16. (★★) 计算:
(1) $79 - (-79)$;
(2) $-8 - (-32)$;
(3) $0 - (-2024)$;
(4) $\vert -2.5\vert - \vert -4.5\vert$;
(5) $\left(-1\frac{2}{3}\right) - \left(-2\frac{1}{2}\right)$;
(6) $(-32) - (-27) - (-72) - 87$.
(1) $79 - (-79)$;
(2) $-8 - (-32)$;
(3) $0 - (-2024)$;
(4) $\vert -2.5\vert - \vert -4.5\vert$;
(5) $\left(-1\frac{2}{3}\right) - \left(-2\frac{1}{2}\right)$;
(6) $(-32) - (-27) - (-72) - 87$.
答案
解:(1)原式=79+79
=158
解:(2)原式=-8+32
=24
解:(3)原式=0+2024
=2024
解:(4)原式=2.5-4.5
=-(4.5-2.5)
=-2
解:(5)原式$=2\frac{1}{2}-1\frac{2}{3}$
$=\frac{5}{6}$
解:(6)原式=-32+27+72-87
=(27+72)-(32+87)
=99-119
=-20.
=158
解:(2)原式=-8+32
=24
解:(3)原式=0+2024
=2024
解:(4)原式=2.5-4.5
=-(4.5-2.5)
=-2
解:(5)原式$=2\frac{1}{2}-1\frac{2}{3}$
$=\frac{5}{6}$
解:(6)原式=-32+27+72-87
=(27+72)-(32+87)
=99-119
=-20.
17. (★★★) 规定符号“$f$”表示一种对应关系,按照这种对应关系,一些数的对应结果如下:
① $f(1) = -1$,$f(2) = 0$,$f(3) = 1$,$f(4) = 2$,…$$;
② $f\left(\frac{1}{2}\right) = 2$,$f\left(\frac{1}{3}\right) = 3$,$f\left(\frac{1}{4}\right) = 4$,$f\left(\frac{1}{5}\right) = 5$,…$$.
利用以上规律计算:$f(2025) - f\left(\frac{1}{2026}\right)$.
① $f(1) = -1$,$f(2) = 0$,$f(3) = 1$,$f(4) = 2$,…$$;
② $f\left(\frac{1}{2}\right) = 2$,$f\left(\frac{1}{3}\right) = 3$,$f\left(\frac{1}{4}\right) = 4$,$f\left(\frac{1}{5}\right) = 5$,…$$.
利用以上规律计算:$f(2025) - f\left(\frac{1}{2026}\right)$.
答案
解:由题中规律,得f(2024)=2022
$f(\frac{1}{2025})=2025,$
所以$f(2024)-f(\frac{1}{2025})$
=2022-2025
=-3.
$f(\frac{1}{2025})=2025,$
所以$f(2024)-f(\frac{1}{2025})$
=2022-2025
=-3.
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