6-2 10/13

To simplify the expression \( 6 - 2 \frac{10}{13} \), first, convert the whole number \(2\) into a fraction with a common denominator of \(13\):

\[ 2 = \frac{2 \times 13}{1 \times 13} = \frac{26}{13} \]

Now, rewrite the expression:

\[ 6 - 2 \frac{10}{13} = 6 - \frac{26}{13} \cdot \frac{10}{13} \]

Now determine \(2 \frac{10}{13}\) (which means \(2 + \frac{10}{13}\)):

\[ 2 \frac{10}{13} = \frac{26}{13} + \frac{10}{13} = \frac{26 + 10}{13} = \frac{36}{13} \]

Now, we rewrite the original equation:

\[ 6 - \frac{36}{13} \]

Next, convert \(6\) to a fraction with a denominator of \(13\):

\[ 6 = \frac{6 \times 13}{1 \times 13} = \frac{78}{13} \]

Now, subtract the fractions:

\[ \frac{78}{13} - \frac{36}{13} = \frac{78 - 36}{13} = \frac{42}{13} \]

Thus, the final answer is:

\[ 6 - 2 \frac{10}{13} = \frac{42}{13} \]

If desired, this can also be expressed as a mixed number:

\[ \frac{42}{13} = 3 \frac{3}{13} \]

So, \(6 - 2 \frac{10}{13} = 3 \frac{3}{13}\) or \(\frac{42}{13}\).