Issolvi {l}{1+1/2+1/3+1/4-1/5+frac{1}{6}}{+frac{1}{7}+frac{1}{8}+frac{1}{9}+frac{1}{10}+frac{1}{11}}{+frac{1}{12}+2}

$$\left. \begin{array} { l } { 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 5 } + \frac { 1 } { 6 } } \\ { + \frac { 1 } { 7 } + \frac { 1 } { 8 } + \frac { 1 } { 9 } + \frac { 1 } { 10 } + \frac { 1 } { 11 } } \\ { + \frac { 1 } { 12 } + 2 } \end{array} \right.$$

Evalwa

$$\frac{130373}{27720}\approx 4.703210678$$

Passi tas-Soluzzjonijiet

Ikkonverti 1 fi frazzjoni \frac{2}{2}.

$$\frac{2}{2}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{2}{2} u \frac{1}{2} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{2+1}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 2 u 1 biex tikseb 3.

$$\frac{3}{2}+\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 2 u 3 huwa 6. Ikkonverti \frac{3}{2} u \frac{1}{3} fi frazzjonijiet bid-denominatur 6.

$$\frac{9}{6}+\frac{2}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{9}{6} u \frac{2}{6} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{9+2}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 9 u 2 biex tikseb 11.

$$\frac{11}{6}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 6 u 4 huwa 12. Ikkonverti \frac{11}{6} u \frac{1}{4} fi frazzjonijiet bid-denominatur 12.

$$\frac{22}{12}+\frac{3}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{22}{12} u \frac{3}{12} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{22+3}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 22 u 3 biex tikseb 25.

$$\frac{25}{12}-\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 12 u 5 huwa 60. Ikkonverti \frac{25}{12} u \frac{1}{5} fi frazzjonijiet bid-denominatur 60.

$$\frac{125}{60}-\frac{12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{125}{60} u \frac{12}{60} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$\frac{125-12}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Naqqas 12 minn 125 biex tikseb 113.

$$\frac{113}{60}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 60 u 6 huwa 60. Ikkonverti \frac{113}{60} u \frac{1}{6} fi frazzjonijiet bid-denominatur 60.

$$\frac{113}{60}+\frac{10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{113}{60} u \frac{10}{60} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{113+10}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 113 u 10 biex tikseb 123.

$$\frac{123}{60}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Naqqas il-frazzjoni \frac{123}{60} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 3.

$$\frac{41}{20}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 20 u 7 huwa 140. Ikkonverti \frac{41}{20} u \frac{1}{7} fi frazzjonijiet bid-denominatur 140.

$$\frac{287}{140}+\frac{20}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{287}{140} u \frac{20}{140} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{287+20}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 287 u 20 biex tikseb 307.

$$\frac{307}{140}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 140 u 8 huwa 280. Ikkonverti \frac{307}{140} u \frac{1}{8} fi frazzjonijiet bid-denominatur 280.

$$\frac{614}{280}+\frac{35}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{614}{280} u \frac{35}{280} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{614+35}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 614 u 35 biex tikseb 649.

$$\frac{649}{280}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 280 u 9 huwa 2520. Ikkonverti \frac{649}{280} u \frac{1}{9} fi frazzjonijiet bid-denominatur 2520.

$$\frac{5841}{2520}+\frac{280}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{5841}{2520} u \frac{280}{2520} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{5841+280}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 5841 u 280 biex tikseb 6121.

$$\frac{6121}{2520}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 2520 u 10 huwa 2520. Ikkonverti \frac{6121}{2520} u \frac{1}{10} fi frazzjonijiet bid-denominatur 2520.

$$\frac{6121}{2520}+\frac{252}{2520}+\frac{1}{11}+\frac{1}{12}+2$$

Billi \frac{6121}{2520} u \frac{252}{2520} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{6121+252}{2520}+\frac{1}{11}+\frac{1}{12}+2$$

Żid 6121 u 252 biex tikseb 6373.

$$\frac{6373}{2520}+\frac{1}{11}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 2520 u 11 huwa 27720. Ikkonverti \frac{6373}{2520} u \frac{1}{11} fi frazzjonijiet bid-denominatur 27720.

$$\frac{70103}{27720}+\frac{2520}{27720}+\frac{1}{12}+2$$

Billi \frac{70103}{27720} u \frac{2520}{27720} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{70103+2520}{27720}+\frac{1}{12}+2$$

Żid 70103 u 2520 biex tikseb 72623.

$$\frac{72623}{27720}+\frac{1}{12}+2$$

L-inqas multipli komuni ta' 27720 u 12 huwa 27720. Ikkonverti \frac{72623}{27720} u \frac{1}{12} fi frazzjonijiet bid-denominatur 27720.

$$\frac{72623}{27720}+\frac{2310}{27720}+2$$

Billi \frac{72623}{27720} u \frac{2310}{27720} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{72623+2310}{27720}+2$$

Żid 72623 u 2310 biex tikseb 74933.

$$\frac{74933}{27720}+2$$

Ikkonverti 2 fi frazzjoni \frac{55440}{27720}.

$$\frac{74933}{27720}+\frac{55440}{27720}$$

Billi \frac{74933}{27720} u \frac{55440}{27720} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{74933+55440}{27720}$$

Żid 74933 u 55440 biex tikseb 130373.

$$\frac{130373}{27720}$$

Fattur

$$\frac{17 \cdot 7669}{2 ^ {3} \cdot 3 ^ {2} \cdot 5 \cdot 7 \cdot 11} = 4\frac{19493}{27720} = 4.703210678210678$$