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# How much is

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3 1/2 - 2 2/3 =

Mar 29, 2015

#1
+20848
+5

3 1/2 - 2 2/3 = ?

$$3 \frac12 - 2 \frac23 \\\\ =3 +\frac12 - 2 -\frac23 \\\\ =3-2 +\frac12-\frac23 \\\\ =1+\frac12-\frac23 \\\\ =1\cdot \frac22 \cdot \frac33 +\frac12\cdot\frac33- \frac23\cdot \frac22\\\\ =\frac{1\cdot 2 \cdot 3+ 1\cdot 3 - 2 \cdot 2}{2\cdot 3}\\\\ =\frac{6+3-4}{6}\\\\ =\frac{5}{6}$$

or

$$3 \frac12 - 2 \frac23 \\\\ =\frac{3\cdot2+1} {2}-\frac{2\cdot 3+2}{3}\\\\ =\frac{7} {2}-\frac{8}{3}\\\\ =\frac{3\cdot 7-2\cdot 8}{2\cdot 3}\\\\ =\frac{21-16}{6}\\\\ =\frac{5}{6}$$

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Mar 30, 2015

#1
+20848
+5

3 1/2 - 2 2/3 = ?

$$3 \frac12 - 2 \frac23 \\\\ =3 +\frac12 - 2 -\frac23 \\\\ =3-2 +\frac12-\frac23 \\\\ =1+\frac12-\frac23 \\\\ =1\cdot \frac22 \cdot \frac33 +\frac12\cdot\frac33- \frac23\cdot \frac22\\\\ =\frac{1\cdot 2 \cdot 3+ 1\cdot 3 - 2 \cdot 2}{2\cdot 3}\\\\ =\frac{6+3-4}{6}\\\\ =\frac{5}{6}$$

or

$$3 \frac12 - 2 \frac23 \\\\ =\frac{3\cdot2+1} {2}-\frac{2\cdot 3+2}{3}\\\\ =\frac{7} {2}-\frac{8}{3}\\\\ =\frac{3\cdot 7-2\cdot 8}{2\cdot 3}\\\\ =\frac{21-16}{6}\\\\ =\frac{5}{6}$$

heureka Mar 30, 2015