1/3 +(-5/6 ) + (-1/2 ) =
(1/3) + (-5/6) + (-1/2)
Find a common denominator for these three fractions; try 6
Now, take (1/3);
3 goes into 6 two times, multiplied by the numerator = (2/6)
Now (-5/6); 6 goes into 6 one time, multiplied by the numerator = -5/6 (obviously)
And finally, (-1/2); 2 goes into 6 three times, multiplied by -1 = -3/6
Now, we have (2/6) + (-5/6) + (-3/6)
= (2/6) - (5/6) - (3/6)
(2 - 5 - 3)/6 = -6/6 = -1
lcm of 3,6,2 is 6 (any other common multiple can also be used)
change to a common denominator
now 6 / 3 = 2 therefore change 1/3 to (1*2)/(3*2) = 2 / 6
{multiplying numerator and denominator with 2}
similarly 6/6 = 1 no need to change (-5/6 )
6/2 = 3 therefore change (-1/2 ) to (-1*3)/(2*3) = -3 / 6
{multiplying numerator and denominator with 3}
therefore
1/3 +(-5/6 ) + (-1/2 ) = 2 / 6 + (-5/6 ) + (-3 / 6)
=[ 2 + (-5) + (-3) ] / 6 {common denominator 6}
= (2 - 8) /6
= (-6) / 6
= -1