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17. (★★) 计算：
(1) (-8)×$(-4\frac{1}{20})$×1.25×(-0.1)；
(2) $(\frac{1}{2}-\frac{5}{6}+\frac{5}{12}-\frac{7}{24})$×(-24)；
(3) 71 $\frac{15}{16}$×(-8)；
(4) (-3.59)×$(-\frac{7}{22})$ - 2.41×$(-\frac{7}{22})$ + 6×$(-\frac{7}{22})$.
(1) (-8)×$(-4\frac{1}{20})$×1.25×(-0.1)；
(2) $(\frac{1}{2}-\frac{5}{6}+\frac{5}{12}-\frac{7}{24})$×(-24)；
(3) 71 $\frac{15}{16}$×(-8)；
(4) (-3.59)×$(-\frac{7}{22})$ - 2.41×$(-\frac{7}{22})$ + 6×$(-\frac{7}{22})$.
答案
解:(1)原式$=[(-8)×1.25×(-0.1)]×(-4\frac{1}{20})$
$=1× (-4\frac{1}{20})$
$=-4\frac{1}{20}$
解:(2)原式$=\frac{1}{2}×(-24)-\frac{5}{6}×(-24)$
$+\frac{5}{12}×(-24)-\frac{7}{24}× (-24)$
=-12+20-10+7
=5.
解:(3)原式$=(72-\frac{1}{16})×(-8)$
$=72×(-8)-\frac{1}{16}×(-8)$
$=-576+ \frac{1}{2}$
$=-575\frac{1}{2}$
解:(4)原式$=(-\frac{7}{22})×(-3.59-2.41+6)$
$=(-\frac{7}{22})×0$
=0
$=1× (-4\frac{1}{20})$
$=-4\frac{1}{20}$
解:(2)原式$=\frac{1}{2}×(-24)-\frac{5}{6}×(-24)$
$+\frac{5}{12}×(-24)-\frac{7}{24}× (-24)$
=-12+20-10+7
=5.
解:(3)原式$=(72-\frac{1}{16})×(-8)$
$=72×(-8)-\frac{1}{16}×(-8)$
$=-576+ \frac{1}{2}$
$=-575\frac{1}{2}$
解:(4)原式$=(-\frac{7}{22})×(-3.59-2.41+6)$
$=(-\frac{7}{22})×0$
=0
18. (★★★) 若 a = -$\frac{2025×2025 - 2025}{2024×2024 + 2024}$,b = -$\frac{2026×2026 - 2026}{2025×2025 + 2025}$,c = -$\frac{2027×2027 - 2027}{2026×2026 + 2026}$,求 abc 的值.
答案
解:依题意，得
$a=-\frac{2025×2025-2025}{2024×2024+2024}$
$=-\frac{2025×(2025-1)}{2024×(2024+1)}$
$=-\frac{2025×2024}{2024×2025}$
=-1.
同理b=-1,c=-1.
所以abc=(-1)×(-1)×(-1)=-1.
$a=-\frac{2025×2025-2025}{2024×2024+2024}$
$=-\frac{2025×(2025-1)}{2024×(2024+1)}$
$=-\frac{2025×2024}{2024×2025}$
=-1.
同理b=-1,c=-1.
所以abc=(-1)×(-1)×(-1)=-1.
