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Skryf elk van die rasionale getalle hieronder as'n gewone breuk eenvoudigste vorm (sonder om 'n sakrekenaar te gebruik). \( \begin{array}{ll}\text { a ) } \frac{20}{24} & \text { b) }-\frac{48}{80} \\ \text { c) } 2 \frac{5}{40} & \text { d) }-7 \frac{25}{200} \\ \text { e ) } 5 \frac{6}{8} & \text { f) } \frac{85}{170}\end{array} \)

Ask by Flynn Chambers. in South Africa
Jan 21,2025

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Here are the rational numbers in their simplest fractional forms: a) \(\frac{20}{24} = \frac{5}{6}\) b) \(-\frac{48}{80} = -\frac{3}{5}\) c) \(2 \frac{5}{40} = \frac{17}{8}\) d) \(-7 \frac{25}{200} = -\frac{57}{8}\) e) \(5 \frac{6}{8} = \frac{23}{4}\) f) \(\frac{85}{170} = \frac{1}{2}\)

Solution

Hier is elke van die rasionele getalle in 'n gewone breuk in eenvoudigste vorm: **a) \(\frac{20}{24}\)** \[ \frac{20}{24} = \frac{5}{6} \] *Deelingsfaktor: 4* --- **b) \(-\frac{48}{80}\)** \[ -\frac{48}{80} = -\frac{3}{5} \] *Deelingsfaktor: 16* --- **c) \(2 \frac{5}{40}\)** \[ 2 \frac{5}{40} = \frac{85}{40} = \frac{17}{8} \] *Omgerekend na 'n eenvoudige breuk en daarna vereenvoudig deur te deel met 5.* --- **d) \(-7 \frac{25}{200}\)** \[ -7 \frac{25}{200} = -\frac{1425}{200} = -\frac{57}{8} \] *Omgerekend na 'n eenvoudige breuk en daarna vereenvoudig deur te deel met 25.* --- **e) \(5 \frac{6}{8}\)** \[ 5 \frac{6}{8} = \frac{46}{8} = \frac{23}{4} \] *Vereenvoudig deur te deel met 2.* --- **f) \(\frac{85}{170}\)** \[ \frac{85}{170} = \frac{1}{2} \] *Deel beide tellers en noemers deur 85.* --- Elke breuk is nou geskryf in sy eenvoudigste vorm sonder die gebruik van 'n sakrekenaar.

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Vir elke van die opgegewe rasionale getalle, is hier die gewone breuke in eenvoudigste vorm: a) \( \frac{20}{24} = \frac{5}{6} \) - jy kan beide die teller en die noemer deur 4 deel. b) \( -\frac{48}{80} = -\frac{3}{5} \) - hier deel jy deur 16 om dit te vereenvoudig. c) \( 2 \frac{5}{40} = 2 \frac{1}{8} \) - want 5 gedeel deur 40 is 1/8. Dit kan ook as \( \frac{17}{8} \) geskryf word. d) \( -7 \frac{25}{200} = -7 \frac{1}{8} \) - omdat 25 gedeel deur 200 is 1/8. Dit kan ook as \( -\frac{57}{8} \) geskryf word. e) \( 5 \frac{6}{8} = 5 \frac{3}{4} \) - aangesien 6 gedeel deur 8 is 3/4. Dit kan sowel as \( \frac{23}{4} \) geskryf word. f) \( \frac{85}{170} = \frac{1}{2} \) - deur beide die teller en die noemer met 85 te deel.

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