छेद समान नसतांना
1) \[\frac{1}{2}+\frac{3}{4}+\frac{5}{6}=?\]
Explanation: 1) 2, 4 व 6 च्या पाठयातील संख्या 12 म्हणून छेद 12 घ्यावे.
2) छेदाला 12 येण्यासाठी ज्या संख्येने गुणावे लागते त्याच संख्येने अंशाला गुणावे.
\[\frac{1\times 6+3\times 3+5\times 2}{12}=\frac{6+9+10}{12}=\frac{25}{12}\]
2)\[\frac{2}{5}+\frac{2}{4}+\frac{2}{10}=?\]
Explanation:\[\frac{2\times 4+2\times 5+2\times 2}{20}=\frac{8+10+4}{20}\: \\=\frac{22}{20}=\frac{11}{10}\]
3) \[2\frac{1}{3}+6\frac{1}{4}-1\frac{2}{8}=?\]
Explanation: \[\frac{7}{3} +\frac{25}{4}-\frac{10}{8}\: \: \\\frac{7\times 8+25\times 6-10\times 3}{24}\: \\=\: \frac{56+150-30}{24}\: \\=\frac{206-30}{24}=\frac{176}{24}(\div 8)\: \\=\frac{22}{3}=7\frac{1}{3}\]
4) \[\frac{5}{6}+3\frac{2}{5}+\frac{6}{4}=?\]
Explanation: \[=\frac{5}{6} +\frac{17}{5}+\frac{6}{4}\: \: \\=\frac{5\times 10+17\times 12+6\times 15}{60}\: \\=\: \frac{50+204+90}{60}\: \\=\frac{344}{60}=\frac{86}{15}\: \: (\div \: by\: 4)\: \\=5\frac{11}{15}\]
5) \[2\frac{4}{6}-\frac{1}{3}-\frac{5}{8}=?\]
Explanation:\[=\frac{16}{6} -\frac{1}{3}-\frac{5}{8}\: \: \\=\frac{16\times 4-1\times 8-5\times 3}{24}\: \\=\: \frac{64-8-15}{24}\: \\=\frac{64-23}{24}=\frac{41}{24}\: \: \\=1\frac{17}{24}\]
6)\[3\frac{2}{4}-\frac{1}{3}-1\frac{1}{8}=?\]
Explanation:\[=\frac{14}{4} -\frac{1}{3}-\frac{9}{8}\: \: \\=\frac{14\times 6-1\times 8-9\times 3}{24}\: \\=\: \frac{84-8-27}{24}\: \\=\frac{84-35}{24}=\frac{49}{24}\: \: \\=2\frac{1}{24}\]
7) \[\frac{6}{5}-\frac{4}{3}-\frac{2}{4}=?\]
Explanation: \[\: \\=\frac{6\times 12-4\times 20-2\times 15}{60}\: \\=\: \frac{72-80-30}{60}\: \\=\frac{72-110}{60}=\frac{-38}{60}\:\: \: (\div \: by\: \: 2) \: \\=\frac{-19}{30}\]
8)\[1\frac{9}{4}-2\frac{2}{6}+2\frac{1}{16}=?\]
Explanation: \[=\frac{13}{4}-\frac{14}{6}+\frac{33}{16}\: \\=\frac{13\times 12-14\times 8+33\times 3}{48}\: \\=\: \frac{156-112+99}{48}\: \\=\frac{255-112}{48}=\frac{143}{48}\:\: \: \\=2\frac{47}{48}\]
9)\[1\frac{5}{6}+2\frac{3}{7}-\frac{1}{14}=?\]
Explanation: \[=\frac{11}{6}+\frac{17}{7}-\frac{1}{14}\: \\=\frac{11\times 7+17\times 6-1\times 3}{42}\: \\=\: \frac{77+102-3}{42}\: \\=\frac{179-3}{42}=\frac{176}{42}\:\:(\div \:by \: 2) \: \\=\frac{88}{21}\:\:(\div \:by \: 2)=4\frac{4}{21}\]