Răspuns:
Respectăm ordinea efectuării operațiilor. Introducem întregii în fracții:
[tex]2,3:\dfrac{4}{3} -\bigg\{13\dfrac{2}{3} -\bigg[11 + \bigg(\dfrac{3}{4} + \dfrac{3}{4} \cdot 1 \dfrac{2}{3}\bigg)\bigg]\bigg\} =\\[/tex]
[tex]= 2,3:\dfrac{4}{3} -\bigg\{\dfrac{41}{3} -\bigg[11 + \bigg(\dfrac{3}{4} + \dfrac{3}{4} \cdot \dfrac{5}{3}\bigg)\bigg]\bigg\} \\[/tex]
[tex]= 2,3:\dfrac{4}{3} - \bigg\{\dfrac{41}{3} -\bigg[11 + \bigg(\dfrac{3}{4} + \dfrac{5}{4}\bigg)\bigg]\bigg\} \\[/tex]
[tex]= 2,3:\dfrac{4}{3} - \bigg[\dfrac{41}{3} -\bigg(11 + \dfrac{8}{4}\bigg)\bigg][/tex]
[tex]= 2,3:\dfrac{4}{3} - \bigg(\dfrac{41}{3} - 13\bigg) \\[/tex]
[tex]= 2,3:\dfrac{4}{3} - \dfrac{41-39}{3}[/tex]
[tex]= \dfrac{23}{10} : \dfrac{4}{3} - \dfrac{2}{3} = \dfrac{23}{10} \cdot \dfrac{3}{4} - \dfrac{2}{3} = \dfrac{69}{40} - \dfrac{2}{3}\\[/tex]
[tex]= \dfrac{^{3)} 69}{40} - \dfrac{^{40)} 2}{3} = \dfrac{207 - 80}{120} = \bf\dfrac{127}{120}[/tex]
Mai multe detalii ordinea efectuării operațiilor despre https://brainly.ro/tema/5773279
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Dacă ai nevoie de numerotarea operațiilor, atunci:
[tex]1) \ 1 \dfrac{2}{3} = \dfrac{3+2}{3} = \dfrac{5}{3}\\[/tex]
[tex]2) \ \dfrac{3}{4} + \dfrac{5}{4} = \dfrac{3 + 5}{4} = \dfrac{8}{4} = 2\\[/tex]
[tex]3) \ 11 + 2 = 13[/tex]
[tex]4) \ \dfrac{41}{3} - 13 = \dfrac{41 - 13 \cdot 3}{3} = \dfrac{41 - 39}{3} = \dfrac{2}{3} \\[/tex]
[tex]5) \ 2,3:\dfrac{4}{3} = \dfrac{23}{10} : \dfrac{4}{3}[/tex]
[tex]6) \ \dfrac{23}{10} \cdot \dfrac{3}{4} = \dfrac{69}{40}[/tex]
[tex]7) \ \dfrac{69}{40} - \dfrac{2}{3} = \dfrac{^{3)} 69}{40} - \dfrac{^{40)} 2}{3} = \dfrac{207 - 80}{120} = \dfrac{127}{120}[/tex]
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