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Learn from your mistakes and have another attempt by clicking on 'Try another question like this one' until you get full marks.

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$\\displaystyle\\frac{\\var{a}}{\\var{b}}+\\frac{\\var{c}}{\\var{b}}=$[[0]]

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$\\displaystyle\\frac{\\var{d}}{\\var{c}}-\\frac{\\var{a}}{\\var{c}}=$[[1]]

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Legg sammen tellerne, behold nevner.

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Disse brøkene har felles nevner, og kan enkelt legges sammen. La oss illustrere det med eksempler (som ikke er like oppgaven): 

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\\[\\frac{2}{3}+\\frac{5}{3}=\\frac{2+5}{3}=\\frac{7}{3}\\]

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Den samme fremgangsmåten kan brukes for subtraksjon: 

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\\[\\frac{7}{4}-\\frac{3}{4}=\\frac{7-3}{4}=\\frac{4}{4}=1\\]

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$\\displaystyle\\simplify{{f}/{g}+{h}/{j}}=$[[0]]

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$\\displaystyle\\simplify{{h}/{f}-{j}/{g}}=$[[1]]

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$\\displaystyle \\frac{\\var{a}}{\\var{d}}+\\var{f}=$[[2]]

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Utvid brøkene slik at de får en felles nevner. Deretter kan du addere eller subtrahere slik som i forrige oppgave. 

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Hvis oppgaven var $\\frac{5}{4}+\\frac{3}{8}$ kunne vi utvidet den første brøken til $\\frac{10}{8}$ (ved å multiplisere med 2 i teller og nevner), slik at begge brøkene fikk nevner lik 8. Deretter kunne vi addert brøkene: 

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\\[\\frac{5}{4}+\\frac{3}{8}=\\frac{5\\cdot 2}{4\\cdot 2}+\\frac{3}{8}=\\frac{10}{8}+\\frac{3}{8}=\\frac{13}{8}\\]

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Som regel må vi utvide begge brøkene for å få en felles nevner, for eksempel når vi skal regne ut  $\\frac{5}{4}-\\frac{2}{3}$. Her kan 12 være en felles nevner, og utregningen kan se slik ut: 

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\\[\\frac{5}{4}-\\frac{2}{3}=\\frac{5\\cdot 3}{4\\cdot 3}-\\frac{2\\cdot 4}{3\\cdot 4}=\\frac{15}{12}-\\frac{8}{12}=\\frac{7}{12}\\]

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Et godt valg for fellesnevneren er minste felles multiplum til de to nevnerne.

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NB! Husk at hele tall kan skrives som en brøk med nevner lik 1, for eksempel $3=\\frac{3}{1}$.

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$\\displaystyle\\frac{\\var{a}}{\\var{b}}\\cdot \\frac{\\var{c}}{\\var{d}}=$[[0]]

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$\\displaystyle \\frac{1}{\\var{b}}+\\frac{1}{\\var{f}}-\\frac{2}{\\var{b}}\\cdot \\frac{3}{\\var{2*f}}=$[[1]]

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Multipliser teller med teller, og nevner med nevner.

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For eksempel: 

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\\[\\frac{4}{5}\\cdot \\frac{2}{3}=\\frac{4\\cdot 2}{5 \\cdot 3}=\\frac{8}{15}\\]

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Husk også regnerekkefølge: multiplikasjon før addisjon/subtraksjon. Eksempel:

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$\\frac{1}{3}+\\frac{1}{2}-\\frac{1}{4}\\cdot \\frac{2}{3}$\n

$=$

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$\\frac{1}{3}+\\frac{1}{2}-\\frac{1\\cdot 2}{4 \\cdot 3}$
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$=$

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$=$

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$=$

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$\\frac{1}{3}+\\frac{1}{2}-\\frac{1}{6}$

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$\\frac{2}{6}+\\frac{3}{6}-\\frac{1}{6}$

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$\\frac{4}{6} = \\frac{2}{3}$

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(Husk å forkorte hvis mulig)

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$\\displaystyle \\frac{\\var{f}}{\\var{h}}: \\frac{\\var{g}}{\\var{j}}=$[[0]]

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$\\displaystyle \\var{b}\\cdot(\\frac{1}{\\var{2*b}}+\\frac{1}{\\var{b}}) - \\frac{\\var{2*f}}{\\var{3*h}}:\\frac{2}{\\var{h}}=$[[1]]

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Multipliser med den omvendte brøken.

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Anta du vil finne  $\\frac{3}{7}:\\frac{5}{4}$. Å dividere med  $\\frac{5}{4}$ er ekvivalent med å multiplisere med  $\\frac{4}{5}$, slik at regnestykket blir: 

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\\[\\frac{3}{7}:\\frac{5}{4}=\\frac{3}{7}\\cdot\\frac{4}{5}=\\frac{3\\cdot 4}{7\\cdot 5}=\\frac{12}{35}\\]

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Husk også regnerekkefølge: parenteser først, så multiplikasjon/divisjon før addisjon/subtraksjon. Eksempel:

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$2\\cdot (\\frac{1}{6}+\\frac{2}{3})-\\frac{3}{5}: \\frac{1}{10}$\n

$=$

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$2\\cdot (\\frac{1}{6}+\\frac{4}{6})-\\frac{3}{5}: \\frac{1}{10}$
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$=$

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$=$

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$=$

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$=$

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$2\\cdot\\frac{5}{6}-\\frac{3}{5}:\\frac{1}{10}$

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$\\frac{2\\cdot 5}{6}-\\frac{3}{5}\\cdot \\frac{10}{1}$

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$\\frac{5}{3}-\\frac{3\\cdot 10}{5\\cdot 1}$

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$\\frac{2}{3}-6 =-\\frac{16}{3}$

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(Husk at $6=\\frac{6}{1}=\\frac{18}{3}$)

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$\\displaystyle \\frac{\\frac{\\var{b}}{\\var{c}}}{ \\frac{\\var{a}}{\\var{d}}}=$[[0]]

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$\\displaystyle \\frac{\\frac{\\var{d}}{\\var{g}}}{\\var{f}}=$[[1]]

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$\\displaystyle \\frac{\\var{j}}{\\frac{\\var{h}}{\\var{c}}}=$[[2]]

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Her kan man for eksempel betrakte hovedbrøkstreken som divisjon.

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Eksempler:

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\\[\\frac{7}{\\frac{5}{6}}=7:\\frac{5}{6} =7\\cdot\\frac{6}{5}=\\frac{42}{5}\\]

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\\[\\frac{\\frac{9}{11}}{\\frac{5}{3}}=\\frac{9}{11}:\\frac{5}{3}=\\frac{9}{11}\\cdot \\frac{3}{5}=\\frac{27}{55}\\]

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Regn ut og oppgi svaret ditt som en brøk eller et helt tall (ikke desimaltall). Bruk  /  som brøkstrek, for eksempel skal $\\frac{2}{3}$ skrives som 2/3.

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Add, subtract, multiply and divide numerical fractions.

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