Opgaver til brøker
Opgave 1
Forkort følgende brøker:
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1) {$\displaystyle \frac{13}{91}$}
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2) {$\displaystyle \frac{9}{36}$}
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3) {$\displaystyle \frac{136}{17}$}
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4) {$\displaystyle \frac{117}{6}$}
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5) {$\displaystyle \frac{x^3y}{x^2y^2}$}
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6) {$\displaystyle \frac{6 \cdot 10^5}{2 \cdot 10^3}$}
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7) {$\displaystyle \frac{a^4b^2c^5}{a^3bc^4}$}
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8) {$\displaystyle \frac{xy^2+xz^2}{xyz}$}
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Facitter
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1) {$\displaystyle \frac{1}{7}$}
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2) {$\displaystyle \frac{1}{4}$}
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3) {$8$}
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4) {$\displaystyle \frac{39}{2}$}
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5) {$\displaystyle \frac{x}{y}$}
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6) {$3 \cdot 10^2 = 300$}
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7) {$abc$}
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8) {$\displaystyle \frac{y^2+z^2}{yz}$}
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Opgave 2
Udregn:
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1) {$\displaystyle \frac{13}{3} + \frac{4}{3}$}
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2) {$\displaystyle \frac{4}{3} - \frac{1}{3}$}
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3) {$\displaystyle \frac{12}{5} + \frac{4}{15}$}
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4) {$\displaystyle \frac{10}{3} - \frac{3}{4}$}
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5) {$\displaystyle \frac{12}{7} + \frac{5}{8}$}
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6) {$\displaystyle \frac{6}{5} - \frac{4}{9}$}
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7) {$\displaystyle \frac{2}{3} + \frac{3}{4}+ \frac{4}{5}$}
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8) {$\displaystyle \frac{2}{3} - \frac{2}{5}+ \frac{2}{7}$}
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Facitter
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1) {$\displaystyle \frac{17}{3}$}
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2) {$1$}
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3) {$\displaystyle \frac{8}{3}$}
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4) {$\displaystyle \frac{31}{12}$}
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5) {$\displaystyle \frac{131}{56}$}
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6) {$\displaystyle \frac{34}{45}$}
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7) {$\displaystyle \frac{133}{60}$}
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8) {$\displaystyle \frac{58}{105}$}
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Opgave 3
Udregn:
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1) {$\displaystyle 4 \cdot \frac{1}{3}$}
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2) {$\displaystyle \frac{3}{5} \cdot 7$}
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3) {$\displaystyle \frac{x}{y^2} \cdot y$}
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4) {$\displaystyle \frac{x^2}{y} : x$}
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5) {$\displaystyle x \cdot \frac{1+y}{3}$}
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6) {$\displaystyle (a-b) \cdot \frac{(a+b)^2}{(a-b)} : (a+b)$}
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7) {$\displaystyle \frac{x+y}{2} \cdot y :(x-y)$}
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8) {$\displaystyle \frac{3x-3}{3} : (x-1)$}
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Facitter
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1) {$\displaystyle \frac{4}{3}$}
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2) {$\displaystyle \frac{21}{5}$}
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3) {$\displaystyle \frac{x}{y}$}
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4) {$\displaystyle \frac{x}{y}$}
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5) {$\displaystyle \frac{x+xy}{3}$}
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6) {$a+b$}
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7) {$\displaystyle \frac{xy+y^2}{2(x-y)}$}
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8) {$1$}
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Opgave 4
Udregn:
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1) {$\displaystyle \frac{3}{5} \cdot \frac{1}{3}$}
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2) {$\displaystyle \frac{2}{5} \cdot \frac{a}{b}$}
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3) {$\displaystyle \frac{x+1}{y^2-1} \cdot \frac{3}{2}$}
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4) {$\displaystyle \frac{x+y}{x^2} \cdot \frac{x-y}{y^2}$}
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5) {$\displaystyle 4 : \frac{2}{3}$}
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6) {$\displaystyle \frac{3}{2} : \frac{13}{2}$}
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7) {$\displaystyle \frac{x+y}{2} : \frac{x^2-y^2}{x-y}$}
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8) {$\displaystyle \frac{3x-3}{3} : \frac{x-1}{2}$}
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Facitter
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1) {$\displaystyle \frac{1}{5}$}
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2) {$\displaystyle \frac{2a}{5b}$}
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3) {$\displaystyle \frac{3x+3}{2y^2-2}$}
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4) {$\displaystyle \frac{x^2-y^2}{x^2y^2}$}
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5) {$6$}
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6) {$\displaystyle \frac{3}{13}$}
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7) {$\displaystyle \frac{1}{2}$}
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8) {$2$}
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Opgave 5
Udregn:
1)
{$\displaystyle (\frac{2}{x+y}-\frac{1}{x}) \cdot \frac{x^2+xy}{x+y}$}
2)
{$\displaystyle \frac{a^2c^3}{b^2}: \frac{ac^2}{b^3} - ( \frac{(a+b)^2}{a^2-b^2}(a-b)-b)bc$}
3)
{$\displaystyle (m+n)n: \frac{m}{m+n} \cdot \frac{m}{n}-2mn$}
Facitter
1)
{$\displaystyle \frac{x-y}{x+y}$}
2)
{$0$}
3)
{$m^2+n^2$}