Help me with this LoF Fractions question please

[funschooler5]

DD is on the Final Bridge, and has been doing the book mostly on her own. I'm pretty rusty at this stuff, and even after looking up the answer I'm not sure I understand the question!

 

It's #7 on pg 162:

 

To change the diameter of a circle into its circumference, you use the function "multiply by 3 1/7". What would be the diameter of a circle whose circumference is 11"? (Hint: Use the inverse function.)

 

Answer: 11 ÷ 3 1/7 = 11/1 ÷ 22/7 = 3 1/2 inches

 

I understand where it says that you multiply by 3 1/7" by 11, but the hint about the inverse function confuses me. It made me think (before I saw the answer) that you're supposed to invert the 11/1 to 1/11 before multiplying (so, divide it in other words). Could somebody explain to me what they mean by inverse function in reference to this problem?

 

Thanks!

[Sasharowan]

Inverse funstion would be what we used to call invert and multiply. So 11/1 divided by 22/7 would become 11/1 times 7/22. Then I would cross the 11 and 22 and change them to 1 and 2 and get 7/2 for my answer which would then turn into the mixed number 3 1/2. Clear as mud?

[K&Rs Mom]

I took it as dividing is the inverse/opposite of multiplying. So if you get from d to c by multiplying, you can get from c to d by dividing. :001_huh:

[petepie2]

If you're given the diameter, you multiply by 3 1/7 (or 22/7) to get the circumference. In this problem, you're given the circumference and asked to calculate the diameter. So the circumference (11) is divided by 22/7. Dividing by a fraction is the same as multiplying by it's inverse:

 

11 times 7/22 = 3.5

[funschooler5]

Aha! Thanks so much everyone!

 

It clicked finally. So it's the diameter we're looking for, not the circumference. Now inverting it makes sense. How could I miss the wording in the problem? I read it about five times.