Issolvi 50(1-1/1.02^5)+100/1.02^5

$$50 ( 1 - \frac { 1 } { 1.02 ^ { 5 } } ) + \frac { 100 } { 1.02 ^ { 5 } }$$

Evalwa

$$\frac{32876262550}{345025251}\approx 95.286540491$$

Passi tas-Soluzzjonijiet

Ikkalkula 1.02 bil-power ta' 5 u tikseb 1.1040808032.

$$50\left(1-\frac{1}{1.1040808032}\right)+\frac{100}{1.02^{5}}$$

Espandi \frac{1}{1.1040808032} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10000000000.

$$50\left(1-\frac{10000000000}{11040808032}\right)+\frac{100}{1.02^{5}}$$

Naqqas il-frazzjoni \frac{10000000000}{11040808032} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 32.

$$50\left(1-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Ikkonverti 1 fi frazzjoni \frac{345025251}{345025251}.

$$50\left(\frac{345025251}{345025251}-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Billi \frac{345025251}{345025251} u \frac{312500000}{345025251} għandhom l-istess denominatur, naqqashom billi tnaqqas in-numeraturi tagħhom.

$$50\times \frac{345025251-312500000}{345025251}+\frac{100}{1.02^{5}}$$

Naqqas 312500000 minn 345025251 biex tikseb 32525251.

$$50\times \frac{32525251}{345025251}+\frac{100}{1.02^{5}}$$

Esprimi 50\times \frac{32525251}{345025251} bħala frazzjoni waħda.

$$\frac{50\times 32525251}{345025251}+\frac{100}{1.02^{5}}$$

Immultiplika 50 u 32525251 biex tikseb 1626262550.

$$\frac{1626262550}{345025251}+\frac{100}{1.02^{5}}$$

Ikkalkula 1.02 bil-power ta' 5 u tikseb 1.1040808032.

$$\frac{1626262550}{345025251}+\frac{100}{1.1040808032}$$

Espandi \frac{100}{1.1040808032} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10000000000.

$$\frac{1626262550}{345025251}+\frac{1000000000000}{11040808032}$$

Naqqas il-frazzjoni \frac{1000000000000}{11040808032} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 32.

$$\frac{1626262550}{345025251}+\frac{31250000000}{345025251}$$

Billi \frac{1626262550}{345025251} u \frac{31250000000}{345025251} għandhom l-istess denominatur, żidhom billi żżid in-numeraturi tagħhom.

$$\frac{1626262550+31250000000}{345025251}$$

Żid 1626262550 u 31250000000 biex tikseb 32876262550.

$$\frac{32876262550}{345025251}$$

Fattur

$$\frac{2 \cdot 101 \cdot 6510151 \cdot 5 ^ {2}}{3 ^ {5} \cdot 17 ^ {5}} = 95\frac{98863705}{345025251} = 95.2865404914958$$