What is the value of this expression? Please express as a reduced fraction. Remember ... show all workings (use calculator as a check). (Value: 2 pts)
\frac{6}{7}-1\frac{3}{4}=\frac{8^{2}}{28}
To solve this expression, we can start by converting the mixed number, $1\frac{3}{4}$, into an improper fraction. To do this, we multiply the whole number, 1, by the denominator, 4, and add the numerator, 3. This gives us $\frac{4}{4}+\frac{3}{4} = \frac{7}{4}$.
Now, we can rewrite the expression as $\frac{6}{7} - \frac{7}{4}$.
To subtract fractions, we need a common denominator. In this case, the least common multiple (LCM) of 7 and 4 is 28.
Now, we can rewrite the expression with the common denominator: $\frac{6}{7} \cdot \frac{4}{4} - \frac{7}{4} \cdot \frac{7}{7}$.
Simplifying the numerators gives us $\frac{24}{28} - \frac{49}{28}$.
Now, we can combine the fractions by subtracting the numerators and keeping the denominator: $\frac{24-49}{28} = \frac{-25}{28}$.
Therefore, the value of the expression $\frac{6}{7} - 1\frac{3}{4}$ is $\frac{-25}{28}$.