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Visually dividing unit fraction by a whole number

CCSS Math: 5.NF.B.7, 5.NF.B.7a

Video transcript

- 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.