Prozente und Prozentrechnung: Unterschied zwischen den Versionen

Aus ZUM-Unterrichten
Keine Bearbeitungszusammenfassung
Markierung: 2017-Quelltext-Bearbeitung
Keine Bearbeitungszusammenfassung
Markierung: 2017-Quelltext-Bearbeitung
Zeile 35: Zeile 35:


TEST
TEST
<syntaxhighlight lang="html">
<!DOCTYPE html>
<html>
<head>
<meta name=viewport content="width=device-width,initial-scale=1">
<meta charset="utf-8"/>
<script src="https://cdn.geogebra.org/apps/deployggb.js"></script>
</head>
<body>
<div id="ggbApplet"></div>
<script>
var parameters = {
"id": "ggbApplet",
"width":1920,
"height":1017,
"showMenuBar":true,
"showAlgebraInput":true,
"showToolBar":true,
"customToolBar":"0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71  14  68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6",
"showToolBarHelp":true,
"showResetIcon":false,
"enableLabelDrags":false,
"enableShiftDragZoom":true,
"enableRightClick":false,
"errorDialogsActive":false,
"useBrowserForJS":false,
"allowStyleBar":false,
"preventFocus":false,
"showZoomButtons":true,
"capturingThreshold":3,
// add code here to run when the applet starts
"appletOnLoad":function(api){ /* api.evalCommand('Segment((1,2),(3,4))');*/ },
"showFullscreenButton":true,
"scale":1,
"disableAutoScale":false,
"allowUpscale":false,
"clickToLoad":false,
"appName":"classic",
"buttonRounding":0.7,
"buttonShadows":false,
"language":"de",
// use this instead of ggbBase64 to load a material from geogebra.org
// "material_id":"RHYH3UQ8",
// use this instead of ggbBase64 to load a .ggb file
// "filename":"myfile.ggb",
"ggbBase64":"UEsDBBQAAAAIAHi6FFP7dINnCwUAAP0lAAAXAAAAZ2VvZ2VicmFfZGVmYXVsdHMyZC54bWztmk9z2jgUwM/bT+HRafcQsAEDycTppJ3Z2cykaWeT2dmrMMJoIySvJQeTT98nydgmxCmYtEBTDshP1t/fe5KeJJ+/z2bMeSCJpIIHyGu5yCE8FGPKowClanIyRO8v3p1HRERklGBnIpIZVgHydcoiH0itvt/XcTiOAxQyLCUNkRMzrHSWAInJhFFOkONkkp5xcYNnRMY4JLfhlMzwtQixMmVNlYrP2u35fN5a1toSSdSGgmU7k+N2FKkWhMiBpnMZoPzhDMpdyT3vmnwd1/Xa/366tvWcUC4V5iE0BLo1JhOcMiXhkTAyI1w5ahGTAMWCcoUchkeEBeiLlpzfJwkhfyAnzwS0XHTx7rdzORVzR4z+IyHEqSSFovN8RmjrNPD6o2AicZIADQbIAbg6GAWo4/sAjcVTHCDXJmZ4QRLnAUMJeQxOlQhNfhM7wUzmBZuaPokxsW96eXpOQUuA05GKgD7cloccGRMyhlajvI/wAOpZGE1XSgyFSMbSyQJ0g2+Qs8jDRxuaJIbOLX3MK/WrsWrB8mjT9vN2DnYzxGMSEz6GRCucvUac+0PDWQfAWQfHjTmv9Pth7h8J5j1AhqG+LeXPvMq204it14HJAbpkwl+TxQrfK/43iaDVVcrd46F8FIxXbbjXiC74BNAf+D9KsiaJZSj1P/g2YhYzkr0ieOsX5RCvjVBA7zTzMarQtVO2jykD6m0IXQOx+NSUhvecSHDzwHKKcvXDX3QMK5ipT4AfSRWU5A2GtgTyP19RGgWdUUjzsiImKQ91rwq4H9PkoaqNbs/dhz7KMhuPgBpl7Eq6nqUkkZYKLrdLuTTtZm7dWzdtkSqma77iCrZfQA3aKtc6d09IfAdFfeZ3CeZS78FWbalecwlevKQ1/xi09tZ0tpy5+ANOCk1UtdbMM6pdu1tgBntW3RbTeBXE7k7MQZnvlra5kxH1mw39jtt7nl5rcMBG9ADdEyWGf3KxdAV+OWZNZsJn/GmcKCIp5t/anbBFVBnTX5ZyoZGB1cjubdx6/+h3jVZ9KO2JhXuu/Xm9U9fz+nAMsHdFv4x4ZS+iGduIErJ12n485IMdOPU8Q8H1GfhyL2GlgmTvp5tAXmHbRiPC7cwr4aLANckWEEDmRy3pG4bMM/ICAnj7qAOINvmh6QnNnEub49ImvOzYoGuDng38AlGzvaJRbgxzV8VXfrJE9JptcA5hOnnTSv8B/jpPZySpTA43S7kwHt9OD1BeWj1F2mgyqLOTequQjI7BhGYUlHQC2pthcAO0vz+SgqUKLung7ouXl3TWjOd0rKbawYO6JzTT5mLLdKYioY+Cq4KGo0fBJTPXeSsHGs+ZT+cl/3XFWHeboDGPWDkaL61UasCe2ZtETw/znlNMlSE0xCDstzrDrjf0u+7AG5z6w/6GSL1hidS+2Jjoun2ANexuIVuNc1Dg+jjHSVielIL7XLPeuN6g53c7px3fOz3twQNU8tobwj+LiHJzc4gHe8YC1pJ+tzM7JsJUlifRVioIgUn+ZA4LTjPKKE4Wu1n7VowVyUqX4c4IlQ8KDhBxfVcAfFQ27cpKlVt725kJBYocvvaAswRTCeUfcHgfJSLluW1XF6JX6Xq+UBziucJICEZgs7vs1oelXLkrXlv66wDlq+0+xx98VRPej0S2slp947pLliPg2giVG9xnRsDmvVxf6U72bgpNzui2uliscVGqCmhXPnRqL7+quvgKUEsDBBQAAAAIAHi6FFMwuba3fAMAAE8RAAAXAAAAZ2VvZ2VicmFfZGVmYXVsdHMzZC54bWztmM1u2zgQgM/bpyB4ryXZkhIFUQqje9gF2iKLXvbKUGObuzKpkrRl5dX6Dn2mDn/iyG0S1EESoEV98PBHM0N+MxqJOn+zW7dkC9oIJWuaTVJKQHLVCLms6cYuXp/SNxevzpeglnClGVkovWa2poW7cq+HvUlZlG6MdV1NecuMEZySrmXWqdRULRatkEAJ2RlxJtUHtgbTMQ4f+QrW7J3izHpbK2u7syTp+35y43Wi9DJBwybZmSZZLu0EJSW4dGlqGhtnaPdAu595vWmaZsm/798FP6+FNJZJjgvBbTWwYJvWGmxCC2uQltihA9yAkoLP0EfLrqCt6d/S4l6BuyUSvtFb1I/KNZ1lRUovXv1xzpXSjSFqV1MkoYYgroPoES8iC3PbMLcNc30Y7MNg7wcTZ9CsVE/U1X/ouKZWb9BrXJDv+Gtw+q1qlSa6plP0gHHLUpRXKKspBqTtVgwtTrI0/LK8SrOszKZBv2UDaLJlaDR6ZRuruDfpRxesNdGXd/5eNRBm8ni9FJgTjoyxgNFH56YDaHwr8MRtYSoMPqvG9jAjPtqhBWJXgv8vwWA8i5GSa/wlmgZccgYdEEuQWySitMFkSr2XAQVefu16Lgt3me8PKHD22gkc9vq4VC12ZB405uHC+TSIWRB5EMUeCXySYZ3G/de0YxrzFw1xN3+exOz5Lo/YTpjZn/uozWN3lDrpzKfOsZHG5SFK/Mcwu7suBvm5QorZ87xBvZ8viW3AXX/5/DBuf2dypi0YweTo/n3rJr4lX/4M5J+T+/0g0b6EEb9L3z/gh3X1UfyqygOcZigRoZf7GlU8FcZYikNhDXU11tq9yQVzT7no5d7qeBfUyPJoqKodVtBoJW+5joZu0c4i2sfcSceGIytmPh5FeGSMMnqSRyRFVaZ5mT9ZbB6b4keRnWu+EmtogB2ixcC+FNppFh7H+YlH68SvwfZywIossDqMub5cyvqSgYuvAtfpL5Ozl1qY9SHV7AWplqEwB6oV9n5CqhLsfp8fXHtcVYvfVfUYlp82rPFvYHGr/9z0x0xDgj5laSzzyv1Oyqw4zXI80jwRoOc4bNx51HCD4TwxBHGNIho89vRB5mUQJ0GcBlHdezIR664VXNiHQ2s2eoFn77telePUYZTzx0UZ9e58WZ6c/Gja3xp+kdflsdKDb3bJ6NNBcvOd4uIrUEsDBBQAAAAIAHi6FFPWN725GQAAABcAAAAWAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc0srzUsuyczPU0hPT/LP88zLLNHQVKiuBQBQSwMEFAAAAAgAeLoUU2Xa+BHICQAA3CwAAAwAAABnZW9nZWJyYS54bWzdWu1y28YV/e08xQ5m0rFbkcTik3RJZyRbsjOjJJrI7XT6DwSW5FYgwAKgRHryOH2TvljO3QVAUJBM0ZRjKbLJBRYXd3fPPfdjQQx/WM1jdi2yXKbJyOBd02AiCdNIJtORsSwmnb7xw5vvhlORTsU4C9gkzeZBMTJckqzvw1nXcz3qCxaLkRHGQZ7L0GCLOCjolpGRTiaxTITBZAR56/TUP/OszonP3Y5zZtmdY+74HXNw6vGzd/7x2empwdgql6+T9OdgLvJFEIrLcCbmwXkaBoUadVYUi9e93s3NTbeaXzfNpj1MIe+t8qg3nY67aA2GRSb5yCgPXkPv1t03trrPMk3e+9dP53qcjkzyIkhCTJkAWMo3370Y3sgkSm/YjYyKGeAaWFjxTMjpDJBwk/sG65HYAsAsRFjIa5Hj5sapWn4xXxhKLEjo+gt9xOJ6ZQaL5LWMRDYyzC4f+APuNf4MlmZSJEUpzPWgLSXob2jxTMvs25u/u5UMe9WchtdS3OjJ0ZE2G7cMVqRpPA5IJ/uNceaa+DA+YEfM89FjMe4yBz199PjMpj6XO8xmJMJt5jhoHermHq7QZXy7rsk4xxVmmcyymMWZZePUdZkLMZ/utSDrDZQ+Ex+SxozwsanPtvFRfbaDj0VHUORqNZiHa3vqyFXffboHo7gY7zemLqHPGWA46nB9zmzMBOe+yaAX6jFjtRrHZPSfM4cGsXxm9ZnSqvSbwOha5nIci5ExCeKcOJ9MMrC4Ps+LdSwUiGVHw2pH+AcJ+Qnirgl+ac4Rv8wj+nj4OHRBW722Du6qxy2y5b7DghF6UM5dUOyhozrbjAABQDSCxQS4qoHZqBc8oVOTzIFGQWeaRAY0rpYBrHQKaFWjZRRh0GCCh+FaLdDeB9V+Y32QI76iISqisRnNGweYPzVOeerpU0VyE2TVvUQ5NGAweHzgYmpr7bUYxxwgRD2YJfr63Rh6AOb2sD4+cOTWsE2P2HfMzUL7UFwE45FxfP7+9OTX4z0840C078TaxVrpv/q0hrT3igItoL9gRG/LEx9nwQ5h/rDhuQVC/MFj+sSIdvDRLTxVtY9jiMEOQwx7Vb4cljNi+YxkS74XYo4CxGS+zTwVPFTiRMZExtDZ07eY7zKfQkeVQ5Hz+syjtkyklEb7W4nUpTTbyKYedSJjUaRhKhHqtGo5VWbFscqtlHe3cyuSoLPJg5ggqeKMIXszj4JXmRAxC6tOiRamjwzoMaRN12IeBch7siPKwTSXNbAzEaNULE2gMJTJYlls4RbOqVxSh0UK6SBWZV4pH6Xh1UmNdKlJBDmKsY1alDSb8kuXOFvV2YthHIwFatPpJdGAsesgJgdSI0zSpGBVXvSob9hTpeBQLMNYRjJI/gm7V/XSz8v5WGTgGw5TWqRSQrezumZU2bWqGQfwWiUTpmkWXa5z8ISt/i0y3D1wur7joPjzbBs1IHcNttZXUPt0uef00WvaLhq4fh4GxHDH7LrOwLYt3+YofQa4554rllrOi6G4vhRFgeXnLFgJkFTDPc3Iw0oY6eTH/CSNN12LVCbF22BRLDO1V0CczmhNx8k0FgpJZWSU0uHVOF1dKggxptL1cb3AWafEZzx9m8ZpxuB/lotVQptqEeqpVTI0tVoKPgcZfEOiNBRpra+jLlcSqoUMtUqKdiDaynqpmKBeZ6klWMlcRRbobtJQMYTK8mUii/PqpJDh1WalJK/tX2G4rbIUOVjlsHeLesPSKSoiztNIaBLbWn7r+vBKZImINecS2H2ZLnMtri2rZr3MxUVQzI6T6FcxhcNeBBQwC0xEi27WF4lQznGj7i9xDogE/8DCdG8kppmo8NCT0VYoZ8nyRSaCKJ8JAZ8obaE9YiOmuoe9avpDlAKxUKlgLhFQOjD1PFipYgNehFih2DXMw0wuiN5sjLB+JTYMjmROKuoOkgYkOdaG2JAmMEZBhrjI0k/YKKFfyIlIsMVdFrMUNIOKoIAA9nJDEYs5hFihmJ0s5yKj/W9pZam2e1jGslxMRWuyMEvH/0E0ukWMDcK4fA/zWRAvZoHaI5r6jzsDk3MP+zTN92BN4agR0JT2n7YZgmmATxBUQEKtwhEqKePpoIVD6uq6vmPavuO7po99kY24swbiXdvnjode2xs4lu3DohO5akANuOQnsK2mjqL2saZCc60bBy1mcAVsRclLKc0rXMuDDzKKhEoiJdvAQGWxyvAglKDhcVTfiEcRaxWpGjQPEb/oPoXFgo3Y99fs+9LJtEF3mja5bVrM9hua9pfJJBcFGatDDwpgnQ4vU8xu0yPmahfCQcvyHKb3vb5vwe4ctR5Uu12L983+wPFMbvum9zztfv7//yVTwSKRs8vSx/PXxIRw3qLCCoEKT7Zwa2nLdyg4Vhj7ZXLEzFfVsCo56upjmz3lhfrmFlGquvhzTOFkH0pv1JZJsubLAx2/GWRzZWFABZPi+1MNsJotZe4yaDV7W4F5g1KYzudBErFE1dg/JpQ2sDi1WF3iBebIWB0jM2LefGSs1aFe57KoBI613lLbDiiPvwxK2sUCSWoAJDWH4rgbxtIdd8LYJttJRTbziHXsW2zbRbaTL0PIxwMDIETNYVS77a2IbG1/xcGd/noL3g4izcE0beP7tuHMLXx3evPbbwxwy5cfBaVtZ75I4/U01Tlv48p4FENuDHoGlkIxsCm43Xboa1iX5LB9I7mxlkMqDRzUiLu8XQ9cYQld9+YNIHhP2mApfkeQBbDhfn9Xmm7wr2mvaouiM7VLa6pT9UPLrjYXtxabiymd1TMJ2sw6bKZ7eu5yJWMZZOvWNmFDOVCtDnuVsoNtA+7EFAvqFAJfbe9VroRY0Ibyl+RjFiQ5/dy0vUl5ONDjpw+0dm3ycCBtP1+ow6cPNcXPmtTPGOro6UNdJqyS1k8a6lbV8L6qGl6uXr59xf7KJOvR7zyvjtgaHfuWEe+fTBnhdumR41ertvALf13N3t467QLp9JvvnB6znH2MTVcb3w+H7BY+/KkA/koMPmt4/rvbnv9ub88/e3Ke//hPA+7eQCAU0MYAeNLGAAGVNgYf2hsIPNslOSBCchMtN9UbiNmeGwjrW20g9IM+7oKTZC8TD1HrHQQeoX2VHYT4shLgM1P9WjWAot5TrwE+i/XkGWDdrGw73APmzxXt6TNAu0xCFbWfN+CzZwD41s7tSUeSVk3xUawKjK7qir/8d5kWf9ff7G+stcF4hc6mzF0lRgF9tW208gf8OsXENb369tAfqfazIF6rzYoLqhvIVla3T6+32rbvenh50qaXaMlbnK7r9i0fr9jiBYe+5eDXrKoWaSKIhL/5yVa9nlG+Cvzmd1BLAQIUABQAAAAIAHi6FFP7dINnCwUAAP0lAAAXAAAAAAAAAAAAAAAAAAAAAABnZW9nZWJyYV9kZWZhdWx0czJkLnhtbFBLAQIUABQAAAAIAHi6FFMwuba3fAMAAE8RAAAXAAAAAAAAAAAAAAAAAEAFAABnZW9nZWJyYV9kZWZhdWx0czNkLnhtbFBLAQIUABQAAAAIAHi6FFPWN725GQAAABcAAAAWAAAAAAAAAAAAAAAAAPEIAABnZW9nZWJyYV9qYXZhc2NyaXB0LmpzUEsBAhQAFAAAAAgAeLoUU2Xa+BHICQAA3CwAAAwAAAAAAAAAAAAAAAAAPgkAAGdlb2dlYnJhLnhtbFBLBQYAAAAABAAEAAgBAAAwEwAAAAA=",
};
// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator DA=Data Analysis, FI=Function Inspector, macro=Macros
var views = {'is3D': 0,'AV': 1,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'macro': 0};
var applet = new GGBApplet(parameters, '5.0', views);
window.onload = function() {applet.inject('ggbApplet')};
applet.setPreviewImage('data:image/gif;base64,R0lGODlhAQABAAAAADs=','https://www.geogebra.org/images/GeoGebra_loading.png','https://www.geogebra.org/images/applet_play.png');
</script>
</body>
</html>
</syntaxhighlight>

Version vom 20. August 2021, 21:20 Uhr

Lernpfad

Herzlich willkommen im Lernpfad Prozente und Prozentrechnung!


Dieser Lernpfad soll dir dabei helfen, dein Wissen aus der Bruchrechnung auf die Prozentrechnung zu übertragen und deine Vorstellung von Prozenten auf- bzw. auszubauen.

Das Schöne daran ist, dass du vieles von dem, was du bereits aus der Bruchrechnung kennst, hier direkt anwenden kannst.

Der Begriff "Prozent" heißt dabei nichts anderes als "von Hundert". Du hast es also im Prinzip mit nichts anderem zu tun, als einem Bruch, dessen Nenner immer 100 ist. Es gibt also keinen Grund, vor der Prozentrechnung Angst zu haben!
Also: Leg los!

Wiederholung: Bruchteil, Anteil und Ganzes

Info
Zunächst rufen wir uns in Erinnerung, was der Bruchteil, der Anteil und das Ganze in der Bruchrechnung war. Noch einmal: Die Prozentrechnung ist nichts anderes als ein Sonderfall der Bruchrechnung.


Beispiel

In diesem Beispiel schauen wir uns noch einmal eines Kreises an.

Darstellung BAG Kreis.png

In der Prozentrechnung gibt es nun andere Begriffe für das, was du bereits aus der Bruchrechnung kennst.
Das Ganze nennt sich hier der Gesamtwert, der Bruchteil entspricht dem Prozentwert und der Anteil wird hier Prozentsatz genannt und nicht mehr als Bruch, sondern als Zahlenwert mit einem Prozentzeichen (%) dahinter angegeben.

506

TEST 

<!DOCTYPE html>
<html>
<head>
<meta name=viewport content="width=device-width,initial-scale=1">
<meta charset="utf-8"/>
<script src="https://cdn.geogebra.org/apps/deployggb.js"></script>

</head>
<body>
<div id="ggbApplet"></div>

<script>
var parameters = {
"id": "ggbApplet",
"width":1920,
"height":1017,
"showMenuBar":true,
"showAlgebraInput":true,
"showToolBar":true,
"customToolBar":"0 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71  14  68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6",
"showToolBarHelp":true,
"showResetIcon":false,
"enableLabelDrags":false,
"enableShiftDragZoom":true,
"enableRightClick":false,
"errorDialogsActive":false,
"useBrowserForJS":false,
"allowStyleBar":false,
"preventFocus":false,
"showZoomButtons":true,
"capturingThreshold":3,
// add code here to run when the applet starts
"appletOnLoad":function(api){ /* api.evalCommand('Segment((1,2),(3,4))');*/ },
"showFullscreenButton":true,
"scale":1,
"disableAutoScale":false,
"allowUpscale":false,
"clickToLoad":false,
"appName":"classic",
"buttonRounding":0.7,
"buttonShadows":false,
"language":"de",
// use this instead of ggbBase64 to load a material from geogebra.org
// "material_id":"RHYH3UQ8",
// use this instead of ggbBase64 to load a .ggb file
// "filename":"myfile.ggb",
"ggbBase64":"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",
};
// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator DA=Data Analysis, FI=Function Inspector, macro=Macros
var views = {'is3D': 0,'AV': 1,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'macro': 0};
var applet = new GGBApplet(parameters, '5.0', views);
window.onload = function() {applet.inject('ggbApplet')};
applet.setPreviewImage('data:image/gif;base64,R0lGODlhAQABAAAAADs=','https://www.geogebra.org/images/GeoGebra_loading.png','https://www.geogebra.org/images/applet_play.png');
</script>
</body>
</html>
Abgerufen von „https://unterrichten.zum.de/index.php?title=Prozente_und_Prozentrechnung&oldid=120629“