III gimnazjum

Matematyka wokół nas 3

Obliczmy najpierw wartosˊcˊ tego wyraz˙enia: (32​)3⋅(−121​)3+(8<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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c69,-144,104.5,-217.7,106.5,-221
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s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​)2:23−(3−4<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
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c69,-144,104.5,-217.7,106.5,-221
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M834 80h400000v40h-400000z'/></svg>​)3

Aby obliczycˊ, jakim ułamkiem liczby a jest liczba b, wystarczy uprosˊcicˊ wyraz˙enie ab​:

(−21​)3=(−2−1)3=−2−3 &nbsp; 22=(2−1)−2=(21​)−2

(0,2)2=(51​)2=(5−1)2=5−2 (−31​)3=(−3−1)3=−3−3

a) 4−2=421​=161​ (−12)−3=(−121​)3=−17281​ &nbsp; (−43​)−1=−34​

a) &nbsp; (231​)−3=(37​)−3=(73​)3=34327​ b)

Wpierw sprawdzˊmy, ile hkm​ ma 1 sm​:

a=5⋅2−2+4⋅3−2−6⋅2−3 &nbsp; =5⋅221​+4⋅321​−6⋅231​=5⋅41​+4⋅91​−6⋅81​=

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