Simplify:

#1/3+3/4+1/2#

In order to add or subtract fractions, they must have the same denominator, which is called the least common denominator (LCD). To find the LCD, list the multiples of each denominator and find the lowest one they all have in common.

#3:# #3,6,9,color(red)12,15,18,21...#

#4:# #4,8,color(red)12,16,20...#

#2:# #2,4,6,8,10,color(red)12,14...#

The LCD is #12#.

To make each fraction have the LCD, multiply each fraction by a fractional form of #1#, such as #5/5#, that will produce an equivalent fraction with the denominator #12#. The numbers will change, but the value of each fraction won't change.

#(1/3xxcolor(blue)(4/4))+(3/4xxcolor(green)(3/3))+(1/2xxcolor(purple)(6/6))#

Simplify.

#4/12+9/12+6/12#

Put the numerators over the denominator.

#(4+9+6)/12#

Simplify.

#19/12#

#1/3+3/4+1/2=19/12#

#19/12# is an improper fraction. We can convert it to a mixed number #(a b/c)# by dividing the numerator by the denominator using long division to get a whole number quotient with a remainder. The quotient is the whole number in the mixed number, the remainder is the numerator, and the divisor #(12)# is the denominator.

#19-:12="1 remainder 7"#

The mixed number is #1 7/12#.