Thread: Adding fractions

1/3 +(-5/6 ) + (-1/2 ) =

Originally Posted by Patience

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

Originally Posted by Patience

1/3 +(-5/6 ) + (-1/2 ) =

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

Originally Posted by Patience

1/3 +(-5/6 ) + (-1/2 ) =

Here is one way. It's not one of the usual ways, but, for me, it is easy.

1/3 +(-5/6) +(-1/2) = N
Clear the fractions, multiply both sides by 6,
2 +(-5) +(-3) = 6N
-6 = 6N
N = -6/6 = -1 -----------answer.