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\begin{align}
\frac{1}{10}+\frac{1}{5}&=\frac{1}{10}+\frac{1\cdot 2}{5\cdot 2}\\
&=\frac{1}{10}+\frac{2}{10}\\
&=\frac{3}{10}
\end{align}

Oppgave 1

  • Løsningsforslag:
    \begin{align}\frac{1}{2}+\frac{1}{4}&=\frac{1\cdot 2}{2\cdot 2}+\frac{1}{4}\\&=\frac{2}{4}+\frac{1}{4}\\&=\frac{2+1}{4}\\&=\frac{3}{4}\end{align}

  • Løsningsforslag:
    \begin{align}\frac{1}{4}+\frac{1}{3}&=\frac{1\cdot 3}{4\cdot 3}+\frac{1\cdot 4}{3\cdot 4}\\&=\frac{3}{12}+\frac{4}{12}\\&=\frac{7}{12}\end{align}

  • Løsningsforslag:
    \begin{align}\frac{1}{3}+\frac{2}{9}&=\frac{1\cdot 3}{3\cdot }+\frac{2}{9}\\&=\frac{3}{9}+\frac{2}{9}\\&=\frac{3+2}{9}\\&=\frac{5}{9}\end{align}

  • Løsningsforslag:\begin{align}\frac{1}{10}+\frac{4}{5}&=\frac{1}{10}+\frac{4\cdot 2}{5\cdot 2}\\ &=\frac{1}{10}+\frac{8}{20}\\&=\frac{9}{10}\end{align}

  • Løsningsforslag:\begin{align}\frac{1}{3}+\frac{1}{2}&=\frac{1\cdot 2}{3\cdot 2}+\frac{1}{2}\\&=\frac{2}{6}+\frac{3}{6}\\&=\frac{5}{6}\end{align}

Oppgave 2

  • Løsningsforslag:\begin{align}\frac{1}{5}+\frac{4}{15}&=\frac{1\cdot 3}{5\cdot 3}+\frac{4}{15}\\&=\frac{3}{15}+\frac{4}{15}\\&=\frac{3+4}{15}\\&=\frac{7}{15}\end{align}

  • Løsningsforslag:\begin{align}\frac{2}{7}+\frac{5}{14}&=\frac{2\cdot 2}{7\cdot 2}+\frac{5}{14}\\&=\frac{4}{14}+\frac{5}{14}\\&=\frac{4+5}{14}\\&=\frac{9}{14}\end{align}

  • Løsningsforslag:\begin{align}\frac{1}{2}+\frac{1}{4}+\frac{1}{6}&=\frac{1\cdot 6}{2\cdot 6}+\frac{1\cdot 3}{4\cdot 3}+\frac{1\cdot 2}{6\cdot 2}\\&=\frac{6}{12}+\frac{3}{12}+\frac{2}{12}\\&=\frac{6+3+2}{12}\\&=\frac{11}{12}\end{align}

  • Løsningsforslag:\begin{align}\frac{2}{3}+\frac{5}{6}+\frac{9}{12}&=\frac{2\cdot 4}{3\cdot 4}+\frac{5\cdot 2}{6\cdot 2}+\frac{9}{12}\\&=\frac{8}{12}+\frac{10}{12}+\frac{9}{12}\\&=\frac{8+10+9}{12}\\&=\frac{27}{12}\\&=\frac{3\cdot 9}{3\cdot 4}\\&=\frac{9}{4}\end{align}

  • Løsningsforslag:\begin{align}\frac{1}{5}+\frac{4}{10}+\frac{1}{15}&=\frac{1}{5}+\frac{2}{5}+\frac{1}{15}\\&=\frac{3\cdot 3}{5\cdot 3}+\frac{1}{15}\\&=\frac{9+1}{15}\\&=\frac{10}{15}\\&=\frac{2}{3}\end{align}

  • Løsningsforslag:\begin{align}\frac{1}{2}-\frac{1}{4}&=\frac{1\cdot 2}{2\cdot 2}-\frac{1}{4}\\&=\frac{2}{4}-\frac{1}{4}\\&=\frac{1}{4}\end{align}

  • Løsningsforslag:\begin{align}\frac{2}{3}-\frac{1}{6}&=\frac{2\cdot 2}{3\cdot 2}-\frac{1}{6}\\&=\frac{4}{6}-\frac{1}{6}\\&=\frac{4-1}{6}\\&=\frac{3}{6}\\&=\frac{1}{2}\end{align}

  • Løsningsforslag:\begin{align}\frac{4}{5}-\frac{3}{15}&=\frac{4\cdot 3}{5\cdot 3}-\frac{3}{15}\\&=\frac{12-3}{15}\\&=\frac{9}{15}\\&=\frac{3}{5}\end{align}

  • Løsningsforslag:\begin{align}\frac{7}{16}-\frac{1}{4}&=\frac{7}{16}-\frac{1\cdot 4}{4\cdot 4}\\&=\frac{7-4}{16}\\&=\frac{3}{16}\end{align}

Oppgave 3

  • \begin{align}\frac{1}{6}-\frac{1}{12}&=\frac{1\cdot 2}{6\cdot 2}-\frac{1}{12}\\&=\frac{2}{12}-\frac{1}{12}\\&=\frac{1}{12}\end{align}

  • \begin{align}\frac{7}{8}-\frac{1}{4}&=\frac{7}{8}-\frac{1\cdot 2}{4\cdot 2}\\&=\frac{7}{8}-\frac{2}{8}\\&=\frac{5}{8}\end{align}

  • \begin{align}\frac{2}{3}-\frac{3}{4}&=\frac{2\cdot 4}{3\cdot 4}-\frac{3\cdot 3}{4\cdot 3}\\&=\frac{8}{12}-\frac{9}{12}\\&=\frac{8-9}{12}\\&=-\frac{1}{12}\end{align}

  • \begin{align}\frac{4}{7}-\frac{3}{14}-\frac{8}{21}&=\frac{4\cdot 6}{7\cdot 6}-\frac{3\cdot 3}{14\cdot 3}-\frac{8\cdot 2}{21\cdot 2}\\&=\frac{24}{42}-\frac{9}{42}-\frac{16}{42}\\&=\frac{24-9-16}{42}\\&=-\frac{1}{42}\end{align}

Oppgave 4

Oppgave 5

  • \begin{align}2-\frac{3}{5}&=\frac{2}{1}-\frac{3}{5}\\&=\frac{2\cdot 5}{1\cdot 5}-\frac{3}{5}\\&=\frac{10}{5}-\frac{3}{5}\\&=\frac{10-3}{5}\\&=\frac{7}{5}\end{align}

  • \begin{align}\frac{8}{5}-1&=\frac{8}{5}-\frac{5}{5}\\&=\frac{8-5}{5}\\&=\frac{3}{5}\end{align}

  • \begin{align}\frac{1}{2}-\frac{4}{9}-\frac{8}{18}+3&=\frac{1\cdot 9}{2\cdot 9}-\frac{4\cdot 2}{9\cdot 2}-\frac{8}{18}+\frac{3\cdot 18}{1\cdot 18}\\&=\frac{9}{18}-\frac{8}{18}-\frac{8}{18}+\frac{54}{18}\\&=\frac{63-16}{18}\\&=\frac{47}{18}\end{align}

  • \begin{align}\frac{1}{5}+2-\frac{5}{4}&=\frac{1\cdot 4}{5\cdot 4}+\frac{2\cdot 20}{1\cdot 20}-\frac{5\cdot 5}{4\cdot 5}\\&=\frac{4}{20}+\frac{40}{20}-\frac{25}{20}\\&=\frac{4+40-25}{20}\\&=\frac{19}{20}\end{align}