Question

which one is the smallest? a. 3/7 b. 1/3 c. 5/6 or d. 9/14 i know the answer is b. 1/3 but how do i get the answer? to all of them? what is the process?

Answer 1

Get them all to where the denominators are the same. Your least common denominator is 42.
a. 18/42
b. 14/42
c. 35/42
d. 27/42
From this, you can easily tell that b is the smallest. :)

Answer 2

okay so would i do this to every problem i come across with that is just like this one?

Answer 3

Do it for each. You find your least common denominator by checking the factors in your denominator numbers. Let me explain: 7 is a prime number, and is the only factor you need to consider for a. Likewise, 3 is what you need out of b. 6 has factors of 2 and 3, but there's already a 3, so you just need the 2 from there. 14 is 2*7, and both are already represented. So the least common denominator of 7, 3, 6, and 14 is 7*3*2, or 42.

Answer 4

As another example, the least common denominator for something like 1/8 and 1/6 would be something over 24 since 8 has 2 and 4 and 6 has 2 and 3. Disregard repeated factors (the 2, in this case) and multiply the rest of them together. So 2*4*3=24. Don't forget to scale up the numerators! 1/8 and 1/6 become 3/24 and 4/24, respectively.