of the mixed number for number 2 can be simplified we have a greatest common factor of 2 for the 6 and 10 here so we can divide both of these by 2 and we get 4 6 divided by 2 is 3 10 divided by 2 is 5. so our final simplified mixed number is 4 and three-fifths let's move on to numbers 3 and 4 where we have mixed numbers and we are going to convert them to improper fractions and we do this by multiplying and then adding so i'll show you the process first and then show you how and why it works so we start at the bottom and work our way up we multiply and then add so 5 times 4 is 20 plus 2 is 22 so that is our numerator again we did 5 times 4 is 20 plus 2 is 22 we keep the denominator of 5 the same so 22 fifths is our improper fraction and the reason this works is because let's think of four wholes now i'm going to write out four wholes as a fraction using this denominator of five so for example one whole would be five over five and i'm picking five because that's our denominator so this is going to make it easier just using that denominator now we have four holes so five fifths five over five plus five over five that would represent two wholes but we need four so let's do another one there's three holes four holes plus our fractional part of two fifths so these right here represent the four wholes then we have the fractional part two-fifths so let's add all of these up five plus five is ten plus five is fifteen plus five is 20 plus 2 is 22 and our denominator is 5. so we can see that we got 22 fifths now using this method right here is a lot quicker it's a shorter way than writing everything out so again multiply and then add let's try another one and move on to number four where we have seven and one eighth so we start at the bottom and work our way up we multiply and then add so 8 times 7 is 56 plus 1 is 57 and then we keep our denominator of 8. so 57 8 for number 4. there you have it there's how you convert improper fractions to mixed numbers and mixed numbers to improper fractions i hope that helped thanks so much for watching until next time peace you