Dividing a Mixed Number by a Fraction: A Step-By-Step Explanation | Math with Mr. J

welcome to math with Mr Jay [Music] in this video I'm going to cover how to divide a mixed number by a fraction let's jump into our example where we have 2 and 4 7 divided by one-fifth now the first thing that we need to do is convert the mixed number to an improper fraction that way we just have a numerator and a denominator and we can go through our dividing fractions steps keep switch flip so let's convert 2 and 4 7 to an improper fraction so we start at the bottom we multiply and then add so the denominator times the whole number 7 times 2 is 14 and then add the numerator 14 plus 4 is 18. that is our numerator of the improper fraction and then we keep the denominator of seven the same divided by one-fifth so I rewrote the problem with the mixed number as an improper fraction now let's go through our steps keep switch flip so keep eighteen sevenths switch to multiplication and then flip one-fifth so 5 is now the numerator and one is now the denominator now we can multiply straight across let's start with the numerators 18 times 5 that gives us 90. now for the denominators 7 times 1 that gives us seven so we end up with 97 which is our answer but it's an improper fraction so let's convert it to a mixed number we do that by dividing the numerator 90 by the denominator 7. so we have ninety divided by seven so how many whole groups of seven in ninety well let's work through this off to the side here so 90 divided by seven nine divided by seven we have one one whole group of seven in nine multiply one times seven is seven subtract nine minus seven is two bring down and now we repeat so we divide twenty divided by seven how many whole groups of seven in twenty well two two times seven is fourteen subtract 20 minus 14 gives us a remainder of 6. so 12 whole groups of seven in ninety that's the whole number of our mixed number and then we have a remainder of six we don't hit 90 exactly that remainder is the numerator of the mixed number and then we keep the denominator of seven the same so we end up with 12 and 6 7. we can always look to see if we can simplify the fractional part of a mixed number 6 7 is in simplest form the only common factor between six and seven is one so we are done 12 and 6 7. so there you have it there's how to divide a mixed number by a fraction convert the mixed number to an improper fraction and then go through the steps keep switch flip I hope that helped thanks so much for watching until next time peace