основное правило при сложении дробей

[tex] \frac{a}{b} + \frac{c}{d} = \frac{a \times d}{b \times d} + \frac{b \times c}{b \times d} = \frac{a \times d + c \times b}{b \times d} [/tex]

поэтому :

[tex] \frac{7}{13} + 3 \frac{1}{2} - \frac{1}{26} = \\ = \frac{7}{13 } + 3 + \frac{1}{2} - \frac{1}{26} = \\ =3 + ( \frac{7}{13} + \frac{1}{2} - \frac{1}{26} ) = \\ = 3 + ( \frac{7 \times 2}{13 \times 2} + \frac{1 \times 13}{2 \times 13} - \frac{1}{26} ) = \\ = 3 + \frac{14 + 13 - 1}{26} = \\ = 3 + \frac{26}{26} = 3 + 1 = 4[/tex]