Multiply and simplify, if possible

$6$

Explanation

Write \(5\frac15\) and \(1\frac{2}{13}\) as improper fractions

$5\frac15 \left( 1\frac{2}{13} \right) = \frac{26}{5} \cdot \frac{15}{13}$

Multiply the numerators.  Multiply the denominators

$ = \frac{26 \cdot 15}{5 \cdot 13}$

To prepare to simplify, factor 26 as 2 • 13 and 15 as 3 • 5

$= \frac{2 \cdot 13 \cdot 3 \cdot 5}{5 \cdot 13}$

Remove the common factors of 13 and 5 from the numerator and denominator

$\require{cancel} = \frac{2 \cdot \cancel{13}^1 \cdot 3 \cdot \cancel{5}^1}{\cancel{5}_1 \cdot \cancel{13}_1} $

Multiply the remaining actors in the numerator: 2 • 1 • 3 • 1 = 6.  Multiply the remaining factors in the denominator: 1 • 1 = 1

$= \frac61$

Any whole number divided by 1 remains the same

$= 6$