Question

How do I place 3/8, 2/7, 8/11, and 5/16 in order from least to greatest? Thanks!

Answer 1

Find the least common multiple of the denominators: 8, 7, 11, and 16. I use a function in Excel (LCM) to do this if you use Excel. The LCM is 1232. Now you have to figure out how much you multiplied EACH denominator by to get 1232 so you can do the same thing to the numerator (divide 1232 by 8, 7, 9, & 11; then multiple each numerator by that number per fraction):

1232/8=154
3/8 = 3*154/8*154
Ans: 462/1232

1232/7=176
2/7 = 2*176/7*176
Ans: 352/1232

1232/11=112
8/11=8*112/11*112
Ans: 896/1232

1232/16=77
5/16=5*77/16*77
Ans: 385/1232

So the fractions from least to greatest are:
2/7 or 352/1232
5/16 or 385/1232
3/8 or 462/1232
8/11 or 896/1232

This is

Answer 2

Typo at the end, cross out "This is"... oops.

Answer 3

Thanks! My dad found the the formula in excel. But problem is I can't use excel in my classroom. any faster way than to find LCM? That may be a big number for example my next problem is 11/23, 19,27,7/10, and 15/17. The LCM is 105,570. That will take for ever to do long hand

Answer 4

I know a shortcut for 2 numbers: Find the greatest common factor, then divide one of the numbers (doesn't matter which one) by the GCF, then multiply your answer by the 2nd number:
18 & 30
GCF=6
18/6=3
3*30=90

However, since the numbers you have don't do that nicely, I'm afraid your best bet is to multiply all of the denominators together: 23x27x17x10=105,570. In fact, the first 3 are prime and then you're multiplying by 10 at the end, so it's kind of the only way to do that one quickly.

If you notice in your first problem, 8 and 16 are multiples of each other. So if you're trying to find the LCM for 8,7,11, and 16, well since 16 is just 8*2, you don't have to multiply by 8. 7x11x16=1232. So if 1232 divisible by 16, it will be divisible by 8.