Rešite ((11/7-23/49):22/147-(06:33/4)2frac{1}{2}+375:1frac{1}{2}):22

$$( ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 06 : 3 \frac { 3 } { 4 } ) 2 \frac { 1 } { 2 } + 375 : 1 \frac { 1 } { 2 } ) : 22$$

Ovrednoti

$$\frac{509}{44}\approx 11,568181818$$

Koraki rešitve

Pomnožite 1 in 7, da dobite 7.

$$\frac{\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Seštejte 7 in 1, da dobite 8.

$$\frac{\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Najmanjši skupni mnogokratnik 7 in 49 je 49. Pretvorite \frac{8}{7} in \frac{23}{49} v ulomke z imenovalcem 49.

$$\frac{\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

\frac{56}{49} in \frac{23}{49} imata isti imenovalec, zato ju odštejte tako, da odštejete njuna imenovalca.

$$\frac{\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Odštejte 23 od 56, da dobite 33.

$$\frac{\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Delite \frac{33}{49} s/z \frac{22}{147} tako, da pomnožite \frac{33}{49} z obratno vrednostjo \frac{22}{147}.

$$\frac{\frac{33}{49}\times \frac{147}{22}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Pomnožite \frac{33}{49} s/z \frac{147}{22} tako, da pomnožite števec s števcem in imenovalec z imenovalcem.

$$\frac{\frac{33\times 147}{49\times 22}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Izvedite množenja v ulomku \frac{33\times 147}{49\times 22}.

$$\frac{\frac{4851}{1078}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Zmanjšajte ulomek \frac{4851}{1078} na najmanjši imenovalec tako, da izpeljete in okrajšate 539.

$$\frac{\frac{9}{2}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Pomnožite 0 in 6, da dobite 0.

$$\frac{\frac{9}{2}-\frac{0}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Pomnožite 3 in 4, da dobite 12.

$$\frac{\frac{9}{2}-\frac{0}{\frac{12+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Seštejte 12 in 3, da dobite 15.

$$\frac{\frac{9}{2}-\frac{0}{\frac{15}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Vrednost nič, deljena s poljubno vrednostjo, ki ni nič, da vrednost nič.

$$\frac{\frac{9}{2}-0\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Pomnožite 2 in 2, da dobite 4.

$$\frac{\frac{9}{2}-0\times \frac{4+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Seštejte 4 in 1, da dobite 5.

$$\frac{\frac{9}{2}-0\times \frac{5}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Pomnožite 0 in \frac{5}{2}, da dobite 0.

$$\frac{\frac{9}{2}-0+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Odštejte 0 od \frac{9}{2}, da dobite \frac{9}{2}.

$$\frac{\frac{9}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Delite 375 s/z \frac{1\times 2+1}{2} tako, da pomnožite 375 z obratno vrednostjo \frac{1\times 2+1}{2}.

$$\frac{\frac{9}{2}+\frac{375\times 2}{1\times 2+1}}{22}$$

Pomnožite 375 in 2, da dobite 750.

$$\frac{\frac{9}{2}+\frac{750}{1\times 2+1}}{22}$$

Pomnožite 1 in 2, da dobite 2.

$$\frac{\frac{9}{2}+\frac{750}{2+1}}{22}$$

Seštejte 2 in 1, da dobite 3.

$$\frac{\frac{9}{2}+\frac{750}{3}}{22}$$

Delite 750 s/z 3, da dobite 250.

$$\frac{\frac{9}{2}+250}{22}$$

Pretvorite 250 v ulomek \frac{500}{2}.

$$\frac{\frac{9}{2}+\frac{500}{2}}{22}$$

\frac{9}{2} in \frac{500}{2} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

$$\frac{\frac{9+500}{2}}{22}$$

Seštejte 9 in 500, da dobite 509.

$$\frac{\frac{509}{2}}{22}$$

Izrazite \frac{\frac{509}{2}}{22} kot enojni ulomek.

$$\frac{509}{2\times 22}$$

Pomnožite 2 in 22, da dobite 44.

$$\frac{509}{44}$$

Faktoriziraj

$$\frac{509}{2 ^ {2} \cdot 11} = 11\frac{25}{44} = 11,568181818181818$$