Issolvi 52/3-31/3div22/3*4/5+2frac{1}{5}div2frac{3}{4}

$$5 \frac { 2 } { 3 } - 3 \frac { 1 } { 3 } \div 2 \frac { 2 } { 3 } \times \frac { 4 } { 5 } + 2 \frac { 1 } { 5 } \div 2 \frac { 3 } { 4 }$$

Evalwa

$$\frac{82}{15}\approx 5.466666667$$

Passi tas-Soluzzjonijiet

Immultiplika 5 u 3 biex tikseb 15.

$$\frac{15+2}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Żid 15 u 2 biex tikseb 17.

$$\frac{17}{3}-\frac{\frac{3\times 3+1}{3}}{\frac{2\times 3+2}{3}}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Iddividi \frac{3\times 3+1}{3} b'\frac{2\times 3+2}{3} billi timmultiplika \frac{3\times 3+1}{3} bir-reċiproku ta' \frac{2\times 3+2}{3}.

$$\frac{17}{3}-\frac{\left(3\times 3+1\right)\times 3}{3\left(2\times 3+2\right)}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Annulla 3 fin-numeratur u d-denominatur.

$$\frac{17}{3}-\frac{1+3\times 3}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{17}{3}-\frac{1+9}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Żid 1 u 9 biex tikseb 10.

$$\frac{17}{3}-\frac{10}{2+2\times 3}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Immultiplika 2 u 3 biex tikseb 6.

$$\frac{17}{3}-\frac{10}{2+6}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Żid 2 u 6 biex tikseb 8.

$$\frac{17}{3}-\frac{10}{8}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Naqqas il-frazzjoni \frac{10}{8} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 2.

$$\frac{17}{3}-\frac{5}{4}\times \frac{4}{5}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Annulla \frac{5}{4} u r-reċiproku tiegħu \frac{4}{5}.

$$\frac{17}{3}-1+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Ikkonverti 1 fi frazzjoni \frac{3}{3}.

$$\frac{17}{3}-\frac{3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Billi \frac{17}{3} u \frac{3}{3} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{17-3}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Naqqas 3 minn 17 biex tikseb 14.

$$\frac{14}{3}+\frac{\frac{2\times 5+1}{5}}{\frac{2\times 4+3}{4}}$$

Iddividi \frac{2\times 5+1}{5} b'\frac{2\times 4+3}{4} billi timmultiplika \frac{2\times 5+1}{5} bir-reċiproku ta' \frac{2\times 4+3}{4}.

$$\frac{14}{3}+\frac{\left(2\times 5+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Immultiplika 2 u 5 biex tikseb 10.

$$\frac{14}{3}+\frac{\left(10+1\right)\times 4}{5\left(2\times 4+3\right)}$$

Żid 10 u 1 biex tikseb 11.

$$\frac{14}{3}+\frac{11\times 4}{5\left(2\times 4+3\right)}$$

Immultiplika 11 u 4 biex tikseb 44.

$$\frac{14}{3}+\frac{44}{5\left(2\times 4+3\right)}$$

Immultiplika 2 u 4 biex tikseb 8.

$$\frac{14}{3}+\frac{44}{5\left(8+3\right)}$$

Żid 8 u 3 biex tikseb 11.

$$\frac{14}{3}+\frac{44}{5\times 11}$$

Immultiplika 5 u 11 biex tikseb 55.

$$\frac{14}{3}+\frac{44}{55}$$

Naqqas il-frazzjoni \frac{44}{55} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 11.

$$\frac{14}{3}+\frac{4}{5}$$

L-inqas multipli komuni ta' 3 u 5 huwa 15. Ikkonverti \frac{14}{3} u \frac{4}{5} fi frazzjonijiet bid-denominatur 15.

$$\frac{70}{15}+\frac{12}{15}$$

Billi \frac{70}{15} u \frac{12}{15} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{70+12}{15}$$

Żid 70 u 12 biex tikseb 82.

$$\frac{82}{15}$$

Fattur

$$\frac{2 \cdot 41}{3 \cdot 5} = 5\frac{7}{15} = 5.466666666666667$$