Addisjon og subtraksjon av brøker

Fellesnevneren er 36. Vi utvider brøkene slik at alle får nevner 36.

$\begin{array}{rcl}\frac{5}{12}& = & \frac{5·3}{12·3}=\frac{15}{36}\\ & & \\ \frac{7}{3}& =& \frac{7·12}{3·12}=\frac{84}{36}\\ & & \\ \frac{11}{18}& =& \frac{11·2}{18·2}=\frac{22}{36}\\ & & \\ \frac{8}{9}& =& \frac{8·4}{9·4}=\frac{32}{36}\\ & & \\ \frac{13}{6}& =& \frac{13·6}{6·6}=\frac{78}{36}\\ & & \\ \frac{15}{2}& =& \frac{15·18}{2·18}=\frac{270}{36}\\ & & \\ \frac{3}{4}& =& \frac{3·9}{4·9}=\frac{27}{36}\end{array}$

$\begin{array}{rcl}\frac{6}{12}& = & \frac{6:6}{12:6} =\frac{1}{2}\\ & & \\ \frac{21}{3}& =& \frac{21:3}{3:3}=7\\ & & \\ \frac{30}{18}& =& \frac{30:6}{18:6}=\frac{5}{3}\\ & & \\ \frac{6}{9}& =& \frac{6:3}{9:3}=\frac{2}{3}\\ & & \\ \frac{84}{6}& =& \frac{84:6}{6:6}=14\\ & & \\ \frac{72}{420}& =& \frac{72:2}{420:2}=\frac{36:2}{210:2}=\frac{18:3}{105:3}=\frac{6}{35}\\ & & \\ \frac{384}{256}& =& \frac{384:2}{256:2}=\frac{192:2}{128:2}=\frac{96:2}{64:2}=\frac{48:2}{32:2}=\frac{24:8}{16:8}=\frac{3}{2}\end{array}$

$\begin{array}{rcl}\frac{3}{4 } \boxed{<} \frac{4}{5}& & \\ & & \\ \frac{1}{4}& = & 0,25\\ & & \\ \frac{3}{4}& =& 3·0,25=0,75\\ & & \\ \frac{1}{5}& =& 0,2\\ & & \\ \frac{4}{5}& =& 0,2·4=0,8\end{array}$

$\begin{array}{rcl}\frac{12}{18}& \boxed{=}& \frac{2}{3}\\ & & \\ \frac{12}{18}& = & \frac{12:6}{18:6}=\frac{2}{3}\end{array}$

$\begin{array}{rcl}\frac{37}{18} \boxed{>} 2 & & \\ & & \\ 2·18& = & 36\\ & & \\ \frac{36}{18}& =& 2\end{array}$

$\begin{array}{rcl}\frac{4}{20} \boxed{>} \frac{1}{6}& & \\ & & \\ \frac{4}{20}& = & \frac{4:4}{20:4}=\frac{1}{5}\\ & & \\ \frac{1}{5}& >& \frac{1}{6}\end{array}$

$=\frac{1·6}{2·6}+\frac{2·4}{3·4}-\frac{1·3}{4·3}=\frac{6}{12}+\frac{8}{12}-\frac{3}{12}=\frac{6+8-3}{12}=\frac{11}{12}$

$=\frac{4·7}{3·7}+\frac{2·21}{1·21}-\frac{1·3}{7·3}=\frac{28+42-3}{21}=\frac{67}{21}$

$\begin{array}{lcl}\frac{1·36}{1·36}-\frac{1·18}{2·18}+\frac{4·4}{9·4}-\frac{3·9}{4·9}+\frac{7·2}{18·2}& =& \\ & & \\ \frac{36-18+16-27+14}{36}=\frac{21:3}{36:3}=\frac{7}{12}& & \end{array}$

$=\frac{1·3}{4·3}+\frac{5·2}{6·2}=\frac{3}{12}+\frac{10}{12}=\frac{13}{12}$

$=\frac{3}{4}-\frac{2}{1}=\frac{3}{4}-\frac{2·4}{1·4}=\frac{3-8}{4}=\frac{-5}{4}=-\frac{5}{4}$

$=\frac{3·6}{1·6}-\frac{1}{6}+\frac{2·2}{3·2}=\frac{18}{6}-\frac{1}{6}+\frac{4}{6}=\frac{18-1+4}{6}=\frac{21}{6}=\frac{7}{2}$

$=\frac{2·12}{1·12}-\frac{1·3}{4·3}+\frac{2·4}{3·4}=\frac{24}{12}-\frac{3}{12}+\frac{8}{12}=\frac{24-3+8}{12}=\frac{29}{12}$

$=\frac{1·36}{1·36}+\frac{1·9}{4·9}-\frac{7·4}{9·4}=\frac{36}{36}+\frac{9}{36}-\frac{28}{36}=\frac{36+9-28}{36}=\frac{17}{36}$

$\begin{array}{rcl}\frac{2}{1}+\frac{1}{5}-\frac{3}{1}-\frac{2}{3}& = & \frac{2·15}{1·15}+\frac{1·3}{5·3}-\frac{3·15}{1·15}-\frac{2·5}{3·5}=\\ & & \\ \frac{30+3-45-10}{15}& =& -\frac{22}{15}\end{array}$

$\begin{array}{lcl}\frac{1·4}{5·4}+\frac{2·20}{1·20}-\frac{1·20}{1·20}-\frac{1·5}{4·5}& = & \frac{4}{20}+\frac{40}{20}-\frac{20}{20}-\frac{5}{20}=\\ & & \\ \frac{4+40-20-5}{20}=\frac{19}{20}& & \end{array}$