Addisjon og subtraksjon av brøker

Fellesnevneren er 36. Utvider brøkene slik at alle brøkene får 36 i nevner.

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

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

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

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

c)

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