<prompt> Kokotoa leftfloor dfrac 200532003 cdot 2004 - dfrac 200332004 cdot 2005 kuliasakafu,ambapo floor x floor inaashiria nambari kamili chini ya au sawa na x.  <response>: Acha n 2004, ili usemi uwe leftfloor fracn13n-1n - fracn-13n n1 kuliasakafu.Tukichanganya sehemu chini ya kiashiria cha kawaida n-1nn1, tunapata beginaligned leftfloor frac n13n-1n - fracn-13nn1 kuliasakafu leftfloor frac n14 - n-14n-1nn1 kuliasakafu kushotosakafu fracn44n 36n24n1 - n4-4n36n2-4n1n-1nn1 kuliasakafu kushotosakafu frac8n38nn-1nn1 kuliasakafu kushotosakafu frac8nn21 n-1nn1 kuliasakafu leftfloor frac8n21n2-1 rightfloor . endalignedKwa sababu fracn21n2-1 ni kubwa kidogo kuliko 1, tunatarajia frac8n21 n2-1 kuwa kubwa kidogo kuliko 8, ambayo hufanya sakafu kuwa sawa na 8.Hakika, tunayo fracn21n2-1 1 frac2n2-1 1 frac220042 - 1 1 frac21000 1.002,hivyo frac8n21n2-1 8.016, hivyo 8 frac8 n21n2-1 8.016 9, kama inavyodaiwa. 