Quick help: fractions

[AngelBee]

Are 30/45 and 54/81 equivalent fractions?

 

K...we know the answer but Khan's explains it

 

30 2x15 divided by 15

--- ------------------------

45 3x15 divided by 15

 

Never says why you divide it by 15. Why do you?

 

Also when comparing equivalent fractions do you always look for greatest common denominator? Ds originally picked 3 to go into each number, but you get a different answer.

[kiana]

Are 30/45 and 54/81 equivalent fractions?

 

K...we know the answer but Khan's explains it

 

30 2x15 divided by 15

--- ------------------------

45 3x15 divided by 15

 

Never says why you divide it by 15. Why do you?

 

Also when comparing equivalent fractions do you always look for greatest common denominator? Ds originally picked 3 to go into each number, but you get a different answer.

 

He divided by 15 because that's the largest factor the numerator and denominator have in common. Did he then divide the second one by 27?

[misty.warden]

Using 15 for the GCF of 30 and 45 makes sure you have the completely reduced fraction to compare with the second one. Dividing again by 15 gets you back to the original fraction, I don't feel like he explained that part very well.

 

Personally I would have used 3 too because it goes into both fractions, but it doesn't get you the most simplified fractions (it gives you 10/15 and 18/27) so you have to reduce further to be able to see if they're equivalent.

[Arcadia]

You can look for the greatest common denominator but it is not the only way. Your son's way would work too.

 

30/45 = 10/15 (dividing numerator and denominator by 3) = 2/3 (dividing numerator and denominator by 5)

54/81 = 18/27 (dividing numerator and denominator by 3) = 6/9 (dividing numerator and denominator by 3) = 2/3 (dividing numerator and denominator by 3)

 

 

So 30/45 = 54/81

[AngelBee]

We wrote it out wrong. Ds way did work. Im getting confused because he did not use largest common with 2nd fraction....just the one that jumped out at him.

 

Got me thinking we were doing it wrong. :p

[PachiSusan]

It's just the greatest common denominator that he picked. It could have been any number that divides evenly into both. I actually went where your son did - 3.

[AngelBee]

We have struggled so bad with fractions, both of our confidence is shot. :( Second guessing everything we are coming up with.

[misty.warden]

I feel your pain about the second guessing. I very rarely work math problems the textbook way myself so the thought of teaching them makes me want to run and hide some days.

[nmoira]

Another way to think of 30/45 is as a prime factorization, common factors in red:

 

2x3x5

-------

3x3x5

 

You can cancel in any order or combination... 3, 5, or 15 (which is 3x5), until you can cancel no more. You're not always going to just "see" the GCF, and you'll still get to the right answer if you do it in multiple steps. It's usually quicker to start canceling with smaller number than it is to figure out the GCF if you don't "see" it.

 

I'd probably cancel with 5 first, because it's an easy calculation, unless I "saw" the 15.

[kiwik]

With the second one I divided by 9 because that was obvious, to get 6/9. Obviously this needs to be simplified to 2/3: so have divided by 27. If your son used 3 for the first half he would presumably then done a second division to get the 15.

 

Next time he sees something similar he may get there is one step.