Dividing a whole number by a fraction

let's see if we can figure out what 4 divided by 2/3 is and like always pause this video and see if you can figure it out on your own well one way to approach it is to realize that this is the same thing as 4 times the reciprocal of 2/3 so it'd be 4 times 3 over 2 and what is this going to be equal to you could pause the video again if you're so inspired well what need to realize is this is the same thing for could be written as a fraction as 4 over 1 so 4 over 1 times 3 halves and we've multiplied fractions before to do that you just multiply the numerators 4 times 3 is equal to 12 and you multiply the denominators 1 times 2 is equal to 2 12 halves well that's the same thing as 6 this is the same thing as 12 divided by 2 but a key question is why does this make sense you know I you know I said dividing by something is the same thing as multiplying by the reciprocal and to think about that let's draw 4 wholes so let me draw it in the same red color so let's say that this is one whole right over here this is 2 wholes this is 3 wholes and then this is four wholes so I have four wholes there and imagine splitting it up into groups that are each two-thirds of a whole so actually let me just divide everything into thirds real fast so I'm gonna divide everything into thirds into thirds so I'm gonna make each group a different color so here's one group that is 2/3 here is another group that is 2/3 here is another group that is or another section that I could say that represents 2/3 here is another section that represents 2/3 here is another section Ochs let me do it in a different color here is here is another section that can represent two thirds if I take those two blue thirds together that's two thirds and then last but not least I have another two thirds so how many sections that are each two thirds large do I have well I have one and then these is two and then I have three and then I have four and then these two combined to make a make my fifth section that is two thirds large and then finally I have six so I have six I can take four wholes and split it into six equal sections that are each two-thirds of a whole so 4 divided into sections that are two-thirds of a whole you will get six sections