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A recipe for banana oat muffins calls for 3/4 of a cup of old-fashioned oats. You are making 1/2 of the recipe. How much oats should you use? So if the whole recipe requires 3/4 of a cup and you're making half of the recipe, you want half of 3/4, right? You want half of the number of old-fashioned oats as the whole recipe. So you want 1/2 of 3/4. So you just multiply 1/2 times 3/4, and this is equal to-- you multiply the numerators. 1 times 3 is 3. 2 times 4 is 8. And we're done! You need 3/8 of a cup of old-fashioned oats. And let's visualize that a little bit, just so it makes a little bit more sense. Let me draw what 3/4 looks like, or essentially how much oats you would need in a normal situation, or if you're doing the whole recipe. So let me draw. Let's say this represents a whole cup, and if we put it into fourths-- let me divide it a little bit better. So if we put it into fourths, 3/4 would represent three of these, so it would represent one, two, three. It would represent that many oats. Now, you want half of this, right? Because you're going to make half of the recipe. So we can just split this in half. Let me do this with a new color. So you would normally use this orange amount of oats, but we're going to do half the recipe, so you'd want half as many oats. So you would want this many oats. Now, let's think about what that is relative to a whole cup. Well, one way we can do it is to turn each of these four buckets, or these four pieces, or these four sections of a cup into eight sections of a cup. Let's see what happens when we do that. So we're essentially turning each piece, each fourth, into two pieces. So let's divide each of them into two. So this is the first piece. We're going to divide it into two right there, so now it is two pieces. And then this is the second piece right here. We divide it into one piece and then two pieces. This is the third piece, so we divide it into one, two pieces, and this is the fourth piece, or the fourth section, and we divide it into two sections. Now, what is this as a fraction of the whole? Well, we have eight pieces now, right? One, two, three, four, five, six, seven, eight, because we turned each of the four, we split them again into eight, so we have 8 as the denominator, and we took half of the 3/4, right? Remember, 3/4 was in orange. Let me make this very clear because this drawing can get confusing. This was 3/4 right there. So that is 3/4. This area in this purple color is 1/2 of the 3/4. But let's think about it in terms of the eights. How many of these sections of eight is it? Well, you have one section of eight here, two sections of eight there, three sections of eight, so it is 3/8. So hopefully that makes some sense or gives you a more tangible feel for what it means when you take 1/2 of 3/4.

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Multiplying fractions word problem: muffins (video) | Khan Academy

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A recipe for banana oat muffins calls for 3/4 of a cup of old-fashioned oats. You are making 1/2 of the recipe. How much oats should you use? So if the whole recipe requires 3/4 of a cup and you're making half of the recipe, you want half of 3/4, right?

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solve the practice problems. Take a photo of your scrap work and add it below! Watch for how to reduce fractions before multiplying!

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Multiply 1 and 3/4 times 7 and 1/5. Simplify your answer and write it as a mixed fraction. So the first thing we want to do is rewrite each of these mixed numbers as improper fractions. It's very difficult, or at least it's not easy for me, to directly multiply mixed numbers. One can do it, but it's much easier if you just make them improper fractions. So let's convert each of them. So 1 and 3/4 is equal to-- it's still going to be over 4, so you're still going to have the same denominator, but your numerator as an improper fraction is going to be 4 times 1 plus 3. And the reason why this makes sense is 1 is 4/4, or 1 is 4 times 1 fourths, right? 1 is the same thing as 4/4, and then you have three more fourths, so 4/4 plus 3/4 will give you 7/4. So that's the same thing as 1 and 3/4. Now, let's do 7 and 1/5. Same exact process. We're going to still be talking in terms of fifths. That's going to be the denominator. You take 5 times 7, because think about it. 7 is the same thing as 35/5. So you take 5 times 7 plus this numerator right here. So 7 is 35/5, then you have one more fifth, so you're going to have 35 plus 1, which is equal to 36/5. So this product is the exact same thing as taking the product of 7/4 times 36/5. And we could multiply it out right now. Take the 7 times 36 as our new numerator, 4 times 5 as our new denominator, but that'll give us large numbers. I can't multiply 7 and 36 in my head, or I can't do it too easily. So let's see if we can simplify this first. Both our numerator and our denominator have numbers that are divisible by 4, so let's divide both the numerator and the denominator by 4. So in the numerator, we can divide the 36 by 4 and get 9. If you divide something in the numerator by 4, you need to divide something in the denominator by 4, and the 4 is the obvious guy, so 4 divided by 4 is 1. So now this becomes 7 times 9, and what's the 7 times 9? It's 63, over 1 times 5. So now we have our answer as an improper fraction, but they want it as a mixed number or as a mixed fraction. So what are 63/5? So to figure that out-- let me pick a nice color here-- we take 5 into 63. 5 goes into 6 one time. 1 times 5 is 5. You subtract. 6 minus 5 is 1. Bring down the 3. 5 goes into 13 two times. And you could have immediately said 5 goes into 63 twelve times, but this way, at least to me, it's a little bit more obvious. And then 2 times 5 is 12, and then we have sorry! 2 times 5 is 10. That tells you not to switch gears in the middle of a math problem. 2 times 5 is 10, and then you subtract, and you have a remainder of 3. So 63/5 is the same thing as 12 wholes and 3 left over, or 3/5 left over. And if you wanted to go back from this to that, just think: 12 is the same thing as 60 fifths, or 60/5. 60/5 plus 3/5 is 63/5, so these two things are the same thing. These two things are equivalent. This is as an improper fraction. This is as a mixed number or a mixed fraction. But this is our answer right there: 12 and 3/5.

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Multiplying mixed numbers (video) | Khan Academy

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Multiply 1 and 3/4 times 7 and 1/5. Simplify your answer and write it as a mixed fraction. So the first thing we want to do is rewrite each of these mixed numbers as improper fractions. It's very difficult, or at least it's not easy for me, to directly multiply mixed numbers.

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Use any of the PLACE VALUE task cards in class and a wipe off board to describe how you know your answer is correct. Take a photo of your work and post it down below.

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Use any of the PLACE VALUE task cards in class and a wipe off board to describe how you know your answer is correct. Take a photo of your work and post it down below.

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USE A MENTOR EXPLANATION to help!

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Changing Mixed Numbers to Improper Fractions!

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Changing Mixed Numbers to Improper Fractions!

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Video transcript

right 5 and 1/4 as an improper fraction and an improper fraction is just a pure fraction where the numerator is greater than the denominator this right here it's not a pure fraction we have a whole number mixed with the fraction so we call this a mixed number so let's think about what 5 and 1/4 represents and let me rewrite it so if we're talking about 5 and 1/4 5 and 1/4 and you can literally think of this as 5 and 1/4 or 5 plus 1/4 that's what 5 and 1/4 represents so let's think about 5 5 is 5 holes or if you're thinking of pie we could draw literally 5 pies we could draw 5 pie so let me just cut up the pies from the get-go into 4 pieces since we're dealing with fourths so let me just cut up the pies right over here so that's 1 pie right over there let me copy and paste this copy and paste so I have two pies and then I have three pies and then I have four pies and then I have five pies so this is what the five represents five literally represents so let me circle all of this together that is the five part right there that is what five literally represents it represents five whole pies five whole pies now I have cut up the pies into four pieces so you can imagine each piece represents a fourth now how many pieces do I have in these five pies well I have four pieces per pie I have four pieces per pie four pieces per pie four pieces well let me just write it here four pieces per pie times times five pies is equal to 20 20 pieces or another way to think of it since each piece is 1/4 this is also equal to 20 times 1/4 or you could just write this as be equal to 20 fourths so we have five whole pies is equal to 20 24th let me write it like that twenty-fourths or we could write it as we can write it as 20 over 4 I've kind of done the same thing twice so that's what the five pies represent twenty-fourths or 20 pieces where each piece is 1/4 now the 1/4 right here represents literally one more fourth of a pie or one more piece of a pie so let me draw another pie here so let me draw another pie here so that is another pie cut it into 4 pieces but this 1/4 only represents one one of these pieces right this is one of the 4 pieces the 4 the denominator tells us how many pieces the one tells us how many of those pieces were dealing with so it's just this one piece over here that right there is the 1/4 now if we write 5 and 1/4 we just saw that the 5 the 5 right here is 20 fourths so we could write this so we could rewrite this so let me write it like this 5 and 1/4 5 and 1/4 can be re-written as this is the same thing as 5 plus 1/4 5 plus 1/4 which is the same thing as we just saw that 5 whole pie is the same thing as 20 fourths twenty-fourths and to see that these are the same thing you literally just divide 4 into 20 you get 5 and nothing is left over so 5 is the same thing is twenty-fourths and then this plus 1/4 the same thing as plus 1/4 so if I have twenty-fourths and I add one more fourth to it how many fourths do I have well I have 21 I have 21 fourths or another way of thinking about it this 5 is so this right here is that right there is 20 pieces 20 pieces of and you can even count it 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 but the quicker way is to say well we have 5 pies each of them have 4 pieces 5 times 4 is 20 this 1/4 right here represents one piece plus one piece so total we're going to have 21 21 pieces so we have 21 pieces where each piece is 1/4 so you could say we have 21 times 1/4 or 21 fourths pieces of pie however you want to think of it but we've we've solved the problem we're at an improper fraction we've written 5 and 1/4 is an improper fraction now I've gone through great pains to give you the intuition of what 5 and 1/4 means but there is a fairly straightforward process for getting straight to the improper fraction if you have if you have let me color code it so if you have 5 + 1 / 5 + 1 / 4 to convert it into an improper fraction you literally you're going to keep the same denominator so you're going to have the / 4 there but your numerator is going to be your your de not your your numerator of the fraction part before so it's going to be 1 plus your whole number times your denominator so 1 plus or actually let me do it the way I tend to think of it what I do is I take 4 times 5 so let me write that down 4 and I want to color code it 4 times 5 4 times 5 and then to that I add to that I add this numerator so I literally do 4 times 5 plus 1 and which is so this is equal to 4 times 5 is 20 plus 1 is 21 and that's over 4 so it's 21 forts and although this is kind of a fast way to do it we're literally doing the exact same thing that we did here in kind of a slower way we're saying ok 5 holes is the same thing as twenty-fourths so you take 5 and I figure that out times 5 times 4 and then I have one more fourth there so 4 times 5 plus 1 gets 20 one

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Writing mixed numbers as improper fractions (video) | Khan Academy

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Follow the lessons and write answers/notes. You should pause the video at times where you need more time to think.

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Strategies for adding and subtracting fractions with unlike denominators

Strategies for adding and subtracting fractions with unlike denominators

Video transcript

let's see if we can calculate what 5/6 plus 1/4 is and to help us I have a visual representation of 5/6 and a visual representation of 1/4 notice I have this whole this whole whole I guess you could say broke it up into 1 2 3 4 5 6 sections and we've shaded in five of them so this is 5/6 and then down here we have another hole and we have one out of the four equal sections and so this is 1/4 and I want to add them and I encourage you to any point pause the video and see if you could figure it out on your own well whenever we're adding fractions we like to think in terms of fractions that have the same denominator and these clearly don't have the same denominator but in order to rewrite them with a common denominator we just have to think of a common multiple of 6 and 4 and ideally the smallest common multiple of 6 and 4 and the way that I like to do that is I like to take the larger of the 2 which is 6 and then think about its multiples so I could first think about 6 itself 6 is clearly divisible by 6 but it's not perfectly divisible by 4 so now let's multiply by 2 so then we get to 12 12 is divisible by both 6 and 4 so 12 is a good common denominator here it's a the least common multiple of 6 and 4 so we can rewrite both of these fractions as something over 12 so something over 12 plus something plus something over 12 is equal to now there's a bunch of ways to tackle it but what I want to do is I just want to visualize it here on this on this drawing so if I go if I were to go from if I were to go from 6 equal sections to 12 equal sections which is what I'm doing if I'm going from 6 to the nominator 12 in the denominator I'm essentially multiplying each of these sections by or I'm essentially multiplying the number of sections I have by 2 or I'm taking each of these existing sections and I'm turning them into two sections so let's do that let's do that let me see if I can do it pretty neatly so I could do it a little bit neater than that so it'll look like that and whoops let me do this one I want to divide them fairly close to evenly I'm doing it by eye so it's not going to be perfect so then you have that one and then last on but last but not least you have that one there and then notice I had six sections but now I've doubled the number of sections I've turned the six sections into 12 sections by turning each of the original six into two so now I have one two three four five six seven eight nine ten eleven twelve sections so if I have 12 sections now how many of those twelve are now shaded in instead of having five of the six I now have ten of the twelve that are shaded in so I now have ten 12 five six is the same thing as 10 12 another way you could have thought about that to go from 6 to 12 I had to multiply by 2 so then I have to do the same thing in the numerator 5 times 2 is 10 but hopefully you see that those two fractions are equivalent that I didn't say I didn't change how much is shaded in I just took each of the original six and I turned it into two or I multiplied the total number of sections by 2 to get 12 and then instead of having five six I now have ten twelve shaded in now let's do the same thing with the four with the one-fourth right here I've depicted 1/4 but I want to turn this into something over 12 so to turn it over something in 12 to something over 12 each section has to be turned into three sections so let's do that let's turn each section into three sections so that's one two and three so then I have one two and three I have I think you see where this is going one two and three I have one two and three and so notice all I did is I multiplied before I had four equal sections turned each of those four sections into three sections so now I have 12 equal sections and I did that essentially by multiplying the number of sections I had by three so now what fraction is shaded in well now this original that was one out of the four we can now see is three out of the 12 equal sections it's now three out of the 12 equal sections and so what is this going to be well if I have ten twelfths and I'm adding it to three twelfths well how many 12 stew I have I'm gonna have 13 13 12 and you could see it visually over here as well up here in green I have 10 twelfths shaded in each of these boxes are 1/12 let me write that down each of these boxes are 1/12 that's 1/12 this is 1/12 so how many twelfths do I have shaded in I have the 10 front that are shaded in green and then I have an 11 12 a 12 12 and then finally a 13 the 13 12 is one way to think about it

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Visually adding fractions: 5/6+1/4 (video) | Khan Academy

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Adding and subtracting mixed number with unlike denominators

Adding and subtracting mixed number with unlike denominators

Video transcript

Let's add 19 and 3/18 to 18 and 2/3. So I like to separate out the whole number parts from the fraction parts. So 19 and 3/18 is the same thing as 19 plus 3/18. And to that, we are going to add 18 and 2/3, which is the same thing as 18 plus 2/3. Now we can separately add the whole number parts. So we could add the 19 to the 18. So we could do 19 plus 18. And then we can add the fraction parts-- let me do this in green-- plus 3/18 plus 2/3. Now 19/18, pretty straightforward. That is what? Let's see. 19 plus 19 would be 38. So this is going to be 1 less than that. It's going to be 37. So that gives me 37. And then 3/18 plus 2/3, to add them, I need to have the same denominator. And the least common multiple of 18 and 3 is 18. So let's convert 2/3 to something over 18. So 2/3, if I want to write it as something over 18, well, I multiplied the denominator by 6, so I'd also have to multiply the numerator by 6. So it's the same thing as 12/18. So I can rewrite 2/3 as 12/18. And now I can add these two things together. That's going to be-- so I have 37 plus-- it's going to be something over 18-- plus something over 18. 3 plus 12 is 15, plus 15/18. And so expressing this as a mixed number, I get 37 and 15/18. And that's the right number. But we can simplify it even more. We can simplify the 15/18. Both the numerator and the denominator are divisible by 3. So let's divide them both by 3. And we're not changing the value because we're doing the same thing to the numerator and the denominator. And so this gives us, we still have our 37, but the numerator is now 5, and the denominator is now 6. So we get 37 and 5/6. And we're done.

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Adding mixed numbers: 19 3/18 + 18 2/3 (video) | Khan Academy

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Can't remember the steps? Forget to estimate for reasonableness? Forget how to adjust the product? Here's a reminder in a song.
https://www.youtube.com/watch?time_continue=22&v=nHg4RVqQ12E

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Multiplying Decimals Song | How to Multiply Decimals

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This song helps relate fractions as division and the steps to divide decimals as well.
https://www.youtube.com/watch?v=WV5VY76Pf5U

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Dividing Decimals Using Standard Algorithm

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Dividing Decimals Using Standard Algorithm

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Dividing whole numbers to get a decimal (video) | Khan Academy

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When watching this video, pause it from time to time to try the problems on your own. Post a pic of your work down below!
https://www.youtube.com/watch?time_continue=1&v=dSFja7Jsg6c

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Using partial products is a 3rd/4th grade skill that we continue to use in 5th grade as an alternative strategy. UNDERSTANDING it well helps students avoid common mistakes when multiplying decimals or fractions.

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Partial Quotient example with a decimal in the divisor

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Partial Quotient example with a decimal in the divisor

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https://www.youtube.com/watch?v=ZXOSCTfFMfA

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Dividing a Decimal by a Decimal with the Partial Quotient Method

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finish your distributive property puzzle assignment! (You may have found it hard in December and left it undone!) Here is your opportunity to try it again! (Requires Google Slides)

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Practice solving! Take a pic of your work and post it below with your name.

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Practice solving! Take a pic of your work and post it below with your name.

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Boom Learning uses cookies to make Boom Cards work.

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ANY set of multiplying decimals problems using partial quotients (find some on  page 156 or 158 of the Envisions textbook)...and post your process on this FLIPGRID board!

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Flipgrid is where social and emotional learning happens! The leading video discussion platform for millions of PreK to PhD educators, students, and families.

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ANY set of dividing decimal problems on page 185 of the Envisions textbook and post your process on this FLIPGRID board!

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Flipgrid is where social and emotional learning happens! The leading video discussion platform for millions of PreK to PhD educators, students, and families.

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Complete any of the following decks to get extra practice...

https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/uhCCR9sKJ5DpbmdtG/

https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/fE7Jz3vPySuN9zXtB/

https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/N4d5fi8EGJEbLgjkj/

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This deck has multiplying and dividing mixed in. Take a photo of your work and post it below!
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/5fh8XLD6TrrqJ7QWA/

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This strategy is useful for building up groups of the divisor until you reach the dividend. Great way to make sense of early decimal division! (This video is with whole numbers as an easy example)

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Mixed Numbers Deck
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/GcwSNzqpF4YZGHr57/

Another Mixed Number Deck
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/maRD3skW5F5GaJB59/

Simple fractions deck
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/PYENp6RZ32rMGLobH/

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Use the identity property to multiply or divide both numerators and denominators by the same number with this St. Patrick's themed boom card deck!
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/GWWk5pm9ShWJDcGao/

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This Kahoot! mixes addition, subtraction and multiplication of decimals. (REQUIRES Kahoot APP!) PIN is 0740672. Be sure to use your REAL name for credit!

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Join a game of kahoot here. Kahoot! is a free game-based learning platform that makes it fun to learn - any subject, in any language, on any device, for all ages!

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When the timer rings, click here to end today's session.

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Choose your name (sorted by 1st name ABC order)

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By Gabriella Schaffer class 5-2

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By Eden

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Multiplying mixed numbers

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Multiplying mixed numbers scrap work.

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Boom Cards

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I got first place against maximum and Jayden

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Multiplying Mixed Numbers

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Pg 185 Number 1

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Ethan’s work for the first multiplying decimals on boom cards

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Play and pause to practice problems on your own! Post your work below!
https://www.youtube.com/watch?v=kwh4SD1ToFc

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https://www.youtube.com/watch?v=U9rfsnhTxH0

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Division:  Partial Quotients with Decimals

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This lesson uses estimation as the primary way to place the decimal point. https://www.youtube.com/watch?v=XmafXNcHmsM

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Dividing decimals using partial quotient

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Watch the video and post your work below!
https://www.youtube.com/watch?v=dHIEejLdIYE

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Dividing Fractions and Mixed Numbers
By Eden

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Rewriting MIXED NUMBERS and IMPROPER FRACTIONS

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Multiplying decimals with Gabriella Schaffer

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Bella’s Work

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Kahoot! Challenge

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Multiplying Decimals On BoomCards By Lucas Decarlo 

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Multiplying Decimals On BoomCards By Lucas Decarlo 

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Multiplying decimals by christine

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My work with a list or factors and dividing 

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My work with a list or factors and dividing 

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ANY multiplication problem using partial products and/or showing your strategy with area (find some in the multiplication chapters of the Envisions textbook)...and post your process on FLIPGRID.

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Flipgrid is where social and emotional learning happens! The leading video discussion platform for millions of PreK to PhD educators, students, and families.

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ANY multiplication problem using the partial quotient method (find some on  page 132-135 of the Envisions textbook)...and post your process on FLIPGRID.

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Make a video or other "how to" artifact that shows why!

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Fractions addition and subtraction trick - do them the fast way!

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Multiplying Fractions #1
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/5jijTdZooxwjGogmu/

Multiplying Fractions #2
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/7X22b6QKdXtwfuH55/

Multiplying Fractions #3
https://wow.boomlearning.com/hyperplay/3G9srT7M3wQ2veD4D/TANCDQ5jd7CbEAZno/

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This Kahoot Challenge involves multiplying and dividing fractions with sophistication. Choose this challenge if 5th grade goals are easy for you!
https://kahoot.it/challenge/0819501
USE YOUR REAL NAME FOR CREDIT!

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6th grade stuff! Watch and solve the practice problems. Take a photo of your scrap work and add it below!

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Video transcript

let's think about what it means to take 8/3 and divide it by one-third so let me draw a number line here so there is my number line this is 0 this is 1 and this is 2 maybe this is 3 right over here and let me plot 8/3 so to do that I just need to break up my each each hole into thirds so let's see it's one-third two-thirds three-thirds 4/3 5/3 6 thirds 7/3 8/3 so right over here and then of course 9/3 would get us to 3 so this right over here is 8/3 8/3 now one way to think about 8/3 divided by 3 is what if we take this length and we say how many jumps would it take to get there if we're doing it in jumps of 1/3 or essentially we're breaking this up if we were to break up 8/3 into sections of 1/3 how many sections would I have or how many jumps what I have well let's think about that if we're trying to take jumps of 1/3 we're gonna have to go 1 2 3 4 5 6 7 8 jumps so we could view this as we could you let me do this in a different color in this orange so we took these 8 jumps right over here so we could view 8/3 divided by 1/3 as being equal to 8 now why is this actually make sense well when you're dividing things in 2/3 for every hole you're now going to have 3 jumps so whatever value you're trying to get to you're going to have that number times 3 jumps so another way of thinking about it is that 8/3 8/3 divided by divided by 1/3 is the same thing as 8/3 8/3 times 3 now we could either write it like this we could write x 3 like that or if we want to write 3 as a fraction we know that 3 is the same thing three over one and when we already know how to multiply fractions a multiply the numerators eight times three so you have eight let me do that that same color you have eight times three in the numerator now eight times three and then you have three times 1 in the denominator three times three times one in the denominator which would give you 24 thirds which is the same thing as 24 divided by three which once again is equal is equal to is equal to is equal to eight now let's see if this still makes sense instead of dividing by one-third if we were divided by two-thirds so let's think about what 8/3 divided by two-thirds is divided by two-thirds well once again this is like asking the question if we wanted to break up this section from zero to 8/3 into sections of 2/3 or jumps of two-thirds how many sections or how many jumps would I have to make well let's think about it one jump just in a different color we could make one jump that's the same color as my 8/3 we could do one jump my computer is doing something strange we could do one jump two jumps three jumps and four jumps so we see 8/3 divided by 2/3 is equal is equal to four now does this make sense in this world right over here well if we take 8/3 and we do the same thing saying hey look dividing by a fraction is the same thing as multiplying by a reciprocal well let's multiply by three halves let's multiply by the reciprocal of 2/3 so we swap the numerator and the denominator so we multiply it times three halves and then what do we get in the numerator once again we get eight times three which is 24 and in the denominator we get 3 times 2 which is 6 so now we get 24 divided by 6 is equal to four now does it make sense that we got half the answer if you think about the difference between what we did here and what we did here these are almost the same except here we really just didn't divide or you could say you divided by one while here you / - well does that make sense well sure because here you jumped twice as far you jumped twice as far so you had to take half the number of steps and so in the first example you saw why it makes sense to multiply by 3 when you divide by a fraction for every hole you're making 3 jumps so that's why when you divide by this fraction you multiply or when you divide whatever's in the denominator you multiply by it and now when the numerator is greater than 1 every jump you're going twice as far as you did in this first one right over here and so you would have to do half as many jumps hopefully that makes sense it's easy to think about just mechanically how to divide fractions dividing 8/3 divided by 1/3 is the same thing as 8/3 times 3 over 1 or 8/3 divided by 2/3 is the same thing as 8/3 times 3 over 2 but hopefully this this video gives you a little bit more of an intuition of why this is the case

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Understanding division of fractions (video) | Khan Academy

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