Visually dividing unit fraction by a whole number

we're asked to figure out what is 1/7 divided by 4 and they help us out with this diagram we have a whole divided into 7 equal sections each of those is 1/7 and we have one of those sevenths filled in so this is 1/7 right over here and then they divide it into four equal sections in fact they divide all of the seventh into four equal sections and so 1/7 which is this whole green bar divided by 4 well that would be this fraction of the whole that is in a question mark so can you pause this video and figure out what fraction of the whole is this question mark well when we divided the first seventh into four equal sections we also divided all of the seventh into four equal sections and so now the entire whole is twenty-eight equal sections because you have a four by seven grid you have one two three four rows and you still have your seven columns and you could count them 7 14 21 28 and so 1/7 divided by 4 is going to be one of these 28 sections so this right over here is 1 over 28 so this is 128 let's do another example we're told to use the number line below to help visualize one-fifth being divided by 3 so when as we go from 0 to 1 on the number line you could divide into five equal sections where that's 1/5 2/5 3/5 4/5 that of course 5/5 is equal to 1 but we want 1/5 divided by 3 so we took the section from 0 to 1/5 and we divide it into three equal sections and so the first of those sections this one right over here that would be 1/5 divided by 3 so what is this going to be equal to pause this video again and see if you can figure that out well the key realization is is when we divided each of the fifths into 3 more equal sections we can now think of each of these steps as a 15th because now we have 1 two three four five six seven eight nine 10 11 12 13 14 15 equal sections between 0 & 1 and where did that 15 come from well we had 5 equal sections and then we split each of those 5 into 3 more equal sections so 5 times 3 is 15 so this right over here is 1 15 this is to 15 this is 3 15th which is equivalent to 1/5 and we could keep going on and on and on but the key realization here is if I take that first 1/5 and if I divide into three equal sections and I go only as far as that first of the three equal sections that is going to be one fifteenth one fifteenth and we are done