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Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
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Ok the first thing you have to do is to divide the two numbers (16 and 48) in the denominator by 2. If they both are divisible by 2, then you save this number 2.
Next, you have to devide the remaining of the last divison by two again. the new two numbers are 8 and 26. If both numbers are divisible by 2 again. You save this number (2) again.
16 48 *
.----------
8 26 * 2 This number is saved
4 13 * 2 This number is saved too
*
Of course the remaining numbers are not divisible by 2 nor 3, and so on. This means the the common denominator is 2*2 =4
Question? Remember this is the first step
So 16 * 3 = 48. Now we need to make both of the fractions have that denominator. Since 5/48 already has that for the denominator we don't need to change it.
So you can just write 5/48 on the next column over.
But to make 3/16 have a denominator of 48, we need to multiply the bottom by 3. In order to do that and keep the ratio the same, we must also multiply the top by 3.
If you are having trouble with this still I suggest this video:
http://www.khanacademy.org/video/adding-fractions-with-unlike-denominators?playlist=Developmental%20Math