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\\cdot 4 = 24",[577,1079,1081,1099,1119],{"className":1080,"ariaHidden":615},[614],[577,1082,1084,1087,1090,1093,1096],{"className":1083},[619],[577,1085],{"className":1086,"style":870},[623],[577,1088,889],{"className":1089},[628],[577,1091],{"className":1092,"style":634},[633],[577,1094,602],{"className":1095},[638],[577,1097],{"className":1098,"style":634},[633],[577,1100,1102,1105,1108,1112,1116],{"className":1101},[619],[577,1103],{"className":1104,"style":870},[623],[577,1106,858],{"className":1107},[628],[577,1109],{"className":1110,"style":1111},[633],"margin-right:0.2778em;",[577,1113,1071],{"className":1114},[1115],"mrel",[577,1117],{"className":1118,"style":1111},[633],[577,1120,1122,1125],{"className":1121},[619],[577,1123],{"className":1124,"style":870},[623],[577,1126,1074],{"className":1127},[628],[942,1129,1130,1160],{},[957,1131,1132],{},[577,1133,1135,1148],{"className":1134},[580],[577,1136,1138],{"className":1137},[584],[586,1139,1140],{"xmlns":588},[590,1141,1142,1146],{},[593,1143,1144],{},[685,1145,919],{},[607,1147,919],{"encoding":609},[577,1149,1151],{"className":1150,"ariaHidden":615},[614],[577,1152,1154,1157],{"className":1153},[619],[577,1155],{"className":1156,"style":870},[623],[577,1158,919],{"className":1159},[628],[957,1161,1162],{},[577,1163,1165,1189],{"className":1164},[580],[577,1166,1168],{"className":1167},[584],[586,1169,1170],{"xmlns":588},[590,1171,1172,1186],{},[593,1173,1174,1176,1179,1181,1183],{},[685,1175,1074],{},[600,1177,1178],{},":",[685,1180,919],{},[600,1182,1071],{},[685,1184,1185],{},"8",[607,1187,1188],{"encoding":609},"24 : 3 = 8",[577,1190,1192,1210,1228],{"className":1191,"ariaHidden":615},[614],[577,1193,1195,1198,1201,1204,1207],{"className":1194},[619],[577,1196],{"className":1197,"style":870},[623],[577,1199,1074],{"className":1200},[628],[577,1202],{"className":1203,"style":1111},[633],[577,1205,1178],{"className":1206},[1115],[577,1208],{"className":1209,"style":1111},[633],[577,1211,1213,1216,1219,1222,1225],{"className":1212},[619],[577,1214],{"className":1215,"style":870},[623],[577,1217,919],{"className":1218},[628],[577,1220],{"className":1221,"style":1111},[633],[577,1223,1071],{"className":1224},[1115],[577,1226],{"className":1227,"style":1111},[633],[577,1229,1231,1234],{"className":1230},[619],[577,1232],{"className":1233,"style":870},[623],[577,1235,1185],{"className":1236},[628],[564,1238,1239],{},"Mit der Formel:",[577,1241,1244],{"className":1242},[1243],"katex-display",[577,1245,1247,1285],{"className":1246},[580],[577,1248,1250],{"className":1249},[584],[586,1251,1253],{"xmlns":588,"display":1252},"block",[590,1254,1255,1282],{},[593,1256,1257,1263,1265,1278,1280],{},[680,1258,1259,1261],{},[596,1260,605],{},[685,1262,782],{},[600,1264,1071],{},[1266,1267,1268,1276],"mfrac",{},[593,1269,1270,1272,1274],{},[685,1271,858],{},[600,1273,602],{},[685,1275,889],{},[685,1277,919],{},[600,1279,1071],{},[685,1281,1185],{},[607,1283,1284],{"encoding":609},"y_2 = \\frac{4 \\cdot 6}{3} = 8",[577,1286,1288,1344,1445],{"className":1287,"ariaHidden":615},[614],[577,1289,1291,1294,1335,1338,1341],{"className":1290},[619],[577,1292],{"className":1293,"style":648},[623],[577,1295,1297,1300],{"className":1296},[628],[577,1298,605],{"className":1299,"style":652},[628,629],[577,1301,1303],{"className":1302},[710],[577,1304,1306,1327],{"className":1305},[714,715],[577,1307,1309,1324],{"className":1308},[719],[577,1310,1312],{"className":1311,"style":724},[723],[577,1313,1315,1318],{"style":1314},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[577,1316],{"className":1317,"style":732},[731],[577,1319,1321],{"className":1320},[736,737,738,739],[577,1322,782],{"className":1323},[628,739],[577,1325,747],{"className":1326},[746],[577,1328,1330],{"className":1329},[719],[577,1331,1333],{"className":1332,"style":754},[723],[577,1334],{},[577,1336],{"className":1337,"style":1111},[633],[577,1339,1071],{"className":1340},[1115],[577,1342],{"className":1343,"style":1111},[633],[577,1345,1347,1351,1436,1439,1442],{"className":1346},[619],[577,1348],{"className":1349,"style":1350},[623],"height:2.0074em;vertical-align:-0.686em;",[577,1352,1354,1359,1432],{"className":1353},[628],[577,1355],{"className":1356},[1357,1358],"mopen","nulldelimiter",[577,1360,1362],{"className":1361},[1266],[577,1363,1365,1423],{"className":1364},[714,715],[577,1366,1368,1420],{"className":1367},[719],[577,1369,1372,1385,1396],{"className":1370,"style":1371},[723],"height:1.3214em;",[577,1373,1375,1379],{"style":1374},"top:-2.314em;",[577,1376],{"className":1377,"style":1378},[731],"height:3em;",[577,1380,1382],{"className":1381},[628],[577,1383,919],{"className":1384},[628],[577,1386,1388,1391],{"style":1387},"top:-3.23em;",[577,1389],{"className":1390,"style":1378},[731],[577,1392],{"className":1393,"style":1395},[1394],"frac-line","border-bottom-width:0.04em;",[577,1397,1399,1402],{"style":1398},"top:-3.677em;",[577,1400],{"className":1401,"style":1378},[731],[577,1403,1405,1408,1411,1414,1417],{"className":1404},[628],[577,1406,858],{"className":1407},[628],[577,1409],{"className":1410,"style":634},[633],[577,1412,602],{"className":1413},[638],[577,1415],{"className":1416,"style":634},[633],[577,1418,889],{"className":1419},[628],[577,1421,747],{"className":1422},[746],[577,1424,1426],{"className":1425},[719],[577,1427,1430],{"className":1428,"style":1429},[723],"height:0.686em;",[577,1431],{},[577,1433],{"className":1434},[1435,1358],"mclose",[577,1437],{"className":1438,"style":1111},[633],[577,1440,1071],{"className":1441},[1115],[577,1443],{"className":1444,"style":1111},[633],[577,1446,1448,1451],{"className":1447},[619],[577,1449],{"className":1450,"style":870},[623],[577,1452,1185],{"className":1453},[628],[564,1455,1456,1457,1486,1487,1516,1517,1545],{},"Ein Vorrat reicht für ",[577,1458,1460,1474],{"className":1459},[580],[577,1461,1463],{"className":1462},[584],[586,1464,1465],{"xmlns":588},[590,1466,1467,1472],{},[593,1468,1469],{},[685,1470,1471],{},"5",[607,1473,1471],{"encoding":609},[577,1475,1477],{"className":1476,"ariaHidden":615},[614],[577,1478,1480,1483],{"className":1479},[619],[577,1481],{"className":1482,"style":870},[623],[577,1484,1471],{"className":1485},[628]," Personen ",[577,1488,1490,1504],{"className":1489},[580],[577,1491,1493],{"className":1492},[584],[586,1494,1495],{"xmlns":588},[590,1496,1497,1502],{},[593,1498,1499],{},[685,1500,1501],{},"12",[607,1503,1501],{"encoding":609},[577,1505,1507],{"className":1506,"ariaHidden":615},[614],[577,1508,1510,1513],{"className":1509},[619],[577,1511],{"className":1512,"style":870},[623],[577,1514,1501],{"className":1515},[628]," Tage. Für ",[577,1518,1520,1533],{"className":1519},[580],[577,1521,1523],{"className":1522},[584],[586,1524,1525],{"xmlns":588},[590,1526,1527,1531],{},[593,1528,1529],{},[685,1530,889],{},[607,1532,889],{"encoding":609},[577,1534,1536],{"className":1535,"ariaHidden":615},[614],[577,1537,1539,1542],{"className":1538},[619],[577,1540],{"className":1541,"style":870},[623],[577,1543,889],{"className":1544},[628]," Personen reicht er",[577,1547,1549],{"className":1548},[1243],[577,1550,1552,1589],{"className":1551},[580],[577,1553,1555],{"className":1554},[584],[586,1556,1557],{"xmlns":588,"display":1252},[590,1558,1559,1586],{},[593,1560,1561,1567,1569,1581,1583],{},[680,1562,1563,1565],{},[596,1564,605],{},[685,1566,782],{},[600,1568,1071],{},[1266,1570,1571,1579],{},[593,1572,1573,1575,1577],{},[685,1574,1471],{},[600,1576,602],{},[685,1578,1501],{},[685,1580,889],{},[600,1582,1071],{},[685,1584,1585],{},"10",[607,1587,1588],{"encoding":609},"y_2 = \\frac{5 \\cdot 12}{6} = 10",[577,1590,1592,1647,1736],{"className":1591,"ariaHidden":615},[614],[577,1593,1595,1598,1638,1641,1644],{"className":1594},[619],[577,1596],{"className":1597,"style":648},[623],[577,1599,1601,1604],{"className":1600},[628],[577,1602,605],{"className":1603,"style":652},[628,629],[577,1605,1607],{"className":1606},[710],[577,1608,1610,1630],{"className":1609},[714,715],[577,1611,1613,1627],{"className":1612},[719],[577,1614,1616],{"className":1615,"style":724},[723],[577,1617,1618,1621],{"style":1314},[577,1619],{"className":1620,"style":732},[731],[577,1622,1624],{"className":1623},[736,737,738,739],[577,1625,782],{"className":1626},[628,739],[577,1628,747],{"className":1629},[746],[577,1631,1633],{"className":1632},[719],[577,1634,1636],{"className":1635,"style":754},[723],[577,1637],{},[577,1639],{"className":1640,"style":1111},[633],[577,1642,1071],{"className":1643},[1115],[577,1645],{"className":1646,"style":1111},[633],[577,1648,1650,1653,1727,1730,1733],{"className":1649},[619],[577,1651],{"className":1652,"style":1350},[623],[577,1654,1656,1659,1724],{"className":1655},[628],[577,1657],{"className":1658},[1357,1358],[577,1660,1662],{"className":1661},[1266],[577,1663,1665,1716],{"className":1664},[714,715],[577,1666,1668,1713],{"className":1667},[719],[577,1669,1671,1682,1690],{"className":1670,"style":1371},[723],[577,1672,1673,1676],{"style":1374},[577,1674],{"className":1675,"style":1378},[731],[577,1677,1679],{"className":1678},[628],[577,1680,889],{"className":1681},[628],[577,1683,1684,1687],{"style":1387},[577,1685],{"className":1686,"style":1378},[731],[577,1688],{"className":1689,"style":1395},[1394],[577,1691,1692,1695],{"style":1398},[577,1693],{"className":1694,"style":1378},[731],[577,1696,1698,1701,1704,1707,1710],{"className":1697},[628],[577,1699,1471],{"className":1700},[628],[577,1702],{"className":1703,"style":634},[633],[577,1705,602],{"className":1706},[638],[577,1708],{"className":1709,"style":634},[633],[577,1711,1501],{"className":1712},[628],[577,1714,747],{"className":1715},[746],[577,1717,1719],{"className":1718},[719],[577,1720,1722],{"className":1721,"style":1429},[723],[577,1723],{},[577,1725],{"className":1726},[1435,1358],[577,1728],{"className":1729,"style":1111},[633],[577,1731,1071],{"className":1732},[1115],[577,1734],{"className":1735,"style":1111},[633],[577,1737,1739,1742],{"className":1738},[619],[577,1740],{"className":1741,"style":870},[623],[577,1743,1585],{"className":1744},[628],[564,1746,1747,1748,1776],{},"also ",[577,1749,1751,1764],{"className":1750},[580],[577,1752,1754],{"className":1753},[584],[586,1755,1756],{"xmlns":588},[590,1757,1758,1762],{},[593,1759,1760],{},[685,1761,1585],{},[607,1763,1585],{"encoding":609},[577,1765,1767],{"className":1766,"ariaHidden":615},[614],[577,1768,1770,1773],{"className":1769},[619],[577,1771],{"className":1772,"style":870},[623],[577,1774,1585],{"className":1775},[628]," Tage.",[559,1778,1780],{"id":1779},"typische-fehler","Typische Fehler",[1782,1783,1784,1791,1794],"ul",{},[661,1785,1786,1787,1790],{},"Proportional rechnen, obwohl die Zuordnung antiproportional ist: Mit weniger Malern dauert es ",[568,1788,1789],{},"länger",", nicht kürzer.",[661,1792,1793],{},"Die Rechenarten aus dem normalen Dreisatz übernehmen: Hier wird im zweiten Schritt multipliziert und im dritten geteilt.",[661,1795,1796],{},"Annehmen, dass jede „je mehr, desto weniger\"-Zuordnung antiproportional ist. Das gilt nur, wenn das Produkt wirklich gleich bleibt, z.B. wenn alle gleich schnell arbeiten.",{"title":1798,"searchDepth":1799,"depth":1799,"links":1800},"",2,[1801,1802,1803],{"id":561,"depth":1799,"text":562},{"id":840,"depth":1799,"text":841},{"id":1779,"depth":1799,"text":1780},[1805,1808,1814,1816,1818],{"lhs":1806,"rhs":1807},"x2*(x1*y1\u002Fx2)","x1*y1",{"lhs":1809,"rhs":1185,"where":1810},"x1*y1\u002Fx2",{"x1":1811,"y1":1812,"x2":1813},4,6,3,{"lhs":1815,"rhs":1074},"4*6",{"lhs":1817,"rhs":1185},"24\u002F3",{"lhs":1819,"rhs":1585},"5*12\u002F6","x_2 \\neq 0,\\ y \\text{ antiproportional zu } x","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x_2 \\neq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>y\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">antiproportional zu\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","inverse-rule-of-three","y_2 = \\frac{x_1 \\cdot y_1}{x_2}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>y\u003C\u002Fmi>\u003Cmn>1\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">y_2 = \\frac{x_1 \\cdot y_1}{x_2}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" 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