Brøkregning

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$=\frac{{\displaystyle \stackrel{1}{\cancel{2}}}·5}{3·{\displaystyle \underset{2}{\cancel{4}}}}=\frac{5}{6}$

$=\frac{18}{15}·\frac{3}{1}=\frac{18·{\displaystyle \stackrel{1}{\cancel{3}}}}{{\displaystyle \underset{5}{\cancel{15}}}·1}=\frac{18}{5}$

$=\frac{27}{16}·\frac{24}{36}=\frac{27·24}{16·36}=\frac{\cancel{3}·\cancel{3}·3·\cancel{2}·\cancel{2}·\cancel{2}·3}{\cancel{2}·\cancel{2}·\cancel{2}·2·2·2·\cancel{3}·\cancel{3}}=\frac{9}{8}$

$=\frac{3}{1}·\frac{5}{18}=\frac{{\displaystyle \stackrel{1}{\cancel{3}}·5}}{{\displaystyle \underset{6}{\cancel{18}}}}=\frac{5}{6}$

$=\frac{{\displaystyle \stackrel{1}{\cancel{3}}}·{\displaystyle \stackrel{1}{\cancel{4}}}}{{\displaystyle \underset{4}{\cancel{16}}}·{\displaystyle \underset{3}{\cancel{9}}}}=\frac{1}{12}$

$=\frac{3}{16}·\frac{4}{3}=\frac{{\displaystyle \stackrel{1}{\cancel{3}}}·{\displaystyle \stackrel{1}{\cancel{4}}}}{{\displaystyle \underset{4}{\cancel{16}}}·{\displaystyle \underset{1}{\cancel{3}}}}=\frac{1}{4}$

$=\frac{3}{16}:\frac{6}{1}=\frac{3}{16}·\frac{1}{6}=\frac{{\displaystyle \stackrel{1}{\cancel{3}}}·1}{16·{\displaystyle \underset{2}{\cancel{6}}}}=\frac{1}{32}$

$=\frac{11}{5}·\frac{7}{4}=\frac{77}{20}$

$\frac{2}{3}·18=\frac{2·{\displaystyle \stackrel{6}{\cancel{18}}}}{{\displaystyle \underset{1}{\cancel{3}}}}=12$

Ole får 12 kroner.

$\frac{1}{2}·\frac{1}{9}=\frac{1}{18}$

$\frac{1}{3}·\frac{2}{5}=\frac{2}{15}$

$\frac{1}{5}:\frac{1}{20}=\frac{1}{5}·\frac{20}{1}=4$

Vi trenger 4 glass.

$1-\frac{2}{3}=\frac{1}{3}$

De 6 elevene som tar buss er $\frac{1}{3}$ av elevene i klassen.

$3·6=18$

Det er 18 elever i klassen.

$=\frac{{\displaystyle \frac{2·{\displaystyle \stackrel{3}{\cancel{21}}}}{\cancel{7}}}}{{\displaystyle \frac{5·{\displaystyle \stackrel{7}{\cancel{21}}}}{\cancel{3}}}}=\frac{6}{35}$

$=\frac{{\displaystyle \frac{3·12}{4}}+3·12}{5·12-{\displaystyle \frac{2·12}{3}}}=\frac{9+36}{60-8}=\frac{45}{52}$

$=\frac{{\displaystyle \frac{7·36}{18}}-1·36-{\displaystyle \frac{1·36}{6}}+{\displaystyle \frac{3·36}{12}}}{{\displaystyle \frac{7·36}{9}}-{\displaystyle \frac{13·36}{4}}}$

$=\frac{14-36-6+9}{28-117}=\frac{-19}{-89}=\frac{19}{89}$

$=\frac{{\displaystyle \frac{2·\cancel{30}}{\cancel{30}}}-1·30-{\displaystyle \frac{1·{\displaystyle \stackrel{10}{\cancel{30}}}}{\cancel{3}}}+{\displaystyle \frac{2·\stackrel{2}{\cancel{30}}}{\cancel{15}}}}{{\displaystyle \frac{7·\stackrel{5}{\cancel{30}}}{\cancel{6}}}-{\displaystyle \frac{3·\stackrel{6}{\cancel{30}}}{\cancel{5}}}}$

$=\frac{2-30-10+4}{35-18}=\frac{-\stackrel{2}{\cancel{34}}}{\cancel{17}}=-2$

$=\frac{{\displaystyle \frac{3·\cancel{42}}{\cancel{42}}}+1·42-{\displaystyle \frac{1·{\cancel{42}}^{14}}{\cancel{3}}}}{{\displaystyle \frac{7·{\cancel{42}}^7}{\cancel{6}}}-{\displaystyle \frac{3·{\cancel{42}}^6}{\cancel{7}}}}=\frac{3+42-14}{49-18}=\frac{31}{31}=1$