The fastest way is to multiply the two denominators together- and use the same number to increase the numerator. But this is NOT the most efficient solution.
For example 3/16 + 1/12= cannot be added together because the denominators are different.
You can multiply 16 X 12 to get 192. When you do this you must also multiply 3 X12 to get 36 because you multiplied 16 X 12. What you do in the denominator, you must also do in the numerator. With this is mind, you must also multiply 1 X 16 to get 16 in the numerator because you multiplied 12 X16 in the denominator.
Your new fractions now become 36/192 + 16/192= 52/192. But you are not done yet! You must now factor the answer to its Least Common Denminator. The numbers are even so we can try dividing the numerator and denominator by 2. We will get 26/ 96. We can divide by 2 again and get 13/48. Now we are done
the answer to 3/16 + 1/12= 13/48.
Now wait a minute-- There is a faster way. 12 and 16 are multiples of 4. As a matter of fact if we multiply 12 X4 we get 48. And 3 X 16 also =48. So if I multiply 3/16 X3 then my new fraction is 9/48 and the new fraction for 1/12 is 4/48. Now the new fractions are: 9/48 + 4/48 = 13/48
and I can't get any lower that that AND I got the answer directly. The short of it is to ALWAYS look for a common denominator before doing any addition or subtraction of fractions. When all else fails, then multiply the 2 denominators together and expect to do a lot of extra math work.
For example 3/16 + 1/12= cannot be added together because the denominators are different.
You can multiply 16 X 12 to get 192. When you do this you must also multiply 3 X12 to get 36 because you multiplied 16 X 12. What you do in the denominator, you must also do in the numerator. With this is mind, you must also multiply 1 X 16 to get 16 in the numerator because you multiplied 12 X16 in the denominator.
Your new fractions now become 36/192 + 16/192= 52/192. But you are not done yet! You must now factor the answer to its Least Common Denminator. The numbers are even so we can try dividing the numerator and denominator by 2. We will get 26/ 96. We can divide by 2 again and get 13/48. Now we are done
the answer to 3/16 + 1/12= 13/48.
Now wait a minute-- There is a faster way. 12 and 16 are multiples of 4. As a matter of fact if we multiply 12 X4 we get 48. And 3 X 16 also =48. So if I multiply 3/16 X3 then my new fraction is 9/48 and the new fraction for 1/12 is 4/48. Now the new fractions are: 9/48 + 4/48 = 13/48
and I can't get any lower that that AND I got the answer directly. The short of it is to ALWAYS look for a common denominator before doing any addition or subtraction of fractions. When all else fails, then multiply the 2 denominators together and expect to do a lot of extra math work.