Simplify 6/7+3/4×7/30

To simplify the expression \( \frac{6}{7} + \frac{3}{4} \times \frac{7}{30} \), we first handle the multiplication:

\[
\frac{3}{4} \times \frac{7}{30} = \frac{3 \times 7}{4 \times 30} = \frac{21}{120}
\]

Next, we can simplify \( \frac{21}{120} \) by finding the greatest common divisor (GCD) of 21 and 120, which is 3:

\[
\frac{21 \div 3}{120 \div 3} = \frac{7}{40}
\]

Now we go back to the original expression and substitute the simplified multiplication:

\[
\frac{6}{7} + \frac{7}{40}
\]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 40 is 280.

Now we convert each fraction:

\[
\frac{6}{7} = \frac{6 \times 40}{7 \times 40} = \frac{240}{280}
\]

\[
\frac{7}{40} = \frac{7 \times 7}{40 \times 7} = \frac{49}{280}
\]

Now we can add these fractions:

\[
\frac{240}{280} + \frac{49}{280} = \frac{240 + 49}{280} = \frac{289}{280}
\]

The fraction \( \frac{289}{280} \) cannot be simplified further since 289 is not divisible by 280.

Thus, the final simplified result of the expression \( \frac{6}{7} + \frac{3}{4} \times \frac{7}{30} \) is:

\[
\frac{289}{280}
\]

or as a mixed number:

\[
1 \frac{9}{280}
\]