What is the value of the expression −6 4/9 −1 1/3 ?
Converting both fractions to improper fractions, we have $-\frac{58}{9}-\frac{4}{3}$. Then we have \begin{align*}
-\frac{58}{9}-\frac{4}{3}&=-\frac{174}{27}-\frac{36}{27}\\
&=-\frac{210}{27}\\
&=\boxed{-\frac{70}{9}}.
\end{align*}
To find the value of the expression -6 4/9 -1 1/3, we need to subtract these two mixed numbers.
Step 1: Convert the mixed numbers into improper fractions.
-6 4/9 can be written as -((6*9 + 4)/9) = -(58/9).
-1 1/3 can be written as -((1*3 + 1)/3) = -(4/3).
Step 2: Subtract the two fractions.
-(58/9) - -(4/3)
When subtracting fractions, we need to find a common denominator. In this case, the common denominator is 9.
-(58/9) + (4/3)
To add these fractions, we also need the same denominator, which is 9.
-(58/9) + (4/3) = -(58/9) + (12/9)
Now we can subtract the numerators and keep the common denominator.
= (-58 + 12)/9
= (-46/9).
Step 3: Simplify the fraction, if necessary.
The fraction -46/9 cannot be simplified further, so that is the final answer.
Therefore, the value of the expression -6 4/9 -1 1/3 is -46/9.