Pam  0:00  
Hello, math-ers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam Harris.

Kim  0:07  
And I'm Kim Montague.

Pam  0:08  
And this is a MathStratChat episode where we chat about our math strategies. Every Wednesday evening, I throw out a math problem on social media, and people from around the world chat about the strategies they use, and comment on each other's thinking.

Kim  0:20  
Okay, so this week, our problem is three-fourths divided by one-twelfth. How would you solve this problem? Pause the podcast. Solve it however you like. The problem is three-fourths divided by one-twelfth.

Pam  0:33  
Nice. Alright, you choose. You or me?

Kim  0:37  
You go.

Pam  0:40  
Okay. I'm thinking about kind of like a compound fraction, like three-fourths with a big divided by line. Like a... So, it's like looking... How do I describe that? Three-fourths divided by one-twelfth is like three-fourths over one-twelfth. But I wouldn't say "over", but just so you can positionally think about it. And I want to make the denominator 1. So, I'm going to scale them both by 12. So, one-twelfth times 12 is 1. Now, I have a denominator of 1. But I have to scale the numerator times 12. And I can think about three-fourths times 12 in a couple different ways. I'm just brain dead today, so I'm thinking about 3 times 12 is 36 divided by 4. And 36 divided by 4 is also 9. Is also. It is 9. And I said "is also" because I was looking at last week's MathStratChat where the answer was 9. Wait, does that mean they're equivalent somehow? Could be maybe.

Kim  1:32  
Okay. I was thinking about kind of similar to you. I wanted to scale it by 12 also. But that got me thinking about how there's twelve-twelfths in 1 whole.

Pam  1:49  
Okay.

Kim  1:52  
And so, help me with the words. Because I don't want the whole which would be 12.

Pam  2:01  
Yeah.

Kim  2:01  
I want three-fourths of the whole. Which would be 9. 

Pam  2:05  
Which 3... Yeah, nice. I think that works.

Kim  2:08  
Okay.

Pam  2:09  
A way to write that down could be that three-fourths is equivalent to nine-twelfths, so you're thinking about how many twelfths are in nine-twelfths. Three-fourths of the whole is nine-twelfths. That's not what you were thinking. 

Kim  2:24  
No. Yeah, I don't think I ever thought about nine-twelfths. But I kind of thought about what would the whole be. And then I want three-fourths of that. 

Pam  2:31  
Three-fourths of the whole.

Kim  2:32  
Three-fourths of 12. Yeah.

Pam  2:34  
Yeah. So, then I got thinking about the fact that the answer to the last couple problems that we did in MathStratChat were 9. So, I started to compare three-fourths divided by one-twelfth, today's problem, to three-halves divided by one-sixth. That was two weeks ago.

Kim  2:50  
Mmhm.

Pam  2:51  
So, they're just scaled by 2.

Kim  2:54  
Yeah.

Pam  2:54  
Like, if I take the problem two weeks ago, three-halves divided by one-sixth, and I divide both of them by 2. In other words, I take half as many. The total is half as many, and the number in each group is half as many, then I would have the same number of groups.

Kim  3:07  
Yeah.

Pam  3:08  
Yeah.

Kim  3:09  
Nice series of problems.

Pam  3:11  
Whoo! Go MathStratChat.

Kim  3:13  
Yeah. We can't wait to see what you do each week. Please join us on MathStratChat and let us know how you think about the problems. Comment on each other's strategies while you're there.

Pam  3:22  
We post the problems on Wednesdays around 7:00 p.m. Central. When you answer, tag me and use the hashtag MathStratChat, and then like Kim said, comment on each other strategies. Then join us here to hear how we're thinking about the problem. We love having you as part of the Math is Figure-Out-Able movement. Y'all, keep making math figure-out-able.