Zhrnutie

test


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    Available courses

    Definícia zlomku, geometrická interpretácia, rozšírenie zlomku, sčitovanie(odčitovanie) zlomkov, násobenie , delenie zlomkov, porovnanie zlomkov delením, 

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    <p class=MsoNormal>MOCNINY S&nbsp;PRIRODZENÝM MOCNITEĽOM</p>
    <p class=MsoNormal>Pre každé prirodzené číslo n , a&nbsp;pre každé reálne číslo
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    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:65.25pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image009.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=87 height=19
    src="YOUTUBE_teória.files/image010.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    style='mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><o:p></o:p></span></p>
    <p class=MsoListParagraphCxSpMiddle style='margin-left:41.25pt;mso-add-space:
    auto;text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r><m:r>.</m:r><m:r>b</m:r></span></i></m:e></m:d></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>b</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:70.5pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image011.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=94 height=19
    src="YOUTUBE_teória.files/image012.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    style='mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><o:p></o:p></span></p>
    <p class=MsoListParagraphCxSpLast style='margin-left:41.25pt;mso-add-space:
    auto;text-indent:-18.0pt;mso-list:l1 level1 lfo2'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:f><m:fPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r></span></i></m:num><m:den><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>b</m:r></span></i></m:den></m:f></m:e></m:d></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>=</m:r></span></i><m:f><m:fPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>b</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:7.0pt;mso-text-raise:-7.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:46.5pt;height:22.5pt'>
    <v:imagedata src="YOUTUBE_teória.files/image013.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=62 height=30
    src="YOUTUBE_teória.files/image014.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    style='mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><o:p></o:p></span></p>
    <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman";
    mso-fareast-theme-font:minor-fareast'>Dôkaz:<o:p></o:p></span></p>
    <p class=MsoNormal>MOCNINY S&nbsp;CELOČÍSLENÝM MOCNITEĽOM<span
    style='mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><o:p></o:p></span></p>
    <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman";
    mso-fareast-theme-font:minor-fareast'>Veta:</span><!--[if gte msEquation 12]><m:oMath><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>Nec</m:r><m:r>h</m:r><m:r>
    &#8704; </m:r><m:r>m</m:r><m:r>,</m:r><m:r>n</m:r><m:r> &#8712;</m:r><m:r>Z</m:r><m:r>
    </m:r><m:r>a</m:r><m:r> čí</m:r><m:r>sla</m:r><m:r> </m:r><m:r>a</m:r><m:r>,</m:r><m:r>b</m:r><m:r>
    &#8712;</m:r><m:r>R</m:r><m:r> , </m:r><m:r>potom</m:r><m:r> </m:r><m:r>platia</m:r><m:r>
    </m:r><m:r>nasledovn</m:r><m:r>é </m:r><m:r>tvrdenia</m:r><m:r>:</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:4.0pt;mso-text-raise:-4.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:333pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image015.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=444 height=19
    src="YOUTUBE_teória.files/image016.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]><span
    style='mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><o:p></o:p></span></p>
    <p class=MsoListParagraphCxSpFirst style='text-indent:-18.0pt;mso-list:l0 level1 lfo3'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>.</m:r></span></i><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r><m:r>+</m:r><m:r>m</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:70.5pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image007.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=94 height=19
    src="YOUTUBE_teória.files/image008.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    <p class=MsoListParagraphCxSpMiddle style='text-indent:-18.0pt;mso-list:l0 level1 lfo3'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:f><m:fPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r></span></i></m:sup></m:sSup></m:num><m:den><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSup></m:den></m:f><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>m</m:r><m:r>-</m:r><m:r>n</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:7.0pt;mso-text-raise:-7.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:51.75pt;height:21pt'>
    <v:imagedata src="YOUTUBE_teória.files/image017.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=69 height=28
    src="YOUTUBE_teória.files/image018.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    <p class=MsoListParagraphCxSpMiddle style='text-indent:-18.0pt;mso-list:l0 level1 lfo3'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>3.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><m:d><m:dPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:dPr><m:e><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>m</m:r></span></i></m:sup></m:sSup></m:e></m:d></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>n</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>=</m:r></span></i><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast;
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif;mso-fareast-font-family:
    "Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif;
    mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast'><m:r>m</m:r><m:r>.</m:r><m:r>n</m:r></span></i></m:sup></m:sSup></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:65.25pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image009.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=87 height=19
    src="YOUTUBE_teória.files/image010.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    <p class=MsoListParagraphCxSpMiddle style='text-indent:-18.0pt;mso-list:l0 level1 lfo3'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>4.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>0</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=1</m:r></span></i></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:3.0pt;mso-text-raise:-3.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:32.25pt;height:14.25pt'>
    <v:imagedata src="YOUTUBE_teória.files/image019.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=43 height=19
    src="YOUTUBE_teória.files/image020.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    <p class=MsoListParagraphCxSpLast style='text-indent:-18.0pt;mso-list:l0 level1 lfo3'><![if !supportLists]><span
    style='mso-bidi-font-family:Calibri;mso-bidi-theme-font:minor-latin'><span
    style='mso-list:Ignore'>5.<span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
    </span></span></span><![endif]><!--[if gte msEquation 12]><m:oMath><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>-</m:r><m:r>n</m:r></span></i></m:sup></m:sSup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>=</m:r></span></i><m:f><m:fPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>1</m:r></span></i></m:num><m:den><m:sSup><m:sSupPr><span
    style='font-family:"Cambria Math",serif;mso-ascii-font-family:"Cambria Math";
    mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
    normal'><m:ctrlPr></m:ctrlPr></span></m:sSupPr><m:e><i style='mso-bidi-font-style:
    normal'><span style='font-family:"Cambria Math",serif'><m:r>a</m:r></span></i></m:e><m:sup><i
    style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math",serif'><m:r>n</m:r></span></i></m:sup></m:sSup></m:den></m:f></m:oMath><![endif]--><![if !msEquation]><span
    style='font-size:11.0pt;line-height:107%;font-family:"Calibri",sans-serif;
    mso-ascii-theme-font:minor-latin;mso-fareast-font-family:Calibri;mso-fareast-theme-font:
    minor-latin;mso-hansi-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman";
    mso-bidi-theme-font:minor-bidi;position:relative;top:7.0pt;mso-text-raise:-7.0pt;
    mso-ansi-language:SK;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'><!--[if gte vml 1]><v:shape
    id="_x0000_i1025" type="#_x0000_t75" style='width:42.75pt;height:19.5pt'>
    <v:imagedata src="YOUTUBE_teória.files/image021.png" o:title="" chromakey="white"/>
    </v:shape><![endif]--><![if !vml]><img width=57 height=26
    src="YOUTUBE_teória.files/image022.png" v:shapes="_x0000_i1025"><![endif]></span><![endif]></p>
    <p class=MsoNormal>Dôkaz:</p>
    <p class=MsoNormal>MOCNINY S&nbsp;RACIONÁLNYM MOCNITEĽOM</p>
    </div>
    </body>
    </html>

    Práca s prirodzenými číslami, delitele , násobky, deliteľnosť 2,3,4,5,6,8,9,10 , delitele čísla, rozklad na súčin čísel, prvočísla, násobky , spoločné delitele a násobky čísel, najväčší spoločný deliteľ, najmenší spoločný násobok, Euklidov algoritmus

    prirodzené číslo, cifra, číslica, rád číslice, zápis prirodzeného čísla, stovky, tisíce, desaťtisíce, susedné čísla, párne, nepárne čísla, číselná os, vzdialenosť na číselnej osi, usporiadanie čísel, zaokrúhľovanie prirodzených čísel, základné počtové operácie(sčitovanie, odčitovanie, násobenie, delenie), 

    Desatinné čísla, definícia, zobrazenie na číselnej osi, zápis , zaokrúhľovanie, vzájomná vzdialenosť, operácie s desatinnými číslami, násobenie a delenie 10, 100, 1000,...., porovnanie des. čísel,