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= \\frac{12 : 6}{18 : 6} = \\frac{2}{3}",[568,917,919,1018,1119],{"className":918,"ariaHidden":598},[597],[568,920,922,926,1006,1011,1015],{"className":921},[602],[568,923],{"className":924,"style":925},[606],"height:2.0074em;vertical-align:-0.686em;",[568,927,929,934,1002],{"className":928},[611],[568,930],{"className":931},[932,933],"mopen","nulldelimiter",[568,935,937],{"className":936},[875],[568,938,942,993],{"className":939},[940,941],"vlist-t","vlist-t2",[568,943,946,988],{"className":944},[945],"vlist-r",[568,947,951,965,976],{"className":948,"style":950},[949],"vlist","height:1.3214em;",[568,952,954,959],{"style":953},"top:-2.314em;",[568,955],{"className":956,"style":958},[957],"pstrut","height:3em;",[568,960,962],{"className":961},[611],[568,963,811],{"className":964},[611],[568,966,968,971],{"style":967},"top:-3.23em;",[568,969],{"className":970,"style":958},[957],[568,972],{"className":973,"style":975},[974],"frac-line","border-bottom-width:0.04em;",[568,977,979,982],{"style":978},"top:-3.677em;",[568,980],{"className":981,"style":958},[957],[568,983,985],{"className":984},[611],[568,986,781],{"className":987},[611],[568,989,992],{"className":990},[991],"vlist-s","​",[568,994,996],{"className":995},[945],[568,997,1000],{"className":998,"style":999},[949],"height:0.686em;",[568,1001],{},[568,1003],{"className":1004},[1005,933],"mclose",[568,1007],{"className":1008,"style":1010},[1009],"mspace","margin-right:0.2778em;",[568,1012,884],{"className":1013},[1014],"mrel",[568,1016],{"className":1017,"style":1010},[1009],[568,1019,1021,1024,1110,1113,1116],{"className":1020},[602],[568,1022],{"className":1023,"style":925},[606],[568,1025,1027,1030,1107],{"className":1026},[611],[568,1028],{"className":1029},[932,933],[568,1031,1033],{"className":1032},[875],[568,1034,1036,1099],{"className":1035},[940,941],[568,1037,1039,1096],{"className":1038},[945],[568,1040,1042,1065,1073],{"className":1041,"style":950},[949],[568,1043,1044,1047],{"style":953},[568,1045],{"className":1046,"style":958},[957],[568,1048,1050,1053,1056,1059,1062],{"className":1049},[611],[568,1051,811],{"className":1052},[611],[568,1054],{"className":1055,"style":1010},[1009],[568,1057,856],{"className":1058},[1014],[568,1060],{"className":1061,"style":1010},[1009],[568,1063,841],{"className":1064},[611],[568,1066,1067,1070],{"style":967},[568,1068],{"className":1069,"style":958},[957],[568,1071],{"className":1072,"style":975},[974],[568,1074,1075,1078],{"style":978},[568,1076],{"className":1077,"style":958},[957],[568,1079,1081,1084,1087,1090,1093],{"className":1080},[611],[568,1082,781],{"className":1083},[611],[568,1085],{"className":1086,"style":1010},[1009],[568,1088,856],{"className":1089},[1014],[568,1091],{"className":1092,"style":1010},[1009],[568,1094,841],{"className":1095},[611],[568,1097,992],{"className":1098},[991],[568,1100,1102],{"className":1101},[945],[568,1103,1105],{"className":1104,"style":999},[949],[568,1106],{},[568,1108],{"className":1109},[1005,933],[568,1111],{"className":1112,"style":1010},[1009],[568,1114,884],{"className":1115},[1014],[568,1117],{"className":1118,"style":1010},[1009],[568,1120,1122,1125],{"className":1121},[602],[568,1123],{"className":1124,"style":925},[606],[568,1126,1128,1131,1184],{"className":1127},[611],[568,1129],{"className":1130},[932,933],[568,1132,1134],{"className":1133},[875],[568,1135,1137,1176],{"className":1136},[940,941],[568,1138,1140,1173],{"className":1139},[945],[568,1141,1143,1154,1162],{"className":1142,"style":950},[949],[568,1144,1145,1148],{"style":953},[568,1146],{"className":1147,"style":958},[957],[568,1149,1151],{"className":1150},[611],[568,1152,912],{"className":1153},[611],[568,1155,1156,1159],{"style":967},[568,1157],{"className":1158,"style":958},[957],[568,1160],{"className":1161,"style":975},[974],[568,1163,1164,1167],{"style":978},[568,1165],{"className":1166,"style":958},[957],[568,1168,1170],{"className":1169},[611],[568,1171,909],{"className":1172},[611],[568,1174,992],{"className":1175},[991],[568,1177,1179],{"className":1178},[945],[568,1180,1182],{"className":1181,"style":999},[949],[568,1183],{},[568,1185],{"className":1186},[1005,933],[564,1188,1189,1190,1218,1219,1327,1328,1218,1356,1454],{},"Es geht auch schrittweise, z.B. erst durch ",[568,1191,1193,1206],{"className":1192},[571],[568,1194,1196],{"className":1195},[575],[577,1197,1198],{"xmlns":579},[581,1199,1200,1204],{},[584,1201,1202],{},[710,1203,909],{},[591,1205,909],{"encoding":593},[568,1207,1209],{"className":1208,"ariaHidden":598},[597],[568,1210,1212,1215],{"className":1211},[602],[568,1213],{"className":1214,"style":724},[606],[568,1216,909],{"className":1217},[611]," zu ",[568,1220,1222,1241],{"className":1221},[571],[568,1223,1225],{"className":1224},[575],[577,1226,1227],{"xmlns":579},[581,1228,1229,1238],{},[584,1230,1231],{},[875,1232,1233,1235],{},[710,1234,841],{},[710,1236,1237],{},"9",[591,1239,1240],{"encoding":593},"\\frac{6}{9}",[568,1242,1244],{"className":1243,"ariaHidden":598},[597],[568,1245,1247,1251],{"className":1246},[602],[568,1248],{"className":1249,"style":1250},[606],"height:1.1901em;vertical-align:-0.345em;",[568,1252,1254,1257,1324],{"className":1253},[611],[568,1255],{"className":1256},[932,933],[568,1258,1260],{"className":1259},[875],[568,1261,1263,1315],{"className":1262},[940,941],[568,1264,1266,1312],{"className":1265},[945],[568,1267,1270,1289,1297],{"className":1268,"style":1269},[949],"height:0.8451em;",[568,1271,1273,1276],{"style":1272},"top:-2.655em;",[568,1274],{"className":1275,"style":958},[957],[568,1277,1283],{"className":1278},[1279,1280,1281,1282],"sizing","reset-size6","size3","mtight",[568,1284,1286],{"className":1285},[611,1282],[568,1287,1237],{"className":1288},[611,1282],[568,1290,1291,1294],{"style":967},[568,1292],{"className":1293,"style":958},[957],[568,1295],{"className":1296,"style":975},[974],[568,1298,1300,1303],{"style":1299},"top:-3.394em;",[568,1301],{"className":1302,"style":958},[957],[568,1304,1306],{"className":1305},[1279,1280,1281,1282],[568,1307,1309],{"className":1308},[611,1282],[568,1310,841],{"className":1311},[611,1282],[568,1313,992],{"className":1314},[991],[568,1316,1318],{"className":1317},[945],[568,1319,1322],{"className":1320,"style":1321},[949],"height:0.345em;",[568,1323],{},[568,1325],{"className":1326},[1005,933],", dann durch ",[568,1329,1331,1344],{"className":1330},[571],[568,1332,1334],{"className":1333},[575],[577,1335,1336],{"xmlns":579},[581,1337,1338,1342],{},[584,1339,1340],{},[710,1341,912],{},[591,1343,912],{"encoding":593},[568,1345,1347],{"className":1346,"ariaHidden":598},[597],[568,1348,1350,1353],{"className":1349},[602],[568,1351],{"className":1352,"style":724},[606],[568,1354,912],{"className":1355},[611],[568,1357,1359,1377],{"className":1358},[571],[568,1360,1362],{"className":1361},[575],[577,1363,1364],{"xmlns":579},[581,1365,1366,1374],{},[584,1367,1368],{},[875,1369,1370,1372],{},[710,1371,909],{},[710,1373,912],{},[591,1375,1376],{"encoding":593},"\\frac{2}{3}",[568,1378,1380],{"className":1379,"ariaHidden":598},[597],[568,1381,1383,1386],{"className":1382},[602],[568,1384],{"className":1385,"style":1250},[606],[568,1387,1389,1392,1451],{"className":1388},[611],[568,1390],{"className":1391},[932,933],[568,1393,1395],{"className":1394},[875],[568,1396,1398,1443],{"className":1397},[940,941],[568,1399,1401,1440],{"className":1400},[945],[568,1402,1404,1418,1426],{"className":1403,"style":1269},[949],[568,1405,1406,1409],{"style":1272},[568,1407],{"className":1408,"style":958},[957],[568,1410,1412],{"className":1411},[1279,1280,1281,1282],[568,1413,1415],{"className":1414},[611,1282],[568,1416,912],{"className":1417},[611,1282],[568,1419,1420,1423],{"style":967},[568,1421],{"className":1422,"style":958},[957],[568,1424],{"className":1425,"style":975},[974],[568,1427,1428,1431],{"style":1299},[568,1429],{"className":1430,"style":958},[957],[568,1432,1434],{"className":1433},[1279,1280,1281,1282],[568,1435,1437],{"className":1436},[611,1282],[568,1438,909],{"className":1439},[611,1282],[568,1441,992],{"className":1442},[991],[568,1444,1446],{"className":1445},[945],[568,1447,1449],{"className":1448,"style":1321},[949],[568,1450],{},[568,1452],{"className":1453},[1005,933],".",[564,1456,1457,1458,1487,1488,1517],{},"Erweitern mit ",[568,1459,1461,1475],{"className":1460},[571],[568,1462,1464],{"className":1463},[575],[577,1465,1466],{"xmlns":579},[581,1467,1468,1473],{},[584,1469,1470],{},[710,1471,1472],{},"5",[591,1474,1472],{"encoding":593},[568,1476,1478],{"className":1477,"ariaHidden":598},[597],[568,1479,1481,1484],{"className":1480},[602],[568,1482],{"className":1483,"style":724},[606],[568,1485,1472],{"className":1486},[611],", z.B. um auf den Nenner ",[568,1489,1491,1505],{"className":1490},[571],[568,1492,1494],{"className":1493},[575],[577,1495,1496],{"xmlns":579},[581,1497,1498,1503],{},[584,1499,1500],{},[710,1501,1502],{},"20",[591,1504,1502],{"encoding":593},[568,1506,1508],{"className":1507,"ariaHidden":598},[597],[568,1509,1511,1514],{"className":1510},[602],[568,1512],{"className":1513,"style":724},[606],[568,1515,1502],{"className":1516},[611]," zu kommen:",[568,1519,1521],{"className":1520},[860],[568,1522,1524,1573],{"className":1523},[571],[568,1525,1527],{"className":1526},[575],[577,1528,1529],{"xmlns":579,"display":869},[581,1530,1531,1570],{},[584,1532,1533,1540,1542,1561,1563],{},[875,1534,1535,1537],{},[710,1536,912],{},[710,1538,1539],{},"4",[882,1541,884],{},[875,1543,1544,1553],{},[584,1545,1546,1548,1551],{},[710,1547,912],{},[882,1549,1550],{},"⋅",[710,1552,1472],{},[584,1554,1555,1557,1559],{},[710,1556,1539],{},[882,1558,1550],{},[710,1560,1472],{},[882,1562,884],{},[875,1564,1565,1568],{},[710,1566,1567],{},"15",[710,1569,1502],{},[591,1571,1572],{"encoding":593},"\\frac{3}{4} = \\frac{3 \\cdot 5}{4 \\cdot 5} = \\frac{15}{20}",[568,1574,1576,1653,1756],{"className":1575,"ariaHidden":598},[597],[568,1577,1579,1582,1644,1647,1650],{"className":1578},[602],[568,1580],{"className":1581,"style":925},[606],[568,1583,1585,1588,1641],{"className":1584},[611],[568,1586],{"className":1587},[932,933],[568,1589,1591],{"className":1590},[875],[568,1592,1594,1633],{"className":1593},[940,941],[568,1595,1597,1630],{"className":1596},[945],[568,1598,1600,1611,1619],{"className":1599,"style":950},[949],[568,1601,1602,1605],{"style":953},[568,1603],{"className":1604,"style":958},[957],[568,1606,1608],{"className":1607},[611],[568,1609,1539],{"className":1610},[611],[568,1612,1613,1616],{"style":967},[568,1614],{"className":1615,"style":958},[957],[568,1617],{"className":1618,"style":975},[974],[568,1620,1621,1624],{"style":978},[568,1622],{"className":1623,"style":958},[957],[568,1625,1627],{"className":1626},[611],[568,1628,912],{"className":1629},[611],[568,1631,992],{"className":1632},[991],[568,1634,1636],{"className":1635},[945],[568,1637,1639],{"className":1638,"style":999},[949],[568,1640],{},[568,1642],{"className":1643},[1005,933],[568,1645],{"className":1646,"style":1010},[1009],[568,1648,884],{"className":1649},[1014],[568,1651],{"className":1652,"style":1010},[1009],[568,1654,1656,1659,1747,1750,1753],{"className":1655},[602],[568,1657],{"className":1658,"style":925},[606],[568,1660,1662,1665,1744],{"className":1661},[611],[568,1663],{"className":1664},[932,933],[568,1666,1668],{"className":1667},[875],[568,1669,1671,1736],{"className":1670},[940,941],[568,1672,1674,1733],{"className":1673},[945],[568,1675,1677,1702,1710],{"className":1676,"style":950},[949],[568,1678,1679,1682],{"style":953},[568,1680],{"className":1681,"style":958},[957],[568,1683,1685,1688,1692,1696,1699],{"className":1684},[611],[568,1686,1539],{"className":1687},[611],[568,1689],{"className":1690,"style":1691},[1009],"margin-right:0.2222em;",[568,1693,1550],{"className":1694},[1695],"mbin",[568,1697],{"className":1698,"style":1691},[1009],[568,1700,1472],{"className":1701},[611],[568,1703,1704,1707],{"style":967},[568,1705],{"className":1706,"style":958},[957],[568,1708],{"className":1709,"style":975},[974],[568,1711,1712,1715],{"style":978},[568,1713],{"className":1714,"style":958},[957],[568,1716,1718,1721,1724,1727,1730],{"className":1717},[611],[568,1719,912],{"className":1720},[611],[568,1722],{"className":1723,"style":1691},[1009],[568,1725,1550],{"className":1726},[1695],[568,1728],{"className":1729,"style":1691},[1009],[568,1731,1472],{"className":1732},[611],[568,1734,992],{"className":1735},[991],[568,1737,1739],{"className":1738},[945],[568,1740,1742],{"className":1741,"style":999},[949],[568,1743],{},[568,1745],{"className":1746},[1005,933],[568,1748],{"className":1749,"style":1010},[1009],[568,1751,884],{"className":1752},[1014],[568,1754],{"className":1755,"style":1010},[1009],[568,1757,1759,1762],{"className":1758},[602],[568,1760],{"className":1761,"style":925},[606],[568,1763,1765,1768,1821],{"className":1764},[611],[568,1766],{"className":1767},[932,933],[568,1769,1771],{"className":1770},[875],[568,1772,1774,1813],{"className":1773},[940,941],[568,1775,1777,1810],{"className":1776},[945],[568,1778,1780,1791,1799],{"className":1779,"style":950},[949],[568,1781,1782,1785],{"style":953},[568,1783],{"className":1784,"style":958},[957],[568,1786,1788],{"className":1787},[611],[568,1789,1502],{"className":1790},[611],[568,1792,1793,1796],{"style":967},[568,1794],{"className":1795,"style":958},[957],[568,1797],{"className":1798,"style":975},[974],[568,1800,1801,1804],{"style":978},[568,1802],{"className":1803,"style":958},[957],[568,1805,1807],{"className":1806},[611],[568,1808,1567],{"className":1809},[611],[568,1811,992],{"className":1812},[991],[568,1814,1816],{"className":1815},[945],[568,1817,1819],{"className":1818,"style":999},[949],[568,1820],{},[568,1822],{"className":1823},[1005,933],[559,1825,1827],{"id":1826},"typische-fehler","Typische Fehler",[616,1829,1830,2161,2164],{},[619,1831,1832,1833,1958,1959,1218,1962,2060,2061,2160],{},"Aus Summen kürzen: ",[568,1834,1836,1867],{"className":1835},[571],[568,1837,1839],{"className":1838},[575],[577,1840,1841],{"xmlns":579},[581,1842,1843,1864],{},[584,1844,1845],{},[875,1846,1847,1856],{},[584,1848,1849,1851,1854],{},[710,1850,909],{},[882,1852,1853],{},"+",[710,1855,1539],{},[584,1857,1858,1860,1862],{},[710,1859,909],{},[882,1861,1853],{},[710,1863,1472],{},[591,1865,1866],{"encoding":593},"\\frac{2+4}{2+5}",[568,1868,1870],{"className":1869,"ariaHidden":598},[597],[568,1871,1873,1877],{"className":1872},[602],[568,1874],{"className":1875,"style":1876},[606],"height:1.2484em;vertical-align:-0.4033em;",[568,1878,1880,1883,1955],{"className":1879},[611],[568,1881],{"className":1882},[932,933],[568,1884,1886],{"className":1885},[875],[568,1887,1889,1946],{"className":1888},[940,941],[568,1890,1892,1943],{"className":1891},[945],[568,1893,1895,1915,1923],{"className":1894,"style":1269},[949],[568,1896,1897,1900],{"style":1272},[568,1898],{"className":1899,"style":958},[957],[568,1901,1903],{"className":1902},[1279,1280,1281,1282],[568,1904,1906,1909,1912],{"className":1905},[611,1282],[568,1907,909],{"className":1908},[611,1282],[568,1910,1853],{"className":1911},[1695,1282],[568,1913,1472],{"className":1914},[611,1282],[568,1916,1917,1920],{"style":967},[568,1918],{"className":1919,"style":958},[957],[568,1921],{"className":1922,"style":975},[974],[568,1924,1925,1928],{"style":1299},[568,1926],{"className":1927,"style":958},[957],[568,1929,1931],{"className":1930},[1279,1280,1281,1282],[568,1932,1934,1937,1940],{"className":1933},[611,1282],[568,1935,909],{"className":1936},[611,1282],[568,1938,1853],{"className":1939},[1695,1282],[568,1941,1539],{"className":1942},[611,1282],[568,1944,992],{"className":1945},[991],[568,1947,1949],{"className":1948},[945],[568,1950,1953],{"className":1951,"style":1952},[949],"height:0.4033em;",[568,1954],{},[568,1956],{"className":1957},[1005,933]," darf man ",[622,1960,1961],{},"nicht",[568,1963,1965,1983],{"className":1964},[571],[568,1966,1968],{"className":1967},[575],[577,1969,1970],{"xmlns":579},[581,1971,1972,1980],{},[584,1973,1974],{},[875,1975,1976,1978],{},[710,1977,1539],{},[710,1979,1472],{},[591,1981,1982],{"encoding":593},"\\frac{4}{5}",[568,1984,1986],{"className":1985,"ariaHidden":598},[597],[568,1987,1989,1992],{"className":1988},[602],[568,1990],{"className":1991,"style":1250},[606],[568,1993,1995,1998,2057],{"className":1994},[611],[568,1996],{"className":1997},[932,933],[568,1999,2001],{"className":2000},[875],[568,2002,2004,2049],{"className":2003},[940,941],[568,2005,2007,2046],{"className":2006},[945],[568,2008,2010,2024,2032],{"className":2009,"style":1269},[949],[568,2011,2012,2015],{"style":1272},[568,2013],{"className":2014,"style":958},[957],[568,2016,2018],{"className":2017},[1279,1280,1281,1282],[568,2019,2021],{"className":2020},[611,1282],[568,2022,1472],{"className":2023},[611,1282],[568,2025,2026,2029],{"style":967},[568,2027],{"className":2028,"style":958},[957],[568,2030],{"className":2031,"style":975},[974],[568,2033,2034,2037],{"style":1299},[568,2035],{"className":2036,"style":958},[957],[568,2038,2040],{"className":2039},[1279,1280,1281,1282],[568,2041,2043],{"className":2042},[611,1282],[568,2044,1539],{"className":2045},[611,1282],[568,2047,992],{"className":2048},[991],[568,2050,2052],{"className":2051},[945],[568,2053,2055],{"className":2054,"style":1321},[949],[568,2056],{},[568,2058],{"className":2059},[1005,933]," kürzen. Richtig ist ",[568,2062,2064,2083],{"className":2063},[571],[568,2065,2067],{"className":2066},[575],[577,2068,2069],{"xmlns":579},[581,2070,2071,2080],{},[584,2072,2073],{},[875,2074,2075,2077],{},[710,2076,841],{},[710,2078,2079],{},"7",[591,2081,2082],{"encoding":593},"\\frac{6}{7}",[568,2084,2086],{"className":2085,"ariaHidden":598},[597],[568,2087,2089,2092],{"className":2088},[602],[568,2090],{"className":2091,"style":1250},[606],[568,2093,2095,2098,2157],{"className":2094},[611],[568,2096],{"className":2097},[932,933],[568,2099,2101],{"className":2100},[875],[568,2102,2104,2149],{"className":2103},[940,941],[568,2105,2107,2146],{"className":2106},[945],[568,2108,2110,2124,2132],{"className":2109,"style":1269},[949],[568,2111,2112,2115],{"style":1272},[568,2113],{"className":2114,"style":958},[957],[568,2116,2118],{"className":2117},[1279,1280,1281,1282],[568,2119,2121],{"className":2120},[611,1282],[568,2122,2079],{"className":2123},[611,1282],[568,2125,2126,2129],{"style":967},[568,2127],{"className":2128,"style":958},[957],[568,2130],{"className":2131,"style":975},[974],[568,2133,2134,2137],{"style":1299},[568,2135],{"className":2136,"style":958},[957],[568,2138,2140],{"className":2139},[1279,1280,1281,1282],[568,2141,2143],{"className":2142},[611,1282],[568,2144,841],{"className":2145},[611,1282],[568,2147,992],{"className":2148},[991],[568,2150,2152],{"className":2151},[945],[568,2153,2155],{"className":2154,"style":1321},[949],[568,2156],{},[568,2158],{"className":2159},[1005,933],". Kürzen darf man nur Faktoren, keine Summanden.",[619,2162,2163],{},"Nur Zähler oder nur Nenner verändern: Dann ändert sich der Wert des Bruchs.",[619,2165,2166,2167,2264,2265,2293],{},"Nicht vollständig kürzen: ",[568,2168,2170,2187],{"className":2169},[571],[568,2171,2173],{"className":2172},[575],[577,2174,2175],{"xmlns":579},[581,2176,2177,2185],{},[584,2178,2179],{},[875,2180,2181,2183],{},[710,2182,841],{},[710,2184,1237],{},[591,2186,1240],{"encoding":593},[568,2188,2190],{"className":2189,"ariaHidden":598},[597],[568,2191,2193,2196],{"className":2192},[602],[568,2194],{"className":2195,"style":1250},[606],[568,2197,2199,2202,2261],{"className":2198},[611],[568,2200],{"className":2201},[932,933],[568,2203,2205],{"className":2204},[875],[568,2206,2208,2253],{"className":2207},[940,941],[568,2209,2211,2250],{"className":2210},[945],[568,2212,2214,2228,2236],{"className":2213,"style":1269},[949],[568,2215,2216,2219],{"style":1272},[568,2217],{"className":2218,"style":958},[957],[568,2220,2222],{"className":2221},[1279,1280,1281,1282],[568,2223,2225],{"className":2224},[611,1282],[568,2226,1237],{"className":2227},[611,1282],[568,2229,2230,2233],{"style":967},[568,2231],{"className":2232,"style":958},[957],[568,2234],{"className":2235,"style":975},[974],[568,2237,2238,2241],{"style":1299},[568,2239],{"className":2240,"style":958},[957],[568,2242,2244],{"className":2243},[1279,1280,1281,1282],[568,2245,2247],{"className":2246},[611,1282],[568,2248,841],{"className":2249},[611,1282],[568,2251,992],{"className":2252},[991],[568,2254,2256],{"className":2255},[945],[568,2257,2259],{"className":2258,"style":1321},[949],[568,2260],{},[568,2262],{"className":2263},[1005,933]," lässt sich noch durch ",[568,2266,2268,2281],{"className":2267},[571],[568,2269,2271],{"className":2270},[575],[577,2272,2273],{"xmlns":579},[581,2274,2275,2279],{},[584,2276,2277],{},[710,2278,912],{},[591,2280,912],{"encoding":593},[568,2282,2284],{"className":2283,"ariaHidden":598},[597],[568,2285,2287,2290],{"className":2286},[602],[568,2288],{"className":2289,"style":724},[606],[568,2291,912],{"className":2292},[611]," kürzen.",{"title":2295,"searchDepth":2296,"depth":2296,"links":2297},"",2,[2298,2299,2300],{"id":561,"depth":2296,"text":562},{"id":762,"depth":2296,"text":763},{"id":1826,"depth":2296,"text":1827},[2302,2305,2307,2310,2312,2314,2317,2319],{"lhs":2303,"rhs":2304},"a\u002Fb","(a*k)\u002F(b*k)",{"lhs":2306,"rhs":841},"gcd(12, 18)",{"lhs":2308,"rhs":2309},"12\u002F18","(12\u002F6)\u002F(18\u002F6)",{"lhs":2308,"rhs":2311},"2\u002F3",{"lhs":2308,"rhs":2313},"6\u002F9",{"lhs":2315,"rhs":2316},"3\u002F4","(3*5)\u002F(4*5)",{"lhs":2315,"rhs":2318},"15\u002F20",{"lhs":2320,"rhs":2321},"(2+4)\u002F(2+5)","6\u002F7","b \\neq 0,\\ k \\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>k\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k \\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\" style=\"margin-right:0.0315em;\">k\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-reducing","\\frac{a}{b} = \\frac{a \\cdot k}{b \\cdot k}","\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>\u003Cmfrac>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmfrac>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\frac{a}{b} = \\frac{a \\cdot k}{b \\cdot k}\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:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\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\" style=\"height:2.0574em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3714em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\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:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","lower",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-kuerzen-und-erweitern",[],[2335,2336,2337],"gcd-lcm","fraction-addition","mixed-number",{"title":548,"description":2295},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-kuerzen-und-erweitern","Multipliziert oder dividiert man Zähler und Nenner mit derselben Zahl, ändert sich der Wert des Bruchs nicht.",[2342,2343,2344,2345,2346],"bruch","bruchrechnung","kürzen","erweitern","ggt",[2348,2352,2356],{"symbol":2349,"meaning":2350,"symbolHtml":2351},"a","Zähler","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\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\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":2353,"meaning":2354,"symbolHtml":2355},"b","Nenner, nicht null","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>b\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":589,"meaning":2357,"symbolHtml":2358},"Zahl, mit der erweitert oder durch die gekürzt wird, nicht null","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">k\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","bsi_XkQbI2MTV7yZyYNzOlrRw18kVCESAuSA1SEhjN0",[2361,2364,2367],{"stem":2362,"title":2363,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fbrueche-addieren-und-subtrahieren","Brüche addieren und subtrahieren",{"stem":2365,"title":2366,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fgemischte-zahl","Gemischte Zahl umwandeln",{"stem":2368,"title":2369,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fggt-und-kgv","Zusammenhang von ggT und kgV",1793824259142]