Rekenvolgorde en deelstreep

Leerdoelen

•Je kunt sommen met een deelstreep uitrekenen.

De rekenvolgorde

De rekenvolgorde vertelt ons in welke volgorde we een som oplossen. Deze is erg belangrijk om de juiste uitkomsten te krijgen. Hieronder staan de stappen die je volgt:

1.Haakjes

2.Machten en wortels

3.Vermenigvuldigen en delen (van links naar rechts)

4.Optellen en aftrekken (van links naar rechts)

De deelstreep: een bijzondere held

Een som met een deelstreep lijkt op een breuk, met een teller (boven de deelstreep) en een noemer (onder de deelstreep). Een belangrijke regel is dat je eerst de berekeningen boven en onder de deelstreep (dus in de teller en de noemer) uitrekent voordat je de deling zelf doet.

Voorbeeld 1

Neem bijvoorbeeld de som:

\frac{6+9\cdot2}{20-14}\frac{6+9\cdot2}{20-14}20-14\frac{6+9\cdot2}{20-1}20-14\frac{6+9\cdot2}{20-}20-14\frac{6+9\cdot2}{20}20-14\frac{6+9\cdot2}{2}20-14\frac{6+9\cdot2}{\placeholder{}}20-146+9\cdot\frac{6+9\cdot2}{\placeholder{}}20-146+9\cdot\frac{+9\cdot2}{\placeholder{}}20-146+9\cdot\frac{9\cdot2}{\placeholder{}}20-146+9\cdot\frac{\cdot2}{\placeholder{}}20-146+9\cdot\frac{2\cdot2}{\placeholder{}}20-146+9\cdot\frac{\cdot2}{\placeholder{}}20-146+9\cdot\frac{2}{\placeholder{}}20-146+9\cdot220-146+9\cdot2/20-146+92/20-146 + 9 x 2 / 20 - 14

Eerst vermenigvuldigen we9\cdot29\cdot9 en dan tellen we er 6 bij op. Hierna delen we dit delen door 6 (namelijk 20-1420-120-202 ) hebben gedaan. Het uiteindelijke antwoord is 4.

\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{24}{6}=4\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{24}{6}=\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{24}{6}\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{24}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{2}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{\placeholder{}}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}=\frac{6+9\cdot2}{20-14}=\frac{6+18}{6}\frac{6+9\cdot2}{20-14}=\frac{6+18}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+1}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{\placeholder{}}{\placeholder{}}\frac{6+9\cdot2}{20-14}=\frac{6+9\cdot2}{20-14}\frac{6+9\cdot2}{20-1}\frac{6+9\cdot2}{20-}\frac{6+9\cdot2}{20}\frac{6+9\cdot2}{20=}\frac{6+9\cdot2}{20}\frac{6+9\cdot2}{2}\frac{6+9\cdot2}{\placeholder{}}6+9\cdot\frac{6+9\cdot2}{\placeholder{}}6+9\cdot\frac{6+92}{\placeholder{}}6+9\cdot\frac{6+2}{\placeholder{}}6+9\cdot\frac{62}{\placeholder{}}6+9\cdot\frac{2}{\placeholder{}}6+9\cdot26+9\cdot6+96+6

Voorbeeld 2

Voor een moeilijkere som zoals:

\frac{32-4\cdot5}{\frac{3+9}{6}}\frac{32-4\cdot5}{\frac{3+9}{6}}=6\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}=6\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}=6\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}=\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{1}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{\placeholder{}}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{\placeholder{}}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{12}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{1}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-2}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{3}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{\placeholder{}}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-4\cdot5}{\frac{3+9}{6}}\frac{32-4\cdot5}{\frac{3+}{6}}\frac{32-4\cdot5}{\frac{\left.3+\right)}{6}}\frac{32-4\cdot5}{\frac{\left.3+9\right)}{6}}\frac{32-4\cdot5}{\frac{\left(3+9\right)}{6}}\frac{32-4\cdot5}{\frac{\left(3+9\right)}{\placeholder{}}}\frac{32-4\cdot5}{\left(3+9\right)}\frac{32-4\cdot5}{\left(3+9\right)\Large\div}\frac{32-4\cdot5}{\left(3+9\right)\Large\div\mathbf{6}}\frac{32-4\cdot5}{\left(3+9\right)\Large\div}\frac{32-4\cdot5}{\left(3+9\right)\Large\div6}\frac{32-4\cdot5}{\left(3+9\right)\Large\div}\frac{32-4\cdot5}{\left(3+9\right)\Large\div\Large 6}\frac{32-4\cdot5}{\left(3+9\right)\Large\div}\frac{32-4\cdot5}{\left(3+9\right)\Large\div6}\frac{32-4\cdot5}{\left(3+9\right)\Large\div}\frac{32-4\cdot5}{\left(3+9\right)\Large\div6}\frac{32-4\cdot5}{\left(3+9\right)}\frac{32-4\cdot5}{\frac{\left(3+9\right)}{\placeholder{}}}\frac{32-4\cdot5}{\left(3+9\right)}\frac{32-4\cdot5}{\left(3+9\right)}\frac{32-4\cdot5}{3+9}\frac{32-4\cdot5}{3+9}:\frac{32-4\cdot5}{3+9}:6\frac{32-4\cdot5}{3+9}(3+9):6\frac{32-4\cdot5}{3+}(3+9):6\frac{32-4\cdot5}{3}(3+9):6\frac{32-4\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{32-4\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{3-4\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{-4\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{4\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{\cdot5}{\placeholder{}}(3+9):632-4\cdot\frac{5}{\placeholder{}}(3+9):632-4\cdot5(3+9):632-4\cdot5/(3+9):632-45/(3+9):6

Volg je dezelfde stappen, waarbij je let op de rekenvolgorde binnen de teller en de noemer.

\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}=6\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}=\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}-\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{2}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{12}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=12\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=1\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}=\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{6}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\frac{12}{\placeholder{}}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{12}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{1}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-20}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-2}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{3}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{\placeholder{}}{\placeholder{}}\frac{32-4\cdot5}{\frac{3+9}{6}}=\frac{32-4\cdot5}{\frac{3+9}{6}}\frac{32-4\cdot5}{\frac{3+9}{\placeholder{}}}\frac{32-4\cdot5}{\frac{3+}{\placeholder{}}}\frac{32-4\cdot5}{\frac{3}{\placeholder{}}}\frac{32-4\cdot5}{\frac{\placeholder{}}{\placeholder{}}}\frac{32-4\cdot5}{\placeholder{}}\frac{32-4\cdot}{\placeholder{}}\frac{32-4}{\placeholder{}}\frac{32-}{\placeholder{}}\frac{32}{\placeholder{}}\frac{\frac{32}{\placeholder{}}}{\placeholder{}}\frac{32}{\placeholder{}}\frac{3}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}

Hoe voer je dit in op een rekenmachine?

Om zo’n som op je rekenmachine in te voeren, gebruik je haakjes om de teller en de noemer van elkaar te scheiden.

Bijvoorbeeld voor:

\frac{12-9\cdot3}{5\cdot\left(4+2\right)}\frac{12-9\cdot3}{5\left(4+2\right)}\frac{12-9\cdot3}{5\left(4+2\right)}\frac{12-9\cdot3}{5\left(4+\right)}\frac{12-9\cdot3}{5\left(4\right)}\frac{12-9\cdot3}{5\left(\right)}\frac{12-9\cdot3}{5}\frac{12-9\cdot3}{\placeholder{}}\frac{12-9\cdot}{\placeholder{}}\frac{12-9\cdot2}{\placeholder{}}\frac{12-9\cdot}{\placeholder{}}\frac{12-9}{\placeholder{}}\frac{12-}{\placeholder{}}\frac{12}{\placeholder{}}\frac{1}{\placeholder{}}\frac{\placeholder{}}{\placeholder{}}1121

Zou je het volgende invoeren:

(12-9\cdot3):(5\cdot(4+2))(12-9\cdot3):(5(4+2))(12-9\cdot3):(5x(4+2))(12-93):(5x(4+2))

Dit geeft je het antwoord (-0,5).