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a) ( 1989 x 1990 + 3978 ) : ( 1992 x 1991 - 3984 )
= 3 962 088 : 3 962 088
= 1
\(a)\)\(\left(1989.1990+3978\right)\div\left(1992.1991-3984\right)\)
\(=\)\(\left(1989.1990+1989.2\right)\div\left(1992.1991-1992.2\right)\)
\(=\)\(\left[1989.\left(1990+2\right)\right]\div\left[1992.\left(1991-2\right)\right]\)
\(=\)\(\left(1989.1991\right)\div\left(1992.1989\right)\)
\(=\)\(1\)
\(b)\)\(\left(637.527-189\right)\div\left(526.637+448\right)\)
\(=\)\(\left[637.\left(526-1\right)-189\right]\div\left(526.637-448\right)\)
\(=\)\(\left[637.526+\left(637-198\right)\right]\div\left(637.526-448\right)\)
\(=\)\(\left(636.526+448\right)\div\left(637.526-448\right)\)
\(=\)\(1\)
\(\dfrac{1989\times1990+3978}{1992\times1991-3984}\)
\(=\dfrac{1989\times1990+1989\times2}{1992\times1991-1992\times2}\)
\(=\dfrac{1989\times\left(1990+2\right)}{1992\times\left(1991+2\right)}\)
\(=\dfrac{1989\times1992}{1992\times1989}\)
\(=1\)
\(\dfrac{637\times527-189}{526\times637+448}\)
\(=\dfrac{637\times\left(526+1\right)-189}{526\times637+448}\)
\(=\dfrac{637\times526+637-189}{526\times637+448}\)
\(=\dfrac{637\times526+448}{526\times637+448}\)
\(=\dfrac{1}{1}\)
\(=1\)
\(\left(1989.1990+3978\right):\left(1992.1991-3984\right)\)
\(=\left[1989.\left(1990+2\right)\right]:\left[1992\left(1991-2\right)\right]=\left(1989.1992\right):\left(1992.1989\right)=1\)