\frac{1}{2}.\ \frac{4}{3\ }\ +\ \frac{5}{6}\ \div\ \frac{7}{8\ }\ =

Answer 1

To solve this expression, we need to follow the order of operations (PEMDAS).

First, let's simplify the division expression:
$\frac{5}{6} \div \frac{7}{8}$

To divide by a fraction, we can multiply by its reciprocal.
So, $\frac{5}{6} \div \frac{7}{8} = \frac{5}{6} \cdot \frac{8}{7}$

Multiplying the numerators and denominators gives us:
$\frac{5 \cdot 8}{6 \cdot 7} = \frac{40}{42}$

Next, let's add this result to the fraction:
$\frac{1}{2} + \frac{40}{42}$

To add fractions, we need to have a common denominator.
The least common multiple of 2 and 42 is 42.
So, we can rewrite the fractions with a common denominator:
$\frac{1}{2} + \frac{40}{42} = \frac{21}{42} + \frac{40}{42}$

Now that the fractions have a common denominator, we can add their numerators:
$\frac{21 + 40}{42} = \frac{61}{42}$

Therefore, $\frac{1}{2} \cdot \frac{4}{3} + \frac{5}{6} \div \frac{7}{8} = \frac{61}{42}$.