Question #fb404

2 Answers
Jul 16, 2017

The answer is: #25/12# or #2 1/12#

Explanation:

#1/2+3/4+5/6#

The way to add fractions is to first get their denominators the same (by finding the LCM). So we will first check the multiples of each denominator.

#2=>2, 4, 6, 8, 10, 12#

#4=>4, 8, 12#

#6=>6, 12#

As we can see, #12# is the LCM.

To make each fraction get that denominator and yet retain its value, we have to multiply both numerator and denominator by the same number. A fraction with the same number in the numerator and denominator is equal to one so the multiplication will not change the value of the other fraction.

#(1/2xx6/6)+(3/4xx3/3)+(5/6xx2/2)#

#6/12+9/12+10/12#

No we simply retain the same denominator and add all the numerators.

#(6+9+10)/12#

#25/12#

This cannot be reduced further, so the answer is: #25/12#.

If you want, you can also give the answer as a mixed fraction since the numerator is larger than the denominator. This is done by seeing how many times the denominator goes into the numerator (in this case, twice, as #12xx2=24#), putting that number (#2#) as the whole number, and the remnant on the denominator.

Hence:

#25/12=2 1/12#

Jul 16, 2017

#25/12 " " or " " 2 1/12#

Explanation:

First, find the common denominator for all three fractions.

This will be the LCM of 2, 4, and 6.

#2# has only one prime factor: #2#

#4# is #2 xx 2#

#6# is #2 xx 3#

The most #2#s that any of these numbers has is #2# (4), and the most #3#s that any of these numbers has is #1# (6).

Therefore, the LCM of 2, 4, and 6 is #2 xx 2 xx 3 = 12#.

Now multiply the tops and bottoms of all of the fractions by a certain number so that all of the bottoms are #12#:

#1/2 + 3/4 + 5/6#

#1/2 * 6/6 + 3/4 * 3/3 + 5/6 * 2/2#

#6/12 + 9/12 + 10/12#

Now combine all three fractions and simplify!

#(6+9+10)/12#

#25/12#

#2 1/12#

Either the mixed number or the improper fraction are valid answers.

Final Answer