Two thirds divided by four fifths?

Answer 1

⅔ ÷ ⅘ = __ Easy, right? Okay, so go ahead, tell me the answer. 10/12 or ⅚, you say? Okay, why? If you said because you flip it and multiply, you are the majority. Why do you do it, though? Because "they" told you to? Unfortunately you're missing a very basic mathematical concept here. And, yes, you have "them" to blame. You have been the victim of mathematical neglect. Don't worry, though, you've caught it early enough. In order to better understand what you're really doing to divide these fractions, I challenge you to create a word problem that describes what is really going on in the problem. After all, practical application is really the way to help people understand, right? My first attempts at word problems were flops. There are a couple of reasons why. The first is that you never want to use people as your items. Why? Well, we're not surgeons and it's probably dangerous to be cutting people into thirds and fifths. Let's write that one down. Okay. So let's keep trying. What about using cake. My class has 20 students. 4/5 of the students are boys. I have 2/3 of a cake left for them. How much of the cake will each receive? This doesn't work, though because then I am getting a different answer. The problem asks me to find the total number of boys, 16. It then has me divide 2/3 by 16 which isn't the problem that I want.

Hmm. Plan B. ⅔ ÷ ⅘ = __ I have ⅔ of a cake box available to take home left overs from the party. I have ⅘ of the cake left. How much of the cake will I be able to take home in the empty part of the cake box? Now, I've been fiddling around with the words, but I think this works. Let's draw it out and see.

Draw a square. Divide it into thirds with vertical lines. Shade in two of the thirds. Draw another square. Divide it into fifths with horizontal lines. Shade in four of the fourths. Now, obviously these do not look easy to divide. So, I will share a secret with you. Now introducing, the…..Philip Halloran Patent Pending Process of Expressing One in terms of Another!! So, in your first square, draw in the fifths lines horizontally. And in your second square, draw in thirds lines vertically.

As you can see, I took the cake box (yellow) and added lines to show fifths. Those lines are horizontal and the thirds are vertical. And these lines are the same in my cake representation (blue). Now, how many of the parts in the second square will fit into the parts of the first square? Go ahead, count them. Number each of the parts.

And now it's easy to see! There are ten pieces out of 12 that will fit in the empty part of the cake box! Now we can actually see what happens when we do this problem instead of just giving the answer because that's what "they" taught us to do. Pretty neat!

⅔ ÷ ⅘ = 10/12 __ == If you said because you flip it and multiply, you are the majority. Why do you do it, though? Because "they" told you to? Unfortunately you're missing a very basic mathematical concept here. And, yes, you have "them" to blame. You have been the victim of mathematical neglect. Don't worry, though, you've caught it early enough. In order to better understand what you're really doing to divide these fractions, I challenge you to create a word problem that describes what is really going on in the problem. After all, practical application is really the way to help people understand, right? My first attempts at word problems were flops. There are a couple of reasons why. The first is that you never want to use people as your items. Why? Well, we're not surgeons and it's probably dangerous to be cutting people into thirds and fifths. Let's write that one down. Okay. So let's keep trying. What about using cake. My class has 20 students. 4/5 of the students are boys. I have 2/3 of a cake left for them. How much of the cake will each receive? This doesn't work, though because then I am getting a different answer. The problem asks me to find the total number of boys, 16. It then has me divide 2/3 by 16 which isn't the problem that I want.

Hmm. Plan B. ⅔ ÷ ⅘ = __ I have ⅔ of a cake box available to take home left overs from the party. I have ⅘ of the cake left. How much of the cake will I be able to take home in the empty part of the cake box? Now, I've been fiddling around with the words, but I think this works. Let's draw it out and see.

Draw a square. Divide it into thirds with vertical lines. Shade in two of the thirds. Draw another square. Divide it into fifths with horizontal lines. Shade in four of the fourths. Now, obviously these do not look easy to divide. So, I will share a secret with you. Now introducing, the…..Philip Halloran Patent Pending Process of Expressing One in terms of Another!! So, in your first square, draw in the fifths lines horizontally. And in your second square, draw in thirds lines vertically.

As you can see, I took the cake box (yellow) and added lines to show fifths. Those lines are horizontal and the thirds are vertical. And these lines are the same in my cake representation (blue). Now, how many of the parts in the second square will fit into the parts of the first square? Go ahead, count them. Number each of the parts.

And now it's easy to see! There are ten pieces out of 12 that will fit in the empty part of the cake box! Now we can actually see what happens when we do this problem instead of just giving the answer because that's what "they" taught us to do. Pretty neat!