Знайди значення виразу:
Розв'язок:
1) $\frac{7}{10} + \frac{3}{5} = \frac{1 \cdot 7}{1 \cdot 10} + \frac{2 \cdot 3}{2 \cdot 5} =$
$= \frac{7}{10} + \frac{6}{10} = \frac{7+6}{10} =$
$= \frac{13}{10} = 1\frac{3}{10}$
$\frac{7}{10} + \frac{3}{10} = \frac{7+3}{10} = \frac{10}{10} = 1$
$\frac{7}{10} + \frac{3}{15} = \frac{3 \cdot 7}{3 \cdot 10} + \frac{2 \cdot 3}{2 \cdot 15} =$
$= \frac{21}{30} + \frac{6}{30} = \frac{21+6}{30} =$
$= \frac{27}{30} = \frac{9 \cdot 3}{10 \cdot 3} = \frac{9}{10}$
$\frac{7}{10} + \frac{3}{20} = \frac{2 \cdot 7}{2 \cdot 10} + \frac{1 \cdot 3}{1 \cdot 20} =$
$= \frac{14}{20} + \frac{3}{20} = \frac{14+3}{20} = \frac{17}{20}$
$\frac{7}{10} + \frac{3}{30} = \frac{3 \cdot 7}{3 \cdot 10} + \frac{1 \cdot 3}{1 \cdot 30} =$
$= \frac{21}{30} + \frac{3}{30} = \frac{21+3}{30} =$
$= \frac{24}{30} = \frac{4 \cdot 6}{5 \cdot 6} = \frac{4}{5}$
$\frac{7}{10} + \frac{3}{45} = \frac{9 \cdot 7}{9 \cdot 10} + \frac{2 \cdot 3}{2 \cdot 45} =$
$= \frac{63}{90} + \frac{6}{90} = \frac{63+6}{90} =$
$= \frac{69}{90} = \frac{23 \cdot 3}{30 \cdot 3} = \frac{23}{30}$
2) $\frac{2}{16} - \frac{1}{2} = \frac{1 \cdot 2}{1 \cdot 16} - \frac{8 \cdot 1}{8 \cdot 2} =$
$= \frac{2}{16} - \frac{8}{16} = \frac{2-8}{16} = -\frac{6}{16} =$
$= -\frac{3 \cdot 2}{8 \cdot 2} = -\frac{3}{8}$
$\frac{4}{16} - \frac{1}{4} = \frac{1 \cdot 4}{1 \cdot 16} - \frac{4 \cdot 1}{4 \cdot 4} =$
$= \frac{4}{16} - \frac{4}{16} = \frac{4-4}{16} = \frac{0}{16} = 0$
$\frac{6}{16} - \frac{1}{6} = \frac{3 \cdot 6}{3 \cdot 16} - \frac{8 \cdot 1}{8 \cdot 6} =$
$= \frac{18}{48} - \frac{8}{48} = \frac{18-8}{48} =$
$= \frac{10}{48} = \frac{5 \cdot 2}{24 \cdot 2} = \frac{5}{24}$
$\frac{8}{16} - \frac{1}{8} = \frac{1 \cdot 8}{1 \cdot 16} - \frac{2 \cdot 1}{2 \cdot 8} =$
$= \frac{8}{16} - \frac{2}{16} = \frac{8-2}{16} =$
$= \frac{6}{16} = \frac{3 \cdot 2}{8 \cdot 2} = \frac{3}{8}$
$\frac{10}{16} - \frac{1}{10} = \frac{5 \cdot 10}{5 \cdot 16} - \frac{8 \cdot 1}{8 \cdot 10} =$
$= \frac{50}{80} - \frac{8}{80} = \frac{50-8}{80} =$
$= \frac{42}{80} = \frac{21 \cdot 2}{40 \cdot 2} = \frac{21}{40}$
$\frac{12}{16} - \frac{1}{12} = \frac{3 \cdot 12}{3 \cdot 16} - \frac{4 \cdot 1}{4 \cdot 12} =$
$= \frac{36}{48} - \frac{4}{48} = \frac{36-4}{48} =$
$= \frac{32}{48} = \frac{2 \cdot 16}{3 \cdot 16} = \frac{2}{3}$