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Writing improper fractions as mixed numbers

CCSS.Math:

Video transcript

right seven over four as a mixed number so right now it's an improper fraction seven is larger than four let's write it as a mixed number so first I'm just going to show you a fairly straightforward way of doing and then we're going to think about a little bit about what it actually means so to figure out what seven over four represents as a mixed number let me write it in different colors so this is going to be equal to let me what the easiest way I do it you say well you take four you divide four into seven so you divide 4 into 7 4 into 7 so 4 if we're dealing with fourths 4 goes into 7 a total of one time four goes into seven a total of let me do this in another color the total of one time one times four is four and then what is our remainder 7 minus 4 is 3 so if we wanted to write this in plane well let me just do the problem then we'll think about what it means in a second so you see that 4 goes into 7 one time so you have one whole here you have one whole and then how much do you have left over well you have three left over you have three left over and that comes from right over there that is the remainder when you divide 4 into 7 three left over but it's three of your 4 or three-fourths left over so that's the way we just converted it from an improper fraction to a mixed number now it might seem a little bit like voodoo what I just did I divided 4 into seven it goes one time and then the remainder is three so I got one and three-fourths but why does that make sense why does that actually make sense so let's draw fourths let's draw literally seven fourths and maybe it'll become maybe it'll become clear so let's do a little square as a fourth so I'm going to do it let's say I have a square like that and that is 1/4 now let's think about what seven of those mean so let me copy and paste that copy and then paste it so that's so here I have two one fourths or you could say I have two fourths now I have three one fourths now I have four one fourths now this is a hole right I have four 1/4 this is a hole so let me start on another hole so now I have five now I have six one fourths and now I have seven one fourths now what does this look like so all I did is I rewrote 7/4 or seven one fourths I just kind of drew it for you now what does this represent well I have four fourths here so this is four over four this right here is 3 over 4 notice 7 over 4 is 4/4 with 3/4 left over so let me write it this way 7 over 4 is 4/4 with 3/4 left over now what is 4/4 what is 4/4 4/4 is one hole so you have one hole with 3/4 left over so you end up with 1 and 3/4 so that is the 3 for its part and that is your one hole hopefully that makes sense and hopefully you understand why it connects because you say well how many holes do you have when you're when you're dividing in the 4 into the 7 and getting the one you're essentially saying how many holes how many how many so the number of holes or you know you can imagine the number of whole pies and then how many pieces do we have left over well we have three pieces and each pieces of 4 so we have 3/4 left over so we have one whole pie and three pieces which are each of fourth left over