Issolvi pi:11/2[31/2div21/3{11/4div(2+3frac{2}{3})}]

$$\pi : 1 \frac { 1 } { 2 } [ 3 \frac { 1 } { 2 } \div 2 \frac { 1 } { 3 } \{ 1 \frac { 1 } { 4 } \div ( 2 + 3 \frac { 2 } { 3 } ) \} ]$$

Evalwa

$$\frac{15\pi }{68}\approx 0.692998379$$

Passi tas-Soluzzjonijiet

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

$$\frac{\pi \times 2}{1\times 2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 1 u 2 biex tikseb 2.

$$\frac{\pi \times 2}{2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Żid 2 u 1 biex tikseb 3.

$$\frac{\pi \times 2}{3}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

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

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

Annulla 1+2\times 3 fin-numeratur u d-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 1 u 4 biex tikseb 4.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Żid 4 u 1 biex tikseb 5.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}$$

Żid 9 u 2 biex tikseb 11.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

Ikkonverti 2 fi frazzjoni \frac{6}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

Billi \frac{6}{3} u \frac{11}{3} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

Żid 6 u 11 biex tikseb 17.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

Iddividi \frac{5}{4} b'\frac{17}{3} billi timmultiplika \frac{5}{4} bir-reċiproku ta' \frac{17}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5}{4}\times \frac{3}{17}$$

Immultiplika \frac{5}{4} b'\frac{3}{17} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5\times 3}{4\times 17}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{5\times 3}{4\times 17}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{15}{68}$$

Immultiplika \frac{3}{2} b'\frac{15}{68} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3\times 15}{2\times 68}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{3\times 15}{2\times 68}.

$$\frac{\pi \times 2}{3}\times \frac{45}{136}$$

Immultiplika \frac{\pi \times 2}{3} b'\frac{45}{136} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2\times 45}{3\times 136}$$

Annulla 2\times 3 fin-numeratur u d-denominatur.

$$\frac{15\pi }{68}$$

Espandi

$$\frac{15 \pi}{68} = 0.6929983794683366$$

Passi tas-Soluzzjonijiet

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

$$\frac{\pi \times 2}{1\times 2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 1 u 2 biex tikseb 2.

$$\frac{\pi \times 2}{2+1}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Żid 2 u 1 biex tikseb 3.

$$\frac{\pi \times 2}{3}\times \frac{\frac{3\times 2+1}{2}}{\frac{2\times 3+1}{3}}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

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

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

Annulla 1+2\times 3 fin-numeratur u d-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{1\times 4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 1 u 4 biex tikseb 4.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{4+1}{4}}{2+\frac{3\times 3+2}{3}}$$

Żid 4 u 1 biex tikseb 5.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{3\times 3+2}{3}}$$

Immultiplika 3 u 3 biex tikseb 9.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{9+2}{3}}$$

Żid 9 u 2 biex tikseb 11.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{2+\frac{11}{3}}$$

Ikkonverti 2 fi frazzjoni \frac{6}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6}{3}+\frac{11}{3}}$$

Billi \frac{6}{3} u \frac{11}{3} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{6+11}{3}}$$

Żid 6 u 11 biex tikseb 17.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{\frac{5}{4}}{\frac{17}{3}}$$

Iddividi \frac{5}{4} b'\frac{17}{3} billi timmultiplika \frac{5}{4} bir-reċiproku ta' \frac{17}{3}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5}{4}\times \frac{3}{17}$$

Immultiplika \frac{5}{4} b'\frac{3}{17} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{5\times 3}{4\times 17}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{5\times 3}{4\times 17}.

$$\frac{\pi \times 2}{3}\times \frac{3}{2}\times \frac{15}{68}$$

Immultiplika \frac{3}{2} b'\frac{15}{68} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2}{3}\times \frac{3\times 15}{2\times 68}$$

Agħmel il-multiplikazzjonijiet fil-frazzjoni \frac{3\times 15}{2\times 68}.

$$\frac{\pi \times 2}{3}\times \frac{45}{136}$$

Immultiplika \frac{\pi \times 2}{3} b'\frac{45}{136} billi timmultiplika n-numeratur bin-numeratur u d-denominatur bid-denominatur.

$$\frac{\pi \times 2\times 45}{3\times 136}$$

Annulla 2\times 3 fin-numeratur u d-denominatur.

$$\frac{15\pi }{68}$$