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