Question

Paul needs 2 1/4 yards of fabric to make a tablecloth. How many tablecloths can he make from 18 1/2 yards of fabric?
A. 72 tablecloths
B. 10 tablecloths
C. 9 tablecloths
D. 8 tablecloths

Answer 1

So this is a division of fractions equation. You're given the mixed number forms for two measurements, but you need the improper fraction form (where everything is above or below the bar). Can you convert 2 1/4 and 18 1/2 to improper fractions? We'll go from there.

Answer 2

2 1/4= 2.25
18 1/2= 18.5

Answer 3

oh wait no I mean 9/4 and 37/2

Answer 4

So that's okay, but those are decimals. To use fraction division, we need improper fractions. (so it is possible to divide 18.5 by 2.25 using long division, but I think the question wants you to understand fraction division).

2 1/4 can be rewritten as 2*1 + 1/4 --> 2*(4/4) + 1/4 --> (2/1)*(4/4) + 1/4 -> (2*4)/(1*4) + 1/4 --> 8/4 + 1/4 = 9/4
can you apply the same math to 18.5? I got (18*2)/(1*2) + 1/2 --> 36/2 + 1/2 = 37/2 for the last step. Are you following this?

Answer 5

Hehe yep! Okay. So do you know the procedure for dividing fractions?

A/B divided by C/D = A/B * D/C (because dividing by 2 is the same as multiplying by 1/2, and dividing by 1/2 is the same as multiplying by 2). Can you apply this to the problem, where you want to find 37/2 divided by 9/4?

Answer 6

yeah let me try hold on....

Answer 7

(37/2) / (9/4) = 8 with a repeating decimal of 2. So.....the right answer for the whole problem would be D, right?

Answer 8

That's correct! Did you calculate it by hand or use a calculator? Ideally I think whoever gave you this problem wants you to understand dividing by fractions on your own.

Answer 9

I used a calculator, but can you show me how to divide the fractions manually? I forget how to do it. You don't have to if you don't want to. You've helped me a lot already :)

Answer 10

I can definitely show you! Give me a sec to type it up.

Answer 11

Thanks!

Answer 12

So given the above equation where A/B divided by C/D = A/B times D/C, I used this math:
\[\frac{ 37 }{ 2 } \div \frac{ 9 }{ 4 } = \frac{ 37 }{ 2 } * \frac{ 4 }{ 9 } \]
The 2 and 4 can simplify to 1 and 2, so you have 37/1 * 2/9, then 37 * 2 / 9, which is 74 / 9, or 8 and some left over. Does this make sense?

Answer 13

yeah! So this is where you flip the the fraction and cross multiply right?

Answer 14

You flip the second fraction (the used to divide, NOT the one that is being divided). There's not cross multiplying in this case. A/B * D/C = (A* D)/ (B* C). I think you're thinking of proportions with cross-multiplying. Does this make sense?

Answer 15

oooooh okay, yes that makes sense...
Thank you so much for helping!

Answer 16

No problem!