#2/3+2 1/4+1/2#
Convert #2 1/4# into an improper fraction. Multiply the numerator by the whole number and add the numerator. Place the result over the denominator.
#2/3+(4xx2+1)/4+1/2#
Simplify.
#2/3+9/4+1/2#
In order to add fractions, they must have the same denominator, the least common denominator (LCD). List the multiples of each denominator. The lowest multiple in common is the LCD.
#3:##3,6,9,color(red)12,15,18,...#
#4:##4,8,color(red)12,16,...#
#6:##6,color(red)12,...#
The LCD is #12#.
Now multiply each fraction by a fraction equal to #1# to create equivalent fractions with #12# as the denominator. For example, #5/5=1#. This keeps the value of each fraction from changing. (If you divide the numerator by the denominator, you will get the same value.)
#2/3xxcolor(red)(4/4)+9/4xxcolor(blue)(3/3)+1/2xxcolor(green)(6/6#
Simplify.
#8/12+27/12+6/12#
Add the numerators.
#(8+27+6)/12=41/12#
We can convert #41/12# to a mixed fraction by using long division, in which the whole-number quotient is the whole number of the mixed fraction, and the remainder is the numerator, which is placed over the denominator #12#.
#41-:12=3" remainder 5"#
#41/12=3 5/12#
