3 3/14*7/15-5/8

To solve this expression, we first need to simplify the mixed number \(3 \frac{3}{14}\) into an improper fraction:

\[3 \frac{3}{14} = \frac{3 \times 14 + 3}{14} = \frac{42 + 3}{14} = \frac{45}{14}\]

Next, we can calculate the expression:

\[\frac{45}{14} \times \frac{7}{15} - \frac{5}{8}\]

To multiply fractions, we multiply the numerators together and the denominators together:

\[\frac{45 \times 7}{14 \times 15} - \frac{5}{8}\]

\[\frac{315}{210} - \frac{5}{8}\]

Next, we need a common denominator to subtract the fractions:

\[\frac{315 \times 8}{210 \times 8} - \frac{5 \times 210}{8 \times 210}\]

\[\frac{2520}{1680} - \frac{1050}{1680}\]

Now we can subtract the fractions:

\[\frac{2520 - 1050}{1680} = \frac{1470}{1680}\]

Finally, we can simplify the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 30:

\[\frac{1470 ÷ 30}{1680 ÷ 30} = \frac{49}{56}\]

Therefore, \(3 \frac{3}{14} \times \frac{7}{15} - \frac{5}{8} = \frac{49}{56}\).