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Deshalb muss auch der Zähler ",[573,821,823,836],{"className":822},[576],[573,824,826],{"className":825},[580],[582,827,828],{"xmlns":584},[586,829,830,834],{},[589,831,832],{},[595,833,597],{},[602,835,597],{"encoding":604},[573,837,839],{"className":838,"ariaHidden":610},[609],[573,840,842,846],{"className":841},[614],[573,843],{"className":844,"style":845},[618],"height:0.4306em;",[573,847,597],{"className":848},[623,667]," des zweiten Bruchs ungleich null sein, denn er wird im Kehrwert zum Nenner.",[559,851,853],{"id":852},"beispiele","Beispiele",[573,855,858],{"className":856},[857],"katex-display",[573,859,861,930],{"className":860},[576],[573,862,864],{"className":863},[580],[582,865,867],{"xmlns":584,"display":866},"block",[586,868,869,927],{},[589,870,871,880,884,892,895,901,904,910,912,919,921],{},[592,872,873,877],{},[874,875,876],"mn",{},"3",[874,878,879],{},"4",[881,882,883],"mo",{},":",[592,885,886,889],{},[874,887,888],{},"1",[874,890,891],{},"2",[881,893,894],{},"=",[592,896,897,899],{},[874,898,876],{},[874,900,879],{},[881,902,903],{},"⋅",[592,905,906,908],{},[874,907,891],{},[874,909,888],{},[881,911,894],{},[592,913,914,917],{},[874,915,916],{},"6",[874,918,879],{},[881,920,894],{},[592,922,923,925],{},[874,924,876],{},[874,926,891],{},[602,928,929],{"encoding":604},"\\frac{3}{4} : \\frac{1}{2} = \\frac{3}{4} \\cdot \\frac{2}{1} = \\frac{6}{4} = \\frac{3}{2}",[573,931,933,1018,1095,1174,1251,1328],{"className":932,"ariaHidden":610},[609],[573,934,936,940,1006,1011,1015],{"className":935},[614],[573,937],{"className":938,"style":939},[618],"height:2.0074em;vertical-align:-0.686em;",[573,941,943,946,1003],{"className":942},[623],[573,944],{"className":945},[627,628],[573,947,949],{"className":948},[592],[573,950,952,994],{"className":951},[635,636],[573,953,955,991],{"className":954},[640],[573,956,959,971,979],{"className":957,"style":958},[644],"height:1.3214em;",[573,960,962,965],{"style":961},"top:-2.314em;",[573,963],{"className":964,"style":653},[652],[573,966,968],{"className":967},[623],[573,969,879],{"className":970},[623],[573,972,973,976],{"style":670},[573,974],{"className":975,"style":653},[652],[573,977],{"className":978,"style":678},[677],[573,980,982,985],{"style":981},"top:-3.677em;",[573,983],{"className":984,"style":653},[652],[573,986,988],{"className":987},[623],[573,989,876],{"className":990},[623],[573,992,698],{"className":993},[697],[573,995,997],{"className":996},[640],[573,998,1001],{"className":999,"style":1000},[644],"height:0.686em;",[573,1002],{},[573,1004],{"className":1005},[711,628],[573,1007],{"className":1008,"style":1010},[1009],"mspace","margin-right:0.2778em;",[573,1012,883],{"className":1013},[1014],"mrel",[573,1016],{"className":1017,"style":1010},[1009],[573,1019,1021,1024,1086,1089,1092],{"className":1020},[614],[573,1022],{"className":1023,"style":939},[618],[573,1025,1027,1030,1083],{"className":1026},[623],[573,1028],{"className":1029},[627,628],[573,1031,1033],{"className":1032},[592],[573,1034,1036,1075],{"className":1035},[635,636],[573,1037,1039,1072],{"className":1038},[640],[573,1040,1042,1053,1061],{"className":1041,"style":958},[644],[573,1043,1044,1047],{"style":961},[573,1045],{"className":1046,"style":653},[652],[573,1048,1050],{"className":1049},[623],[573,1051,891],{"className":1052},[623],[573,1054,1055,1058],{"style":670},[573,1056],{"className":1057,"style":653},[652],[573,1059],{"className":1060,"style":678},[677],[573,1062,1063,1066],{"style":981},[573,1064],{"className":1065,"style":653},[652],[573,1067,1069],{"className":1068},[623],[573,1070,888],{"className":1071},[623],[573,1073,698],{"className":1074},[697],[573,1076,1078],{"className":1077},[640],[573,1079,1081],{"className":1080,"style":1000},[644],[573,1082],{},[573,1084],{"className":1085},[711,628],[573,1087],{"className":1088,"style":1010},[1009],[573,1090,894],{"className":1091},[1014],[573,1093],{"className":1094,"style":1010},[1009],[573,1096,1098,1101,1163,1167,1171],{"className":1097},[614],[573,1099],{"className":1100,"style":939},[618],[573,1102,1104,1107,1160],{"className":1103},[623],[573,1105],{"className":1106},[627,628],[573,1108,1110],{"className":1109},[592],[573,1111,1113,1152],{"className":1112},[635,636],[573,1114,1116,1149],{"className":1115},[640],[573,1117,1119,1130,1138],{"className":1118,"style":958},[644],[573,1120,1121,1124],{"style":961},[573,1122],{"className":1123,"style":653},[652],[573,1125,1127],{"className":1126},[623],[573,1128,879],{"className":1129},[623],[573,1131,1132,1135],{"style":670},[573,1133],{"className":1134,"style":653},[652],[573,1136],{"className":1137,"style":678},[677],[573,1139,1140,1143],{"style":981},[573,1141],{"className":1142,"style":653},[652],[573,1144,1146],{"className":1145},[623],[573,1147,876],{"className":1148},[623],[573,1150,698],{"className":1151},[697],[573,1153,1155],{"className":1154},[640],[573,1156,1158],{"className":1157,"style":1000},[644],[573,1159],{},[573,1161],{"className":1162},[711,628],[573,1164],{"className":1165,"style":1166},[1009],"margin-right:0.2222em;",[573,1168,903],{"className":1169},[1170],"mbin",[573,1172],{"className":1173,"style":1166},[1009],[573,1175,1177,1180,1242,1245,1248],{"className":1176},[614],[573,1178],{"className":1179,"style":939},[618],[573,1181,1183,1186,1239],{"className":1182},[623],[573,1184],{"className":1185},[627,628],[573,1187,1189],{"className":1188},[592],[573,1190,1192,1231],{"className":1191},[635,636],[573,1193,1195,1228],{"className":1194},[640],[573,1196,1198,1209,1217],{"className":1197,"style":958},[644],[573,1199,1200,1203],{"style":961},[573,1201],{"className":1202,"style":653},[652],[573,1204,1206],{"className":1205},[623],[573,1207,888],{"className":1208},[623],[573,1210,1211,1214],{"style":670},[573,1212],{"className":1213,"style":653},[652],[573,1215],{"className":1216,"style":678},[677],[573,1218,1219,1222],{"style":981},[573,1220],{"className":1221,"style":653},[652],[573,1223,1225],{"className":1224},[623],[573,1226,891],{"className":1227},[623],[573,1229,698],{"className":1230},[697],[573,1232,1234],{"className":1233},[640],[573,1235,1237],{"className":1236,"style":1000},[644],[573,1238],{},[573,1240],{"className":1241},[711,628],[573,1243],{"className":1244,"style":1010},[1009],[573,1246,894],{"className":1247},[1014],[573,1249],{"className":1250,"style":1010},[1009],[573,1252,1254,1257,1319,1322,1325],{"className":1253},[614],[573,1255],{"className":1256,"style":939},[618],[573,1258,1260,1263,1316],{"className":1259},[623],[573,1261],{"className":1262},[627,628],[573,1264,1266],{"className":1265},[592],[573,1267,1269,1308],{"className":1268},[635,636],[573,1270,1272,1305],{"className":1271},[640],[573,1273,1275,1286,1294],{"className":1274,"style":958},[644],[573,1276,1277,1280],{"style":961},[573,1278],{"className":1279,"style":653},[652],[573,1281,1283],{"className":1282},[623],[573,1284,879],{"className":1285},[623],[573,1287,1288,1291],{"style":670},[573,1289],{"className":1290,"style":653},[652],[573,1292],{"className":1293,"style":678},[677],[573,1295,1296,1299],{"style":981},[573,1297],{"className":1298,"style":653},[652],[573,1300,1302],{"className":1301},[623],[573,1303,916],{"className":1304},[623],[573,1306,698],{"className":1307},[697],[573,1309,1311],{"className":1310},[640],[573,1312,1314],{"className":1313,"style":1000},[644],[573,1315],{},[573,1317],{"className":1318},[711,628],[573,1320],{"className":1321,"style":1010},[1009],[573,1323,894],{"className":1324},[1014],[573,1326],{"className":1327,"style":1010},[1009],[573,1329,1331,1334],{"className":1330},[614],[573,1332],{"className":1333,"style":939},[618],[573,1335,1337,1340,1393],{"className":1336},[623],[573,1338],{"className":1339},[627,628],[573,1341,1343],{"className":1342},[592],[573,1344,1346,1385],{"className":1345},[635,636],[573,1347,1349,1382],{"className":1348},[640],[573,1350,1352,1363,1371],{"className":1351,"style":958},[644],[573,1353,1354,1357],{"style":961},[573,1355],{"className":1356,"style":653},[652],[573,1358,1360],{"className":1359},[623],[573,1361,891],{"className":1362},[623],[573,1364,1365,1368],{"style":670},[573,1366],{"className":1367,"style":653},[652],[573,1369],{"className":1370,"style":678},[677],[573,1372,1373,1376],{"style":981},[573,1374],{"className":1375,"style":653},[652],[573,1377,1379],{"className":1378},[623],[573,1380,876],{"className":1381},[623],[573,1383,698],{"className":1384},[697],[573,1386,1388],{"className":1387},[640],[573,1389,1391],{"className":1390,"style":1000},[644],[573,1392],{},[573,1394],{"className":1395},[711,628],[564,1397,1398,1399,712,1428,813],{},"Bruch durch ganze Zahl: Der Kehrwert von ",[573,1400,1402,1415],{"className":1401},[576],[573,1403,1405],{"className":1404},[580],[582,1406,1407],{"xmlns":584},[586,1408,1409,1413],{},[589,1410,1411],{},[874,1412,879],{},[602,1414,879],{"encoding":604},[573,1416,1418],{"className":1417,"ariaHidden":610},[609],[573,1419,1421,1425],{"className":1420},[614],[573,1422],{"className":1423,"style":1424},[618],"height:0.6444em;",[573,1426,879],{"className":1427},[623],[573,1429,1431,1449],{"className":1430},[576],[573,1432,1434],{"className":1433},[580],[582,1435,1436],{"xmlns":584},[586,1437,1438,1446],{},[589,1439,1440],{},[592,1441,1442,1444],{},[874,1443,888],{},[874,1445,879],{},[602,1447,1448],{"encoding":604},"\\frac{1}{4}",[573,1450,1452],{"className":1451,"ariaHidden":610},[609],[573,1453,1455,1459],{"className":1454},[614],[573,1456],{"className":1457,"style":1458},[618],"height:1.1901em;vertical-align:-0.345em;",[573,1460,1462,1465,1525],{"className":1461},[623],[573,1463],{"className":1464},[627,628],[573,1466,1468],{"className":1467},[592],[573,1469,1471,1517],{"className":1470},[635,636],[573,1472,1474,1514],{"className":1473},[640],[573,1475,1478,1492,1500],{"className":1476,"style":1477},[644],"height:0.8451em;",[573,1479,1480,1483],{"style":648},[573,1481],{"className":1482,"style":653},[652],[573,1484,1486],{"className":1485},[657,658,659,660],[573,1487,1489],{"className":1488},[623,660],[573,1490,879],{"className":1491},[623,660],[573,1493,1494,1497],{"style":670},[573,1495],{"className":1496,"style":653},[652],[573,1498],{"className":1499,"style":678},[677],[573,1501,1502,1505],{"style":681},[573,1503],{"className":1504,"style":653},[652],[573,1506,1508],{"className":1507},[657,658,659,660],[573,1509,1511],{"className":1510},[623,660],[573,1512,888],{"className":1513},[623,660],[573,1515,698],{"className":1516},[697],[573,1518,1520],{"className":1519},[640],[573,1521,1523],{"className":1522,"style":705},[644],[573,1524],{},[573,1526],{"className":1527},[711,628],[573,1529,1531],{"className":1530},[857],[573,1532,1534,1591],{"className":1533},[576],[573,1535,1537],{"className":1536},[580],[582,1538,1539],{"xmlns":584,"display":866},[586,1540,1541,1588],{},[589,1542,1543,1550,1552,1554,1556,1562,1564,1570,1572,1579,1581],{},[592,1544,1545,1547],{},[874,1546,891],{},[874,1548,1549],{},"5",[881,1551,883],{},[874,1553,879],{},[881,1555,894],{},[592,1557,1558,1560],{},[874,1559,891],{},[874,1561,1549],{},[881,1563,903],{},[592,1565,1566,1568],{},[874,1567,888],{},[874,1569,879],{},[881,1571,894],{},[592,1573,1574,1576],{},[874,1575,891],{},[874,1577,1578],{},"20",[881,1580,894],{},[592,1582,1583,1585],{},[874,1584,888],{},[874,1586,1587],{},"10",[602,1589,1590],{"encoding":604},"\\frac{2}{5} : 4 = \\frac{2}{5} \\cdot \\frac{1}{4} = \\frac{2}{20} = \\frac{1}{10}",[573,1592,1594,1671,1689,1766,1843,1920],{"className":1593,"ariaHidden":610},[609],[573,1595,1597,1600,1662,1665,1668],{"className":1596},[614],[573,1598],{"className":1599,"style":939},[618],[573,1601,1603,1606,1659],{"className":1602},[623],[573,1604],{"className":1605},[627,628],[573,1607,1609],{"className":1608},[592],[573,1610,1612,1651],{"className":1611},[635,636],[573,1613,1615,1648],{"className":1614},[640],[573,1616,1618,1629,1637],{"className":1617,"style":958},[644],[573,1619,1620,1623],{"style":961},[573,1621],{"className":1622,"style":653},[652],[573,1624,1626],{"className":1625},[623],[573,1627,1549],{"className":1628},[623],[573,1630,1631,1634],{"style":670},[573,1632],{"className":1633,"style":653},[652],[573,1635],{"className":1636,"style":678},[677],[573,1638,1639,1642],{"style":981},[573,1640],{"className":1641,"style":653},[652],[573,1643,1645],{"className":1644},[623],[573,1646,891],{"className":1647},[623],[573,1649,698],{"className":1650},[697],[573,1652,1654],{"className":1653},[640],[573,1655,1657],{"className":1656,"style":1000},[644],[573,1658],{},[573,1660],{"className":1661},[711,628],[573,1663],{"className":1664,"style":1010},[1009],[573,1666,883],{"className":1667},[1014],[573,1669],{"className":1670,"style":1010},[1009],[573,1672,1674,1677,1680,1683,1686],{"className":1673},[614],[573,1675],{"className":1676,"style":1424},[618],[573,1678,879],{"className":1679},[623],[573,1681],{"className":1682,"style":1010},[1009],[573,1684,894],{"className":1685},[1014],[573,1687],{"className":1688,"style":1010},[1009],[573,1690,1692,1695,1757,1760,1763],{"className":1691},[614],[573,1693],{"className":1694,"style":939},[618],[573,1696,1698,1701,1754],{"className":1697},[623],[573,1699],{"className":1700},[627,628],[573,1702,1704],{"className":1703},[592],[573,1705,1707,1746],{"className":1706},[635,636],[573,1708,1710,1743],{"className":1709},[640],[573,1711,1713,1724,1732],{"className":1712,"style":958},[644],[573,1714,1715,1718],{"style":961},[573,1716],{"className":1717,"style":653},[652],[573,1719,1721],{"className":1720},[623],[573,1722,1549],{"className":1723},[623],[573,1725,1726,1729],{"style":670},[573,1727],{"className":1728,"style":653},[652],[573,1730],{"className":1731,"style":678},[677],[573,1733,1734,1737],{"style":981},[573,1735],{"className":1736,"style":653},[652],[573,1738,1740],{"className":1739},[623],[573,1741,891],{"className":1742},[623],[573,1744,698],{"className":1745},[697],[573,1747,1749],{"className":1748},[640],[573,1750,1752],{"className":1751,"style":1000},[644],[573,1753],{},[573,1755],{"className":1756},[711,628],[573,1758],{"className":1759,"style":1166},[1009],[573,1761,903],{"className":1762},[1170],[573,1764],{"className":1765,"style":1166},[1009],[573,1767,1769,1772,1834,1837,1840],{"className":1768},[614],[573,1770],{"className":1771,"style":939},[618],[573,1773,1775,1778,1831],{"className":1774},[623],[573,1776],{"className":1777},[627,628],[573,1779,1781],{"className":1780},[592],[573,1782,1784,1823],{"className":1783},[635,636],[573,1785,1787,1820],{"className":1786},[640],[573,1788,1790,1801,1809],{"className":1789,"style":958},[644],[573,1791,1792,1795],{"style":961},[573,1793],{"className":1794,"style":653},[652],[573,1796,1798],{"className":1797},[623],[573,1799,879],{"className":1800},[623],[573,1802,1803,1806],{"style":670},[573,1804],{"className":1805,"style":653},[652],[573,1807],{"className":1808,"style":678},[677],[573,1810,1811,1814],{"style":981},[573,1812],{"className":1813,"style":653},[652],[573,1815,1817],{"className":1816},[623],[573,1818,888],{"className":1819},[623],[573,1821,698],{"className":1822},[697],[573,1824,1826],{"className":1825},[640],[573,1827,1829],{"className":1828,"style":1000},[644],[573,1830],{},[573,1832],{"className":1833},[711,628],[573,1835],{"className":1836,"style":1010},[1009],[573,1838,894],{"className":1839},[1014],[573,1841],{"className":1842,"style":1010},[1009],[573,1844,1846,1849,1911,1914,1917],{"className":1845},[614],[573,1847],{"className":1848,"style":939},[618],[573,1850,1852,1855,1908],{"className":1851},[623],[573,1853],{"className":1854},[627,628],[573,1856,1858],{"className":1857},[592],[573,1859,1861,1900],{"className":1860},[635,636],[573,1862,1864,1897],{"className":1863},[640],[573,1865,1867,1878,1886],{"className":1866,"style":958},[644],[573,1868,1869,1872],{"style":961},[573,1870],{"className":1871,"style":653},[652],[573,1873,1875],{"className":1874},[623],[573,1876,1578],{"className":1877},[623],[573,1879,1880,1883],{"style":670},[573,1881],{"className":1882,"style":653},[652],[573,1884],{"className":1885,"style":678},[677],[573,1887,1888,1891],{"style":981},[573,1889],{"className":1890,"style":653},[652],[573,1892,1894],{"className":1893},[623],[573,1895,891],{"className":1896},[623],[573,1898,698],{"className":1899},[697],[573,1901,1903],{"className":1902},[640],[573,1904,1906],{"className":1905,"style":1000},[644],[573,1907],{},[573,1909],{"className":1910},[711,628],[573,1912],{"className":1913,"style":1010},[1009],[573,1915,894],{"className":1916},[1014],[573,1918],{"className":1919,"style":1010},[1009],[573,1921,1923,1926],{"className":1922},[614],[573,1924],{"className":1925,"style":939},[618],[573,1927,1929,1932,1985],{"className":1928},[623],[573,1930],{"className":1931},[627,628],[573,1933,1935],{"className":1934},[592],[573,1936,1938,1977],{"className":1937},[635,636],[573,1939,1941,1974],{"className":1940},[640],[573,1942,1944,1955,1963],{"className":1943,"style":958},[644],[573,1945,1946,1949],{"style":961},[573,1947],{"className":1948,"style":653},[652],[573,1950,1952],{"className":1951},[623],[573,1953,1587],{"className":1954},[623],[573,1956,1957,1960],{"style":670},[573,1958],{"className":1959,"style":653},[652],[573,1961],{"className":1962,"style":678},[677],[573,1964,1965,1968],{"style":981},[573,1966],{"className":1967,"style":653},[652],[573,1969,1971],{"className":1970},[623],[573,1972,888],{"className":1973},[623],[573,1975,698],{"className":1976},[697],[573,1978,1980],{"className":1979},[640],[573,1981,1983],{"className":1982,"style":1000},[644],[573,1984],{},[573,1986],{"className":1987},[711,628],[564,1989,1990,1991,2019],{},"Ganze Zahl durch Bruch: Wie oft passen zwei Drittel in ",[573,1992,1994,2007],{"className":1993},[576],[573,1995,1997],{"className":1996},[580],[582,1998,1999],{"xmlns":584},[586,2000,2001,2005],{},[589,2002,2003],{},[874,2004,916],{},[602,2006,916],{"encoding":604},[573,2008,2010],{"className":2009,"ariaHidden":610},[609],[573,2011,2013,2016],{"className":2012},[614],[573,2014],{"className":2015,"style":1424},[618],[573,2017,916],{"className":2018},[623],"?",[573,2021,2023],{"className":2022},[857],[573,2024,2026,2065],{"className":2025},[576],[573,2027,2029],{"className":2028},[580],[582,2030,2031],{"xmlns":584,"display":866},[586,2032,2033,2062],{},[589,2034,2035,2037,2039,2045,2047,2049,2051,2057,2059],{},[874,2036,916],{},[881,2038,883],{},[592,2040,2041,2043],{},[874,2042,891],{},[874,2044,876],{},[881,2046,894],{},[874,2048,916],{},[881,2050,903],{},[592,2052,2053,2055],{},[874,2054,876],{},[874,2056,891],{},[881,2058,894],{},[874,2060,2061],{},"9",[602,2063,2064],{"encoding":604},"6 : \\frac{2}{3} = 6 \\cdot \\frac{3}{2} = 9",[573,2066,2068,2086,2163,2181,2258],{"className":2067,"ariaHidden":610},[609],[573,2069,2071,2074,2077,2080,2083],{"className":2070},[614],[573,2072],{"className":2073,"style":1424},[618],[573,2075,916],{"className":2076},[623],[573,2078],{"className":2079,"style":1010},[1009],[573,2081,883],{"className":2082},[1014],[573,2084],{"className":2085,"style":1010},[1009],[573,2087,2089,2092,2154,2157,2160],{"className":2088},[614],[573,2090],{"className":2091,"style":939},[618],[573,2093,2095,2098,2151],{"className":2094},[623],[573,2096],{"className":2097},[627,628],[573,2099,2101],{"className":2100},[592],[573,2102,2104,2143],{"className":2103},[635,636],[573,2105,2107,2140],{"className":2106},[640],[573,2108,2110,2121,2129],{"className":2109,"style":958},[644],[573,2111,2112,2115],{"style":961},[573,2113],{"className":2114,"style":653},[652],[573,2116,2118],{"className":2117},[623],[573,2119,876],{"className":2120},[623],[573,2122,2123,2126],{"style":670},[573,2124],{"className":2125,"style":653},[652],[573,2127],{"className":2128,"style":678},[677],[573,2130,2131,2134],{"style":981},[573,2132],{"className":2133,"style":653},[652],[573,2135,2137],{"className":2136},[623],[573,2138,891],{"className":2139},[623],[573,2141,698],{"className":2142},[697],[573,2144,2146],{"className":2145},[640],[573,2147,2149],{"className":2148,"style":1000},[644],[573,2150],{},[573,2152],{"className":2153},[711,628],[573,2155],{"className":2156,"style":1010},[1009],[573,2158,894],{"className":2159},[1014],[573,2161],{"className":2162,"style":1010},[1009],[573,2164,2166,2169,2172,2175,2178],{"className":2165},[614],[573,2167],{"className":2168,"style":1424},[618],[573,2170,916],{"className":2171},[623],[573,2173],{"className":2174,"style":1166},[1009],[573,2176,903],{"className":2177},[1170],[573,2179],{"className":2180,"style":1166},[1009],[573,2182,2184,2187,2249,2252,2255],{"className":2183},[614],[573,2185],{"className":2186,"style":939},[618],[573,2188,2190,2193,2246],{"className":2189},[623],[573,2191],{"className":2192},[627,628],[573,2194,2196],{"className":2195},[592],[573,2197,2199,2238],{"className":2198},[635,636],[573,2200,2202,2235],{"className":2201},[640],[573,2203,2205,2216,2224],{"className":2204,"style":958},[644],[573,2206,2207,2210],{"style":961},[573,2208],{"className":2209,"style":653},[652],[573,2211,2213],{"className":2212},[623],[573,2214,891],{"className":2215},[623],[573,2217,2218,2221],{"style":670},[573,2219],{"className":2220,"style":653},[652],[573,2222],{"className":2223,"style":678},[677],[573,2225,2226,2229],{"style":981},[573,2227],{"className":2228,"style":653},[652],[573,2230,2232],{"className":2231},[623],[573,2233,876],{"className":2234},[623],[573,2236,698],{"className":2237},[697],[573,2239,2241],{"className":2240},[640],[573,2242,2244],{"className":2243,"style":1000},[644],[573,2245],{},[573,2247],{"className":2248},[711,628],[573,2250],{"className":2251,"style":1010},[1009],[573,2253,894],{"className":2254},[1014],[573,2256],{"className":2257,"style":1010},[1009],[573,2259,2261,2264],{"className":2260},[614],[573,2262],{"className":2263,"style":1424},[618],[573,2265,2061],{"className":2266},[623],[559,2268,2270],{"id":2269},"typische-fehler","Typische Fehler",[2272,2273,2274,2282,2587],"ul",{},[2275,2276,2277,2278,2281],"li",{},"Den Kehrwert vom ",[568,2279,2280],{},"ersten"," Bruch nehmen: Umgedreht wird nur der Bruch, durch den geteilt wird.",[2275,2283,2284,2285,813],{},"Beim Teilen durch eine ganze Zahl den Zähler teilen und den Nenner vergessen umzurechnen: Sicher ist es, mit dem Kehrwert zu multiplizieren, also ",[573,2286,2288,2326],{"className":2287},[576],[573,2289,2291],{"className":2290},[580],[582,2292,2293],{"xmlns":584},[586,2294,2295,2323],{},[589,2296,2297,2303,2305,2307,2309,2315,2317],{},[592,2298,2299,2301],{},[874,2300,891],{},[874,2302,1549],{},[881,2304,883],{},[874,2306,879],{},[881,2308,894],{},[592,2310,2311,2313],{},[874,2312,891],{},[874,2314,1549],{},[881,2316,903],{},[592,2318,2319,2321],{},[874,2320,888],{},[874,2322,879],{},[602,2324,2325],{"encoding":604},"\\frac{2}{5} : 4 = \\frac{2}{5} \\cdot \\frac{1}{4}",[573,2327,2329,2412,2430,2513],{"className":2328,"ariaHidden":610},[609],[573,2330,2332,2335,2403,2406,2409],{"className":2331},[614],[573,2333],{"className":2334,"style":1458},[618],[573,2336,2338,2341,2400],{"className":2337},[623],[573,2339],{"className":2340},[627,628],[573,2342,2344],{"className":2343},[592],[573,2345,2347,2392],{"className":2346},[635,636],[573,2348,2350,2389],{"className":2349},[640],[573,2351,2353,2367,2375],{"className":2352,"style":1477},[644],[573,2354,2355,2358],{"style":648},[573,2356],{"className":2357,"style":653},[652],[573,2359,2361],{"className":2360},[657,658,659,660],[573,2362,2364],{"className":2363},[623,660],[573,2365,1549],{"className":2366},[623,660],[573,2368,2369,2372],{"style":670},[573,2370],{"className":2371,"style":653},[652],[573,2373],{"className":2374,"style":678},[677],[573,2376,2377,2380],{"style":681},[573,2378],{"className":2379,"style":653},[652],[573,2381,2383],{"className":2382},[657,658,659,660],[573,2384,2386],{"className":2385},[623,660],[573,2387,891],{"className":2388},[623,660],[573,2390,698],{"className":2391},[697],[573,2393,2395],{"className":2394},[640],[573,2396,2398],{"className":2397,"style":705},[644],[573,2399],{},[573,2401],{"className":2402},[711,628],[573,2404],{"className":2405,"style":1010},[1009],[573,2407,883],{"className":2408},[1014],[573,2410],{"className":2411,"style":1010},[1009],[573,2413,2415,2418,2421,2424,2427],{"className":2414},[614],[573,2416],{"className":2417,"style":1424},[618],[573,2419,879],{"className":2420},[623],[573,2422],{"className":2423,"style":1010},[1009],[573,2425,894],{"className":2426},[1014],[573,2428],{"className":2429,"style":1010},[1009],[573,2431,2433,2436,2504,2507,2510],{"className":2432},[614],[573,2434],{"className":2435,"style":1458},[618],[573,2437,2439,2442,2501],{"className":2438},[623],[573,2440],{"className":2441},[627,628],[573,2443,2445],{"className":2444},[592],[573,2446,2448,2493],{"className":2447},[635,636],[573,2449,2451,2490],{"className":2450},[640],[573,2452,2454,2468,2476],{"className":2453,"style":1477},[644],[573,2455,2456,2459],{"style":648},[573,2457],{"className":2458,"style":653},[652],[573,2460,2462],{"className":2461},[657,658,659,660],[573,2463,2465],{"className":2464},[623,660],[573,2466,1549],{"className":2467},[623,660],[573,2469,2470,2473],{"style":670},[573,2471],{"className":2472,"style":653},[652],[573,2474],{"className":2475,"style":678},[677],[573,2477,2478,2481],{"style":681},[573,2479],{"className":2480,"style":653},[652],[573,2482,2484],{"className":2483},[657,658,659,660],[573,2485,2487],{"className":2486},[623,660],[573,2488,891],{"className":2489},[623,660],[573,2491,698],{"className":2492},[697],[573,2494,2496],{"className":2495},[640],[573,2497,2499],{"className":2498,"style":705},[644],[573,2500],{},[573,2502],{"className":2503},[711,628],[573,2505],{"className":2506,"style":1166},[1009],[573,2508,903],{"className":2509},[1170],[573,2511],{"className":2512,"style":1166},[1009],[573,2514,2516,2519],{"className":2515},[614],[573,2517],{"className":2518,"style":1458},[618],[573,2520,2522,2525,2584],{"className":2521},[623],[573,2523],{"className":2524},[627,628],[573,2526,2528],{"className":2527},[592],[573,2529,2531,2576],{"className":2530},[635,636],[573,2532,2534,2573],{"className":2533},[640],[573,2535,2537,2551,2559],{"className":2536,"style":1477},[644],[573,2538,2539,2542],{"style":648},[573,2540],{"className":2541,"style":653},[652],[573,2543,2545],{"className":2544},[657,658,659,660],[573,2546,2548],{"className":2547},[623,660],[573,2549,879],{"className":2550},[623,660],[573,2552,2553,2556],{"style":670},[573,2554],{"className":2555,"style":653},[652],[573,2557],{"className":2558,"style":678},[677],[573,2560,2561,2564],{"style":681},[573,2562],{"className":2563,"style":653},[652],[573,2565,2567],{"className":2566},[657,658,659,660],[573,2568,2570],{"className":2569},[623,660],[573,2571,888],{"className":2572},[623,660],[573,2574,698],{"className":2575},[697],[573,2577,2579],{"className":2578},[640],[573,2580,2582],{"className":2581,"style":705},[644],[573,2583],{},[573,2585],{"className":2586},[711,628],[2275,2588,2589,2590,2618,2619,2622,2623,813],{},"Erwarten, dass das Ergebnis kleiner wird: Teilt man durch einen Bruch kleiner als ",[573,2591,2593,2606],{"className":2592},[576],[573,2594,2596],{"className":2595},[580],[582,2597,2598],{"xmlns":584},[586,2599,2600,2604],{},[589,2601,2602],{},[874,2603,888],{},[602,2605,888],{"encoding":604},[573,2607,2609],{"className":2608,"ariaHidden":610},[609],[573,2610,2612,2615],{"className":2611},[614],[573,2613],{"className":2614,"style":1424},[618],[573,2616,888],{"className":2617},[623],", wird das Ergebnis ",[568,2620,2621],{},"größer",", z.B. ",[573,2624,2626,2652],{"className":2625},[576],[573,2627,2629],{"className":2628},[580],[582,2630,2631],{"xmlns":584},[586,2632,2633,2649],{},[589,2634,2635,2637,2639,2645,2647],{},[874,2636,916],{},[881,2638,883],{},[592,2640,2641,2643],{},[874,2642,891],{},[874,2644,876],{},[881,2646,894],{},[874,2648,2061],{},[602,2650,2651],{"encoding":604},"6 : \\frac{2}{3} = 9",[573,2653,2655,2673,2756],{"className":2654,"ariaHidden":610},[609],[573,2656,2658,2661,2664,2667,2670],{"className":2657},[614],[573,2659],{"className":2660,"style":1424},[618],[573,2662,916],{"className":2663},[623],[573,2665],{"className":2666,"style":1010},[1009],[573,2668,883],{"className":2669},[1014],[573,2671],{"className":2672,"style":1010},[1009],[573,2674,2676,2679,2747,2750,2753],{"className":2675},[614],[573,2677],{"className":2678,"style":1458},[618],[573,2680,2682,2685,2744],{"className":2681},[623],[573,2683],{"className":2684},[627,628],[573,2686,2688],{"className":2687},[592],[573,2689,2691,2736],{"className":2690},[635,636],[573,2692,2694,2733],{"className":2693},[640],[573,2695,2697,2711,2719],{"className":2696,"style":1477},[644],[573,2698,2699,2702],{"style":648},[573,2700],{"className":2701,"style":653},[652],[573,2703,2705],{"className":2704},[657,658,659,660],[573,2706,2708],{"className":2707},[623,660],[573,2709,876],{"className":2710},[623,660],[573,2712,2713,2716],{"style":670},[573,2714],{"className":2715,"style":653},[652],[573,2717],{"className":2718,"style":678},[677],[573,2720,2721,2724],{"style":681},[573,2722],{"className":2723,"style":653},[652],[573,2725,2727],{"className":2726},[657,658,659,660],[573,2728,2730],{"className":2729},[623,660],[573,2731,891],{"className":2732},[623,660],[573,2734,698],{"className":2735},[697],[573,2737,2739],{"className":2738},[640],[573,2740,2742],{"className":2741,"style":705},[644],[573,2743],{},[573,2745],{"className":2746},[711,628],[573,2748],{"className":2749,"style":1010},[1009],[573,2751,894],{"className":2752},[1014],[573,2754],{"className":2755,"style":1010},[1009],[573,2757,2759,2762],{"className":2758},[614],[573,2760],{"className":2761,"style":1424},[618],[573,2763,2061],{"className":2764},[623],{"title":2766,"searchDepth":2767,"depth":2767,"links":2768},"",2,[2769,2770,2771],{"id":561,"depth":2767,"text":562},{"id":852,"depth":2767,"text":853},{"id":2269,"depth":2767,"text":2270},[2773,2776,2778,2781,2783,2785,2788,2790,2792,2795],{"lhs":2774,"rhs":2775},"(a\u002Fb)\u002F(c\u002Fd)","(a\u002Fb)*(d\u002Fc)",{"lhs":2774,"rhs":2777},"(a*d)\u002F(b*c)",{"lhs":2779,"rhs":2780},"(3\u002F4)\u002F(1\u002F2)","(3\u002F4)*(2\u002F1)",{"lhs":2780,"rhs":2782},"6\u002F4",{"lhs":2782,"rhs":2784},"3\u002F2",{"lhs":2786,"rhs":2787},"(2\u002F5)\u002F4","(2\u002F5)*(1\u002F4)",{"lhs":2787,"rhs":2789},"2\u002F20",{"lhs":2789,"rhs":2791},"1\u002F10",{"lhs":2793,"rhs":2794},"6\u002F(2\u002F3)","6*(3\u002F2)",{"lhs":2794,"rhs":2061},"b \\neq 0,\\ c \\neq 0,\\ d \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b \\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 mathnormal\">b\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>c\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">c \\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 mathnormal\">c\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>d\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">d \\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 mathnormal\">d\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:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","fraction-division","\\frac{a}{b} : \\frac{c}{d} = \\frac{a}{b} \\cdot \\frac{d}{c} = \\frac{a \\cdot d}{b \\cdot c}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" 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