Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
When adding or subtracting fractions, you need to make sure that the denominators are the same:
[tex]\frac{numerator}{denominator_{x}} -\frac{numerator}{denominator_{y}}[/tex] → [tex]\frac{numerator}{denominator_{z}} -\frac{numerator}{denominator_{z}}[/tex]
To do this, you need to find the LCM of the denominators, and multiply top and bottom by the factor:
[tex]\frac{1}{3} -\frac{5}{6}[/tex]
The denominators are 3 and 6. The lowest common multiple is 6, so you only need to change the first fraction by multiplying by 2. Multiply the top and bottom:
[tex]\frac{2*1}{2*3} =\frac{2}{6}[/tex]
Insert into the expression:
[tex]\frac{2}{6} -\frac{5}{6}[/tex]
Now subtract the numerators. The denominators will not change:
[tex]2-5=-3\\\\\frac{2}{6}-\frac{5}{6}=-\frac{3}{6} =-\frac{1}{2}[/tex]
:Done
