(1) $25×\frac{3}{4} - (-25)×\frac{1}{2} + 25÷(-4)$
$=25×\frac{3}{4} + 25×\frac{1}{2} - 25×\frac{1}{4}$
$=25×(\frac{3}{4} + \frac{1}{2} - \frac{1}{4})$
$=25×1$
$=25$
(2) $7×2.6 + 7×1.5 - 4.1×8$
$=7×(2.6 + 1.5) - 4.1×8$
$=7×4.1 - 4.1×8$
$=4.1×(7 - 8)$
$=4.1×(-1)$
$=-4.1$
(3) $-6×(-\frac{15}{17}) + 14×(-\frac{15}{17}) - 9×(-\frac{15}{17})$
$=(-\frac{15}{17})×(-6 + 14 - 9)$
$=(-\frac{15}{17})×(-1)$
$=\frac{15}{17}$
(4) $(3\frac{1}{8})^{12}×(\frac{8}{25})^{11}×(-2)^3$
$=(\frac{25}{8})^{12}×(\frac{8}{25})^{11}×(-8)$
$=\frac{25}{8}×(\frac{25}{8}×\frac{8}{25})^{11}×(-8)$
$=\frac{25}{8}×1^{11}×(-8)$
$=-25$
(5) $48\frac{24}{25}÷(-48)$
$=(48 + \frac{24}{25})×(-\frac{1}{48})$
$=48×(-\frac{1}{48}) + \frac{24}{25}×(-\frac{1}{48})$
$=-1 - \frac{1}{50}$
$=-\frac{51}{50}$
(6) $(-\frac{5}{8})×(-4)^2 - 0.25×(-5)×(-4)^3$
$=(-\frac{5}{8})×16 - 0.25×(-5)×(-64)$
$=-10 - 80$
$=-90$