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Math Antics - Division With Partial Quotients

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5th Grade Math 2.3, Model Division of 2-digit Divisors with Base 10 Blocks

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5th Grade Math 1.8, Relate Multiplication and Division

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Multiplying Fractions Using Visual Models

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mulitplying fractions videos models - Google Search

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A lot of times with multiplying fractions were asked to illustrate the problem on an area model we’MoreA lot of times with multiplying fractions were asked to illustrate the problem on an area model we’re going to do that today with 3/4 times 1/3 let’s start by solving 3/4 times 1/3.

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Let's say we need to figure out how many times 16 goes into 1,388. And what I want to do is first think about how we traditionally solve a problem like this and then introduce another method that allows for a little bit more approximation. So traditionally you would say, well, 16 does not go into 1 any times. So then you move over one spot. Well, how many times does it go into 13? Well, it still does not go into 13. And then you go all the way to 138. And you say, well, 16 does go into 138. And you say, how many times will it go into 138? And you might try 9 first. And I'll do all my arithmetic here on the right side. So you'll say, 16 times 9-- 6 times 9 is 54. 1 times 9 is 9, plus 5 is 14. So it goes 144 times. So that's still too big. That's larger than 138. So it's going to go into it eight times. Eight times will be less than 138. So you would stick an 8 here. And notice, I had to do this little trial and error here. I had to make sure I got the right exact number. I had to make sure I put an 8 right over here. Then you say, 8 times 6 is 48. And then 8 times 1 is 8, plus 4 is 12. So 8 times 16 is 128. So when I subtract, I get the remainder from 138. So I get a remainder of 8 minus 8 is 0. 3 minus 2 is 1. And then these cancel out. So I have a remainder of 10. But I still have this 8 right over here, so I bring that down. So I have 108. And then I do the same thing again. Let me get rid of this so we don't get distracted. We say, how many times does 16 go into 108? And you can approximate. You say, well, it's definitely not eight times. Eight times is 128. Is it, maybe, seven times? And then you might do a little math on the side. See-- 16 times 7. 6 times 7 is 42. 1 times 7 is 7, plus 4 is 11. So you get 112. So that's still too large, so it's going to be 6. But notice, we had to do this little side work on the side right over here to realize it wasn't seven. Now six is the largest how many times you go into 108 without going over it. So 6 times 6 is 36. Carry the 3, or regroup the 3, depending on how you think about it. 6 times 1 is 6, plus 3 is 9. Then you subtract again. 8 minus 6 is 2. And then you can just say 10 minus 9 is 1, or you could even borrow. You could make this a 10. And then that goes away. 10 minus 9 is 1. So then you have 12. And if we're not going into decimals, you're done. Because 16 does not go into 12. So 16 goes into 1,388 86 times with a remainder of 12. That right over there is your remainder. And that's all a decent way of doing it. And that's the way you traditionally know how to do it. But what I want to do is introduce another maybe a little more interesting way to solve a long-division problem. So once again, let's do our 16 goes into 1,388. And what we're going to do is give us much more leeway for approximation, or for essentially guessing. And what we want to do is just guess. We're going to make guesses for how many times 16 goes into the numbers without overestimating, without jumping too high. And now we're not just going to think about the 1 or the 13 or the 138. We're going to think about the whole number as a whole. And before we do that, I'm going to get two things out of the way, just because it will help us. I'm just going to remind ourselves what 16 times 2 and 16 times 5 are. And I'm just picking these as random numbers that we can use to approximate. You don't have to use 2 and 5. You can use any numbers. Maybe I'll show other examples there. So 16 times 2, we know, is 32. And 16 times 5 is 50 plus 30, is 80. So let's just keep these two results in mind while we try to tackle this right over here. So the first thing to think about is our best guess for how many times does 16 go into 1,388. Or another way to think about, how many times does 16 go into 1,000? Let's just do something at a very rough approximation. Well, we know it's not going to be 100, because 100 times 16 would be 1,600. You would just throw those two 0's at the end of it. And [? you'd ?] say, how many times does it go into 1,000? Well, we know if 16 times 5 is 80, we know that 16 times 50 would be 800. So let's use that. And I'm using the 5-- I'm multiplying it by another 10 to get to 50-- instead of the 2 because 800 is a lot closer than 320 to our 1,000 that we care about. So what we could say is, well, 16 times 50 will get us to 800. And once again, how did I know that? Well, 16 times 5, I know ahead of time, is 80. So 16 times 50, I multiplied by 10-- 5 times 10-- it'll get us to 800. And then I just subtract. So I subtract here. 8 minus 0 is 8. And then you could say 13 minus 5 is 588. And now we ask ourselves, how many times does 16 go into 588? How close can we get to that? And let's just assume that we only know this stuff right over here, or we can multiply 16 times a multiple of 10. So 800 would once again be too big. That gets us above 588. Let's just go with 320 right over here. We know that 16 times 2 is 32. So 16 times 20 is going to be 320. I just multiplied the 2 times 10, which would give us our product times 10. And so we can subtract this right over here. 8 minus 0 is 8. 8 minus 2 is 6. And then 5 minus 3 is 2. So now I'm left with 268. And we say, how many times does 16 go into 268? Well, let's see. 800 is too big. Even 320 is now too big. Well, we could say-- 10 times 16 will get us to 160. Let's just try that out. We don't even have to get the right exact answer. We don't have to get the highest multiple that's less than 260. We just have to make sure that we're still within 268. Let me do a new color over here. If we multiply 16 times 10, we get 160. 160, we subtract again. So 8 minus 0 is 8. 6 minus 6 is 0. 2 minus 1 is 1. And then we're left with, well, how many times does 16 go into 108? And we know 16 times 5 is 80. So let's just try out 5. 16 times 5 is 80. We subtract right over here. 8 minus 0 is 8. 10 minus 8 is 2. So we're left with 28. And now it's pretty simple. How many times does 16 go into 28? Well, it only goes into it one time. And then when you subtract 16 from 28, 8 minus 6 is 2. 2 minus 1 is 1. You're left with a remainder of 12. But you might say, well, how do we know how many times does 16 go into 1,388? Well, it goes 50 times plus 20 times plus 10 times plus 5 times plus 1 time. So that's going to be-- we can just add up all of these things on the right-hand side. This is going to be 50 plus 20 is 70, plus 10 is 80, plus 5 is 85, plus 1 is 86. So there we have it. It went into it 86 times with a remainder of 12. And what's cool about this method is that at every step, I could have put a 60 over here and I could have done the math correctly. Or I could have picked my two multiples to be 16 times 6 and 16 times 3. And I would have gotten different results here. But at the end, I would still have gotten the right answer. So what it does is it gives us a method so that we're always thinking about-- we're always kind of biting away chunks of what we're dividing into. So first we bit off an 800-piece chunk. Then we bit off a 320-piece chunk. And we keep going until we essentially can't divide by 16 any more. So hopefully you found that kind of interesting.

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Partial quotient method of division: introduction (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Partial Quotients Method | Lesson plan | Education.com

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Students will be able to divide using the partial quotients method. The adjustment to the whole group lesson is a modification to differentiate for children who are English learners. Display a simple multiplication chart with no coloring or notations. Conduct a whole-class discussion on which factors are easiest to estimate products (e.g., 2, 5, 10, 100, etc.)

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- [Instructor] What we're going to do in this video is multiply the numbers 352 and 481. And we're gonna do it in two different ways, but realize that the underlying ideas are the same. So first let's just appreciate that 352 can be rewritten as 300 plus 50 plus two or we could think of it as two plus 50 plus 300, plus 300. You add these three numbers together, you're going to have 352. And same idea, 481 that's four hundreds, four hundreds, plus eight tens, which is 80, so plus 80, and then we have one one, so plus one. And you might have be familiar with multiplying like this in the past, setting up this grid. And it's essentially we're applying the distributive property. We're gonna take the two and multiply it times 400 plus 80 plus one. So we're gonna multiply two times each of those numbers, and actually I'm gonna just draw some quick lines here. So we have that, and then we'll have let me do it like this, then we have this, and then let me set up my grid. I'm having trouble drawing straight lines, okay there we go. Then one more in this direction. There you go. And then in this direction, let me draw some horizontal lines to have a neat clean grid here. There we go. Now first we'll multiply two times 400 plus 80 plus one. So two times 400 is 800. Two times, let me do it in that same blue color, so this is 800. Two times 80 is 160, and then two times one is two. And then we can multiply 50 times these. So what's 50 times 400? Well five times four is 20, and then we have another one, two, three zeros. So one, two, three, so that's 20,000. 50 times 80, five times eight is 40, and then we have two zeros, just like that. And then we have 50 times one which is of course going to be equal to 50. And then we go to the 300, which we will distribute and multiply times each of these, each of these numbers. 300 times 400, three times four is 12, and then we have four zeros. One, two, three, four. We get 120,000. 300 times 80, three times eight is 24, and then we have one, two, three zeros. One, two, three, so we get 24,000. And then 300 times one is of course equal to 300. And then what we wanna do is add up all of these numbers. So let's actually add up the rows first. So if we add up the rows, let me draw another line going straight down like that. And so if we sum this up, this is going to be 962. 800 plus 160 is 960 plus two, so this is 962. This right over here is 24,050. 24,050. And then this right over here is what 100 and, 144,300? 144,300. 120,000 plus 24,000 is 144,000 plus 300, there you have it. And then you would add up these numbers just like that to get your final answer. Now I'm gonna hold off doing that for a second as we see the other way of multiplying these numbers. So the other way of doing it, we could've said, 481, and this is sometimes called the standard algorithm, 481 times 300 and 50, let me do the same colors, 352. And in the standard algorithm, the way that we do it is we start with this two in the ones place and then we multiply it times 481. So two times one is two, two times eight is 16. So we put the six here and then we sometimes we will say we carry the one, but really regrouping that as hundreds. That's 10 tens which is hundreds. And then two times four is eight, which is really 800, plus one, so that's nine or really 900. You see a pattern here. This 962 is the exact same thing as that 962 right over there. Why? Well because we multiplied the 200 times the one, times the 80, times the 400. We saw that over here, and then we just added 'em all together to be 962. That's all the standard algorithm did just now. And then we move over to the five. But this is really five tens or 50, and that's why in the standard algorithm we put a zero here before saying all right what's five times one? It's five. What's five times eight? It is 40. We regroup the four. Let's delete this from before. What's five times four? Well that's 20 plus four is 24. Notice 24,050, that's exactly what we had over here, and it makes sense because we're taking a 50 and we're multiplying it times 481 which is exactly what we did right over there. And so you might guess what's gonna happen when we take this three and we multiply it times 481. That's really a 300 times 481. Let me delete that so I don't get confused. So because it's a 300, in the standard algorithm, we put two zeros here first. And when I say algorithm it just means a method of doing something. And so we'll say three times one is three. Three times eight is 24. And then three times four is 12 plus two is 14. And so notice, I have 144,300. And the standard way of doing it at this point we just add 'em all up. So whether we're doing it here or here, we just add everything up. So two plus zero plus zero is two. Six plus five is 11. Regroup that one. So one plus nine plus three is 13. And then one plus four plus four is nine. Two plus four is six. Then we have a one right over there, so we get 169,312. And so when you just learn this method, the standard algorithm we some people might call it, it might seem like hey this just seems like a little bit of magic. But all you're doing is you're going to each of these places and you're distributing it, you're multiplying it times 400 plus 80 plus one to get this. Then you're multiplying 50 times 400 plus 80 plus one, and then 300 times 400 plus 80 plus one, exactly what we did right over here.

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Relate multiplication with area models to the standard algorithm (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Dividing Unit Fractions (Visual) Worksheet

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Dividing Unit Fractions (Visual) Worksheet

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Common Core Sheets - Free Math Worksheets

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Free Dividing Unit Fractions (Visual) worksheets. Easier to grade, more in-depth and best of all... 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!

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Dividing Whole Numbers by Fractions Using Models | Math with Mr. J

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Unit Fractions Divided by Whole Numbers Models | Modeling Dividing Fractions

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Dividing Fractions by Whole Numbers Using Models | Math with Mr. J

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- [Instructor] Let's see if we can figure out what 2/3 divided by five is equal to. Pause this video and see if you can figure this out. Well, there is a couple of ways that we can approach it. We can first do it in a conceptual way, think about it visually. To do that, let me represent 2/3, so let's say that what I'm drawing right over here is a whole. This is a square, and it represents a whole. Now, I can divide into three equal sections. I'm gonna try to hand-draw that. So, this is, that looks pretty good, three equal sections here. Each is 1/3, and we have 2/3, so we are really representing all of this stuff right over here. That is two of my thirds. Now, I wanna divide those 2/3 by five. Well, the way I could do this is I could divide it into five equal sections. But, if I'm doing it, I might as well just divide everything, all the thirds, into five equal sections, so let me do that. So, one, two, three, and then four, and five equal sections. So, what is one of those five equal sections of my original 2/3? Well, this right over here is one of those five equal sections of my original 2/3. Notice I could draw that, I could draw another one here, another one here, another one there, and another one there, and I would have five equal sections that make up those 2/3. But, what does just one of them represent? And if we figure out what this represents of the whole, then we know what 2/3 divided by five is. Well, when I took my thirds and I divided them into five equal sections, I essentially constructed 15ths. How do I know that? Well, I had one, two, three thirds, and then I divided it into one, two, three, four, five sections, so each of these squares right over here is a 15th. You have three times five, and you could count 'em if you like. And, what we have circled off in red is two of these 15ths. We have 1/15 right over here, and then 2/15 right over there. So, this is going to be equal to 2/15. Now, another way that you could think about, and over time this is the way you will approach it, but it's nice to think about it conceptually, when you divide by any number, it's the same thing as multiplying by the reciprocal. So, five is the same thing as five wholes, or 5/1. And so, 2/3 divided by five is the same thing as 2/3 times the reciprocal of five, or the reciprocal of 5/1, which is you just swap the numerator and the denominator, which is 1/5. And so, another way of thinking about this is this is 1/5 of 2/3, which it once again will be this section right over here. The way you could compute this, conceptually, you see that this is 2/15, but you could also say well, I could just multiply it. When I multiply fractions I can just multiply the numerators. Two times one is two. We do that same red color. Two times one is two, and then I could multiply the denominators. Three times five is 15. And, hopefully, what we just drew out may help make sense of why dividing by something is the same thing as multiplying by the reciprocal. Then, when you multiply fractions, it's the same thing as multiplying the numerators to get our new numerator, and then multiplying the denominators to get our new denominator.

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Dividing a fraction by a whole number (video) | Khan Academy

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Instructor] Let's see if we can figure out what 2/3 divided by five is equal to. Pause this video and see if you can figure this out. Well, there is a couple of ways that we can approach it. We can first do it in a conceptual way, think about it visually.

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There are 3 Simple Steps to Divide Fractions:

Step 1. Turn the second fraction (the one you want to divide by) upside down
(this is now a reciprocal).

Step 2. Multiply the first fraction by that reciprocal

Step 3. Simplify the fraction (if needed)

Example:

Step 1. Turn the second fraction upside down (it becomes a reciprocal):

Step 2. Multiply the first fraction by that reciprocal:
(multiply tops ...) (... multiply bottoms)
Step 3. Simplify the fraction:

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

To help you remember:

♫ "Dividing fractions, as easy as pie,
Flip the second fraction, then multiply.
And don't forget to simplify,
Before it's time to say goodbye"

Another way to remember is:
"leave me, change me, turn me over"

How Many?

20 divided by 5 is asking "how many 5s in 20?" (=4) and so:

Now look at the pizzas below ... how many "1/6th slices" fit into a "1/2 slice"?

How many

in

?
Answer: 3

In other words "I have half a pizza, if I divide it into one-sixth slices, how many slices is that?"

Another Example:

Step 1. Turn the second fraction upside down (the reciprocal):

Step 2. Multiply the first fraction by that reciprocal:

Step 3. Simplify the fraction:

Fractions and Whole Numbers

What about division with fractions and whole numbers?
Make the whole number a fraction, by putting it over 1.
Then continue as before.

Example:

Then continue as before.

Step 1. Turn the second fraction upside down (the reciprocal):

Step 2. Multiply the first fraction by that reciprocal:

Step 3. Simplify the fraction:

The fraction is already as simple as it can be.

Example:

Then continue as before.

Step 1. Turn the second fraction upside down (the reciprocal):

Step 2. Multiply the first fraction by that reciprocal:

Step 3. Simplify the fraction:

And Remember ...

You can rewrite a question like "20 divided by 5" into "how many 5s in 20"

So you can also rewrite "3 divided by ¼" into "how many ¼s in 3" (=12)

Why Turn the Fraction Upside Down?

Because dividing is the opposite of multiplying!

A fraction says to:

multiply by the top number

divide by the bottom number

But for DIVISION we:

So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.

937,938,939, 1411, 1412, 1413, 3575, 3576, 3577, 3578

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Turn the second fraction upside down, then multiply, Ther are 3 simple steps:

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Multiply a fraction by fraction using an area model #2

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How to Model Multiplication of Fractions (Area Model)

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Multiplying Fractions Using Area Models | Math with Mr. J

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Multiplying Mixed Numbers and Whole Numbers

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Multiplying Fractions by Whole Numbers | How to Multiply Fractions | 5th Grade Math

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5.NF.4. - About the Math, Learning Targets, and Rigor: Grade 4 Gifted and Talented Mathematics

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Area Models for Multiplication of Fractions | PBS LearningMedia

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Use area models to show a visual representation of the product of two fractions. This interactive exercise focuses on multiplying fractions and reducing them when possible. This resource is part of the Math at the Core: Middle School collection.

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Multiply fractions by fractions using area models

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In this lesson you will learn how to multiply fractions by fractions by using area models.

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Let's think a little bit about what it means to multiply fractions. Say I want to multiply 1/2 times 1/4. Well, one way to think about this is we could view this as 1/2 of a 1/4. And what do I mean there? Well let me take a whole, let me take a whole here, and let me divide it into fourths. So let me divide it into fourths, so I'll divided into 4 equal sections. And so 1/4 would be 1 of these 4 equal sections. But we want to take 1/2 of that. So how do we take half of that? Well, we could divide this into 2 equal sections, and then just take 1 of them. So divide it into 2 equal sections, and then take 1 of them. So we're taking this pink area, this whole pink area is 1/4, and now we're going to take 1/2 of it. We're now going to take 1/2 of it. So that's this yellow square right over here. But what fraction of the whole does this yellow represent? Well, it now represents 1 out of 1, 2, 3, 4, 5, 6, 7, 8 equal sections. So this right over here, this represents 1/8 of the whole. And so we see conceptually that 1/2 times 1/4, it completely makes sense, that 1/2 of 1/4 should be 1/8. And it hopefully makes sense that you get this 8 by multiplying the 2 times the 4. You started with 4 equal sections, but then you divided each of those 4 equal sections into 2 equal sections. So then you have 8 total equal sections that you split your whole into. Let's do another example, but now let's multiply two fractions that don't have 1's in the numerator. So let's multiply, let's multiply 2/3 times 4/5. And I encourage you now to pause the video and do something very similar to what I just did. Try to represent 4/5 of a whole and then try to represent 2/3 of that 4/5 and see what fraction of the whole you actually have. So pause now. So let's think about this. Let's represent 4/5. So if I have a whole like this, let me try to divide it into 5 equal sections. 5 equal sections, so let's say that is 1 equal section, that is 2 equal sections, that is 3, 4, and 5-- I can do a better job than this. This is always the hard part. I'm trying my best to make them look, at least, like equal sections-- 2, 3, 4, and 5. I think you get the point here. I'm trying to make them equal sections. And we want 4/5. So we want 4 of these 5 equal sections. So this would be 1 of the 5 equal sections, 2 of them, 3 of them, and then 4 of them. So that right over there is 4/5. Now we can view this as 2/3 of the 4/5. So how can we think about that? Well, we could take this section and divide it into thirds. So let's do that. Divide it into thirds. So we're going divide it into 3 equal sections. So that's 1/3, and then 2/3. So we took each of the 5 equal sections, and we divided them into 3 equal sections. Now what's going to be 2/3 of the 4/5? Well, that's going to be this part right over here. So let me make this clear. This is 1/3 of the 4/5. And then this would be 2/3 of the 4/5. So this right over here, would be 2/3 of the 4/5, or 2/3 times 4/5. But what fraction of the whole does that represent? Well, how many total, how many total equal sections do we now have? Well, we have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. So we have 15 equal sections. I'm using a new color. We have 15 equal sections, and that make sense. We started with 5 equal sections, but then we divided each of those into 3 equal sections. So now we have 5 times 3 total equal sections. And then how many of those are now colored in? Well, we see it's 2 times 4. 1, 2, 3, 4, 5, 6, 7, 8. How many of them are in the 2/3 of the 4/5, I should say. And there's 8 of them, 8 of the 15 equals sections. And so there you have it. It should hopefully now make visual sense, or it makes conceptual sense, that 2/3 times 4/5-- you can obviously compute it by just multiplying the numerators, 2 times 4 is 8. And then multiplying the denominators, 3 times 5 is 15-- but hopefully this now makes conceptual sense as 2/3 of 4/5.

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Multiplying 2 fractions: fraction model (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Multiplying Fractions Using Area Models | Math with Mr. J

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Multiplying Mixed Numbers | Step by Step | Math with Mr. J

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Video transcript

so let's think about all of the different ways that we can represent 7 9 7 9 so let's just visualize seven ninths so here I have nine equal sections and seven ninths you could represent as seven of those equal sections so let me get our set get myself a bigger thing to draw with so that I can fill this in fast I don't like how that looks I'm going to use the paintbrush so here we go so that's one two three four you know where this is going five six and seven so that's one way of representing seven ninths we already know that that's not too interesting but let's see if we can represent seven ninths as the sum of other fractions so let's imagine maybe we can represent it as let's do it as two ninths give my use a different brush here so it's represented as two ninths two over nine plus plus I don't know let's see maybe three over nine but that doesn't quite get us to seven ninths yet two over nine plus three over nine is going to get us to five over nine so we're going to need two more so it's going to be plus another 2 over nine plus another 2 over 9 plus another 2 over 9 so what would this look like so let's let's just draw another grid here so this is going to look like I'll try to do it right below it so that we can see how they match up so we have two ninths we have two ninths this two ninths right over here well we have each of these is 1/9 we have nine equal sections so two ninths is going to be so we're going to get one and two and then we're going to add three more nights so one one two three so we had three nines right over there and then two more nights and then two more nights one one and two so notice when I added two nines to three nines to two ninths this equals seven ninths and we know that when we add a bunch of fractions like this that have the same denominator we can just add the numerator and this is why this is two 9s plus 3 9 times two 9s is going to give me seven nine so let's do this one more time this is actually a lot of fun so let me draw my grid again let me draw my grid and then let's let's see what we can do so let me get my pen tool out and tool out make sure my my ink is a - they call this is fine and let's add a couple of nights here so let's add let's add first 1/9 and I'm going to stride all the 9s in blue and let's add two nights and then we could add I don't know maybe we could add give some space here so we can add more and maybe we could add three nights three nights and then we could add let's see that won't get a cc 1/9 election let me just write this I'm going to try to add four fractions here so let's head first 1/9 see where that gets us so 1/9 is going to get us right over here so that's 1/9 so let's say we add two nights to that so two nights two nights get my little paintbrush going on so that's one and two more two nights so that still doesn't hat get us there this gives us a total of three nights one plus two is three three nights so let's do that a no let's add let's add let's add 4/9 4/9 and I'll do that in this blue color so four nights that's well that's different enough four nights so let's see where this gets us actually well why not so 4/9 and so that's going to get us one two three four so that looks like it got us all the way because one plus two plus four is going to give us seven seven nine so what can we put here well we could say zero nine why not so we could put in we could call this one right over here zero nine and why would we visualize that well let's lure saying none of these no no ninths right over here so this is 1/9 plus two 9s plus 4/9 is equal to seven nine so these are all different ways to decompose the exact same fraction

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Decomposing a fraction visually (video) | Khan Academy

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Let's now think about different ways to represent a mixed number. And let's say that our mixed number is 2 and 1/8. Actually, let's make it a little bit more interesting. Let's make it 2 and 1/4. So let's first think about the whole number part, the 2. Well, the 2 is literally two wholes. You could literally view that if you want. Right here we've drawn each whole. We've cut it up into sections of 8, so it literally is 8/8. So let me just do it like this. So the 2 is this whole region right over here, that's 1. So this right over here is 1. And then this right over here is 2, 2 wholes, so let me paint that in. So that is 2 wholes. And then I have 1/4. So this last piece, this last whole, is divided into 8 sections. So let me divide it into fourths first. So that's one 1/4, 2/4, and 3/4. So we want one of those four to be filled in-- one of those four in orange. So one of those four to be filled in, just like that. You might notice that I filled in two of the eighths, and that's because 1/4 and 2/8 is the same thing. So there I've represented this mixed number, 2 and 1/4. Let's see how we can decompose this. So let's get our grids back. So how else could we do it? And I'm just going to throw a bunch of fractions up there and see what I get. So the first thing I'm going to throw out is 1/2. So how would I represent 1/2 here? Well, if I take one of these wholes and I put it into two sections right over here, 1/2 would be this section right over there. So let me color that in. So we have 1/2. So I'm first going to add 1/2, which is the same thing as 4/8. And you see that I just filled in four out of the eight sections, which is exactly half of this first whole. So we're making some progress. Now let's throw in 3/8. So what would 3/8 look like? Each of these boxes are literally an 1/8 and I could fill it in however I want, but let me just put this as 1, 2, and 3. And then let's fill in plus another 8/8. Now, what's 8/8? Well, 8/8 is a whole, and I'll do that over here. I still haven't filled this one in yet, but I'll fill in this one right over here. So let's do that. So 8/8-- so that's 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, and 8/8, and it's a whole. So I have a whole whole here, so that's 8/8. I want to make this one a whole, because I want to get to 2, so let me put in a 1/8 there. So plus 1/8, well, that's going to be this one right over here, so that's my 1/8. And then let's add another 2/8, plus another 2/8. Well, this is in eighths right over here, so 2/8 is going to be two of these. And notice, you see that the 2/8 is the same thing as 1/4. If you took this 1/4 and split it into two, so you have two times as many pieces, it becomes 2/8. And you see that if 1 times 2 is 2, 4 times 2 is 8. So that 1/4 is the same thing as 2/8. You see the 8/8 is the same thing as a whole. Now, you see, you could make another whole out of 1/2, plus 3/8, plus 1/8, and they add up to a whole. And just to make sense of why that worked, 1/2 is the same thing as 4/8-- because you see that, we filled in the 4/8-- then you have 3/8, and then you have 1/8. And if you add all of these together, 4/8 plus 3/8 plus 1/8, you are going to get, in terms of eighths, 4/8 plus 3/8 plus 1/8 is going to be 8/8. 4 plus 3 plus 1 is 8, so you get 8/8 which is this entire whole. So hopefully that helps give you a visual understanding of what we're doing when we're adding and decomposing these fractions a little bit more.

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Decomposing a mixed number (video) | Khan Academy

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Let's now think about different ways to represent a mixed number. And let's say that our mixed number is 2 and 1/8. Actually, let's make it a little bit more interesting. Let's make it 2 and 1/4. So let's first think about the whole number part, the 2.

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Please click here if you are not redirected within a few seconds.

To decompose a fraction simply means to take it apart. The most basic way to decompose a fraction is to break into unit fractions, which is when the numerator (top number) is 1. We can see that 5/8 is the same as the unit fraction 1/8 five times.

What is a unit of a fraction?

What is a fraction number Bond?

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how to decompose a fraction - Google Search

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Please click here if you are not redirected within a few seconds. To decompose a fraction simply means to take it apart. The most basic way to decompose a fraction is to break into unit fractions, which is when the numerator (top number) is 1.

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Easily test if one number can be exactly divided by another

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Related Topics:
Lesson Plans and Worksheets for Grade 5
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 5
Common Core For Grade 5

Videos, examples, and solutions to help Grade 5 students learn to interpret a fraction as division of the numerator by the denominator ( a/ b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Common Core: 5.NF.3

Suggested Learning Targets

I can explain that fractions represent division.

I can solve word problems that involve division of whole numbers and interpret the quotient in the context of the problem.

I can explain or illustrate my solution using visual fraction models or equations.

Interpreting fractions as division and solving word problems involving division (5.NF.3)
Connecting Fractions and Division: 5.NF.3
A fraction is a division problem, in which the numerator is divided by the denominator.
Examples:
1. Four students shared one desert. How much desert did each student get?
2. Four students shared three deserts. How much desert did each student get?
3. 11 tomato slices are being shared equally among 3 pizzas. How many slices are on each pizza?

5.NF.B.3 Common Core Standards for Teachers and Parents
Examples:
1. If 4 people want to share 3 sacks of rice equally, how many sacks of rice should each person get?
2. One of the stages of the Tour de France bicycle race is a distance of 138 miles. If a race averages 24 miles per hour, how much time (in hours) will it take to complete that stage?
3. A school bus has a maximum capacity of 48 passengers. There are 208 students and teachers that will be going on a field trip. How many buses will be needed? Dividing Fractions (5.NF.3)
Common Core State Standard 5.NF.3: interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Fractions As Division (solutions, examples, videos, worksheets, lesson plans)

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Related Topics: Lesson Plans and Worksheets for Grade 5 Lesson Plans and Worksheets for all Grades More Lessons for Grade 5 Common Core For Grade 5 Videos, examples, and solutions to help Grade 5 students learn to interpret a fraction as division of the numerator by the denominator ( a/ b = a ÷ b).

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Understanding Fractions as Division | Word Problems Included

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Connecting Fractions and Division: 5.NF.3

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My wife and I have recently purchased an assortment pack of soap, and we both want to experience all 3 bars. And we are not willing to share soap with each other. So we have a little bit of a conundrum. How do we share these 3 bars of soap so that we each get to experience all of the smells? So this might be a nice rose smell. This might be some type of ivory smell. I don't even know if that's a legitimate smell. This might be some type of sandalwood, which is always very nice. And my wife has an idea. She says, look I'm going to take these 3 bars, so we're starting with 3 bars of soap. And I'm going to divide it into 2 equal groups. And I said, how are you going to do that? And she says, well, I'm just going to take out some type of carving saw or carving knife, or who knows what it is, and I'm just going to cut it right down the middle, so right down this. This is my wife cutting the soap right over here with her saw. So she's cutting the soap right over here. So she has divided the soap into 2 equal groups. So she's taken 3 bars, and she's divided into 2 equal groups. So the interesting question here is, how many bars of soap do we each have now? And I encourage you to pause the video and think about that for a second. How many bars of soap do we each have now? Well, let's just visualize my share. Let's say I take this bottom half right over here. So this is Sal's share of the soap. Let me write this out. So this is Sal's share. My wife took this top half. Well, what do I have? Well, I have 1/2, I have another 1/2, and I have another 1/2 of a bar. So I have 3/2 bars of soap. Or you could say that I have 3 times 1/2 bars of soap. Notice, something very interesting happened here. 3 divided by 2 is equal to 3 times 1/2. And we could make it even more interesting, because we know 2 is the exact same thing as 2/1. So 3 divided by 2/1 is equal to 3 times 1/2. Notice we went from a division to a multiplication, and we took the reciprocal. And that makes complete sense. We have 3/2 bars now. But what's 3 times 1/2? Well, 3 times 1/2 is equal to 3/2. So just doing this little simple, smelly soap example, we've got a very interesting result. 3 divided by 2 is the same thing as 3 times 1/2, which is the same thing as 3/2.

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Creating a fraction through division (video) | Khan Academy

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My wife and I have recently purchased an assortment pack of soap, and we both want to experience all 3 bars. And we are not willing to share soap with each other. So we have a little bit of a conundrum.

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Understanding Fractions as Division | Word Problems Included

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Algebra Worksheets & Printables

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online quiz on surface area of complex figures

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online quiz on Surface Area of complex figures

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Algebra Worksheets & Printables These worksheets are printable PDF exercises of the highest quality. Writing reinforces Maths learnt. These worksheets contain pre-algebra & Algebra exercises suitable for preschool, kindergarten, first grade to eigth graders levels .

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Volume through decomposition | Measurement and data | 5th grade | Khan Academy

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Goals and expected skills for section A and B

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Goals and expected skills for section A and B

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https://www.youtube.com/watch?v=LZxXUb9iAZc&t=3s

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Finding Volume with Unit Cubes | How to Find Volume

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Dividing Unit Fractions (Visual) Worksheet

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Dividing Unit Fractions (Visual) Worksheet

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Common Core Sheets - Free Math Worksheets

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Begin with lesson 2 . This shouws modeling

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CCLS - Math: 5.NF.3

Category

Number And Operations-Fractions

Sub-Category

Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions.

State Standard:

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

0:11:16

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Category Number And Operations-Fractions Sub-Category Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. State Standard: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).

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Related Topics:
Lesson Plans and Worksheets for Grade 5
Lesson Plans and Worksheets for all Grades
More Lessons for Grade 5
Common Core For Grade 5

Videos, examples, and solutions to help Grade 5 students learn how to multiply unit fractions by non-unit fractions.

Common Core Standards: 5.NBT.7, 5.NF.4a, 5.NF.6, 5.MD.1, 5.NF.4b

New York State Common Core Math Grade 5, Module 4, Lesson 14

Grade 5, Module 4, Lesson 14 Worksheets (Pdf)

The following example show how to multiply fractions using the area model. Scroll down the page for more examples and solutions.

Lesson 14 Concept Development

Problem 1
Jan had 3/5 pan of crispy rice treats. She sent 1/3 of the treats to school. What fraction of the whole pan did she send to school?

Problem 3
1/2 נ4/5

Problem 4
3/4 of Benjamin's garden is planted in vegetables. Carrots are planted in 1/2 of his vegetable section of the garden. How much of Benjamin's garden is planted in carrots?

Problem 6
Mr. Becker, the gym teacher, uses 3/5 of his kickballs in class. Half of the remaining balls are given to students for recess. What fraction of all the kickballs is given to students for recess?

Lesson 14 Concept Development

Problem 2
Jan had 3/4 pan of crispy rice treats. She sent 1/3 of the treats to school. What fraction of the whole pan did she send to school?

Lesson 14 Application Problem

Solve by drawing an area model and writing a multiplication sentence. Beth had 1/4 box of candy. She ate 1/2 of the candy. What fraction of the whole box does she have left?

Extension: If Beth decides to refill the box, what fraction of the box would need to be refilled?

Lesson 14 Homework

1. Solve. Draw a model to explain your thinking.

1/2 of 2/3 of ____ thirds = ____ thirds

Lesson 14 Problem Set

1. Solve. Draw a model to explain your thinking. Then write a number sentence.
a. 1/2 of 3/4 = 1/3 of ____ fourths = ____ fourth
b. 1/2 of 4/5 = 1/2 of ____ fifths = ____fifths
c. 1/2 of 1/2 =
d. 2/3 of 1/2 =
e. 1/2 of 3/5 =
f. 2/3 of 1/4 =

2. 5/8 of the songs on Harrison's iPod are hip-hop. 1/3 of the remaining songs are rhythm and blues. What fraction of all the songs are rhythm and blues? Use a tape diagram to solve.

3. Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.
a. What fraction of all the students are girls with blond hair?
b. What fraction of all the students are boys without brown hair?

4. Cody and Sam mowed the yard on Saturday. Dad told Cody to mow 1/4 of the yard. He told Sam to mow 1/3 of the remainder of the yard. Dad paid each of the boys an equal amount. Sam said, Dad, that's not fair! I had to mow one-third and Cody only mowed one-fourth! Explain to Sam the error in his thinking. Draw a picture to support your reasoning. Lesson 14 Homework

This video shows how to multiply unit fractions by non-unit fractions using area models. It also shows how to reduce your final answer using the model.

1. Solve. Draw a model to explain your thinking.
c) 1/3 of 3/5
d) 1/2 of 6/8

2. Sarah has a photography blog. 3/7 of her photos are of nature. 1/4 of the rest are of her friends. What fraction of all Sarah's photos is of her friends? Support your answer with a model. Lesson 14 Homework

This video shows how to multiply unit fractions by non-unit fractions using area models. It also shows how to reduce your final answer using the model.

1. Solve. Draw a model to explain your thinking.
c) 1/3 of 3/5
e) 1/3 of 4/5

2. Sarah has a photography blog. 3/7 of her photos are of nature. 1/4 of the rest are of her friends. What fraction of all Sarah's photos is of her friends? Support your answer with a model.

3. At Laurita's Bakery, 3/5 of the baked goods are pies, and the rest are cakes. 1/3 of the pies are coconut. 1/6 of the cakes are angel-food.
a. What fraction of all of the baked goods at Laurita's Bakery are coconut pies?
b. What fraction of all of the baked goods at Laurita's Bakery are angel-food cakes?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

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Multiply Unit Fractions by Non-Unit Fractions (solutions, examples, videos, worksheets, lesson plans)

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Related Topics: Lesson Plans and Worksheets for Grade 5 Lesson Plans and Worksheets for all Grades More Lessons for Grade 5 Common Core For Grade 5 Videos, examples, and solutions to help Grade 5 students learn how to multiply unit fractions by non-unit fractions.

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5.C.7 Use visual fraction models and numbers to divide a unit fraction...: 5th Grade Math

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5.C.7 Use visual fraction models and numbers to divide a unit fraction...

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5.NF.3 - About the Math, Learning Targets, and Rigor: Grade 5 Mathematics

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Let's think about how or what 1/2 times 5 represents. So one way to think about it is that this could be five 1/2's added together. So you could view this as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2, which is equal to 5/2. The other way to think about this is that you start with 5 things. So let's say, that's 1 thing. Let me copy and paste that so they all look the same. So then let me paste it. So that's 2 things. That's 3 things. That's 4 things. And that's 5 things. So the other way to think about it is you start with 5 things, and you take 1/2 of them. So what would be 1/2 of this? Well, let's see. You have 5 things, so you would get-- 5 divided by 2 would be 2 and 1/2. So you would get this far. Let me make it like this. So you would get this one. You would get this one. And you would get this one. Now, is this the same thing as 5/2? Well, what happens if we divide each of these wholes into halves? So let's do that. So if we just multiplied-- so we just divide each of these into 2. So instead of having 5 wholes, we now have 10 halves. How many of those halves have we filled in? Well, we have filled in 1, 2, 3, 4, 5. So this is also equal to 5/2. So far we just did it thinking about what multiplication actually means. But if you said, well, how did I compute this? Well, the way you could think about it, and multiplying fractions is actually straightforward from that point of view, is as long as you can express both of them as fractions, and 5 we already know is the same thing as 5 ones, so this we can just multiply times 5/1. So now that I've expressed both of them as fractions, I can just multiply the numerator. So 1 times 5 over 2 times 1. And what's that going to be equal to? Well, 1 times 5 is 5. 2 times 1 is 2. So once again, we get 5/2.

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Multiplying unit fractions and whole numbers (video) | Khan Academy

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Let's think about how or what 1/2 times 5 represents. So one way to think about it is that this could be five 1/2's added together. So you could view this as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2, which is equal to 5/2.

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Tutorified : Tutoring & Free Practice Questions for CogAT, OLSAT, NNAT, AAP, Woodcock Johnson, InView, WISC IV & V

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5.NF.B.3 5th Grade Interpret a Fraction as Division Worksheets

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5.NF.B.3 5th Grade Interpret a Fraction as Division Worksheets. 5th Grade Interpret a Fraction as Division Worksheets Printable PDF with Answers.

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Multiplying fractions is about combining parts of a whole. When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole. Created by Sal Khan.

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Video transcript

Let's think a little bit about what it means to multiply 2/3 times 6. One way to think about it is to literally take six 2/3 and add them together. This is six 2/3 right over here. And if we wanted to actually compute this, this would be equal to-- well, we're going to take these six 2's and add them together. So we could view it as 2 times 6 over 3. 2 times 6 over 3, which is the same thing, of course, as 2, 4, 6, 8, 10, 12, 12/3. And what is 12/3 equal to? Well, we could rewrite 12 as-- so this is equal to-- we could rewrite 12 as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like this so I don't have to keep switching colors. This is going to be the same thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are obviously a whole. Each of these equal 1. That's 1 and that's 1, so this is going to be equal to 4. So that's one way to conceptualize 2/3 times 6. Another way to think of it is as 2/3 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw the number line up to 6. So what I care about is the section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to take 2/3 of 6, we can think of this whole section of the number line between 0 and 6 as the whole. And then we want to take 2/3 of that. So how do we do that? Well, we divide it into thirds, to three equals sections. So that's one equal section, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. Now where does that get us? That gets us to 4. So we get, obviously, to the same answer. We would be in a tough situation if somehow we got two different answers. Either way, 2/3 times 6 or 6 times 2/3, either way, that is going to be equal to 4. But there are two different ways of viewing this. This first way is literally viewing it as 2/3 six times. And this way is we're taking a fraction of the number 6. We're going 2/3 of the way to 6, which would get us to 4.

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Multiplying fractions and whole numbers (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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teaches Common Core State Standards 4.NF.B.4.a http://corestandards.org/Math/Content/4/NF/B/4/a

teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1

teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6

teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8

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2. Playing Fill Three: Multiplying unit fractions by whole numbers (FP)

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Lesson objective: Multiply a unit fraction by a whole number. This lesson helps to build fluency with multiplying a unit fraction by a whole number. Number lines are used here because they support the understanding that fractions are numbers and can be operated on in the same ways as whole numbers can be operated on.