Brojevni izrazi sa razlomcima - zadaci sa rešenjima

Rešenje:
[tex](5{,}8-2{,}3)\cdot 1{,}24=(3{,}5)\cdot 1{,}24 = 4{,}34[/tex]

Rešenje:
NZS[tex](5; 4; 3)=60[/tex]
[tex](\frac{3}{5}-\frac{1}{4}+\frac{2}{3})\frac{2}{5}=(\frac{12 \cdot 3-15+20\cdot2}{60})\frac{2}{5}[/tex]

[tex](\frac{12\cdot3-15+20\cdot2}{60})\frac{2}{5}[/tex] =[tex]\frac{61}{60}\cdot \frac{2}{5}=\frac{122}{300}=\frac{61}{150}[/tex]

Rešenje:
NZS[tex](5;3)=15[/tex]

[tex](\frac{3}{7}: \frac{3}{2})(\frac{1}{5}+\frac{2}{3})=\frac{6}{21}\cdot (\frac{3+10}{15})=\frac{6}{21}\cdot \frac{13}{15}=\frac{78}{315}=\frac{26}{105}[/tex]

Rešenje:
[tex](3{,}2-1{,}9+2{,}5)\cdot 2{,}35=3{,}8\cdot 2{,}35=8{,}93[/tex]

Rešenje:
Najpre mešovite brojeve pretvaramo u neprave razlomke.

[tex]2\frac{1}{5} = 2+\frac{1}{5} = \frac{10+1}{5} = \frac{11}{5}[/tex]
[tex]3\frac{2}{7} = 3+\frac{2}{7} = \frac{21+2}{7} = \frac{23}{7}[/tex]
[tex]1\frac{1}{4} = 1+\frac{1}{4} = \frac{4+1}{4} = \frac{5}{4}[/tex]

Sada izvodimo operacije
NZS[tex](5; 7; 4) = 140[/tex]
[tex]2\frac{1}{5}-3\frac{2}{7}+1\frac{1}{4} = \frac{11}{5}-\frac{23}{7}+\frac{5}{4}[/tex]

[tex]\frac{11}{5}-\frac{23}{7}+\frac{5}{4} = \frac{308-460+175}{140} = \frac{23}{140}[/tex]

Rešenje:
Najpre mešovite brojeve pretvaramo u decimalne brojeve.

[tex]4\frac{3}{5} = 4+\frac{3}{5} = \frac{20+3}{5} = \frac{23}{5} = 4{,}6[/tex]

[tex]3\frac{1}{4} = 3+\frac{1}{4} = 3 + 0{,}25 = 3{,}25[/tex]

Zatim izvodimo operacije

[tex](4\frac{3}{5}-2{,}24)3\frac{1}{4} = (4{,}6-2{,}24)3{,}25[/tex]

[tex](4{,}6-2{,}24)3{,}25 = 2{,}36\cdot 3{,}25 = 7{,}67[/tex]

Rešenje:
[tex]\frac{27}{8}: \frac{4}{9}+\frac{3-20}{15}=\frac{27}{8}: \frac{4}{9}- \frac{17}{15}[/tex]

[tex]\frac{27}{8}: \frac{4}{9}-\frac{17}{15}=\frac{27 \cdot 9}{8\cdot4}-\frac{17}{15}= \frac{243}{32}-\frac{17}{15}=\frac{243\cdot 15-32 \cdot 17}{480}=\frac{3645-544}{480}= \frac{3101}{480}[/tex]

Rešenje:
[tex]3\frac{1}{3}=3+\frac{1}{3}=\frac{10}{3}\qquad 2\frac{1}{5}=2+\frac{1}{5}=\frac{11}{5}[/tex]

[tex](3{,}25+1{,}25-2{,}01): (3\frac{1}{3}+2\frac{1}{5})=(3{,}25+1{,}25-2{,}01): (\frac{10}{3}+\frac{11}{5})[/tex]

[tex](3{,}25+1{,}25-2{,}01): (\frac{10}{3}+\frac{11}{5})=2{,}49: (\frac{50+33}{15})=2{,}49: \frac{83}{15}[/tex]

[tex]2{,}49: \frac{83}{15}=2{,}49: 5{,}53=0{,}45[/tex]

Rešenje:
[tex]\left[ \left( \frac{3}{4}-\frac{1}{2}\right) +\left( \frac{2}{5}-\frac{1}{4}\right) \right] ^{2} = \left[ \left( \frac{3-2}{4}\right) +\left( \frac{8-5}{20}\right) \right]^{2} = \left[ \left( \frac{1}{4}\right) +\left( \frac{3}{20}\right) \right] ^{2}[/tex]

NZS[tex](4; 20) = 20[/tex]

[tex]\left[ \left( \frac{1}{4}\right) +\left( \frac{3}{20}\right) \right]^{2} = \left[ \frac{5+3}{20}\right] ^{2} = \left[ \frac{8}{20}\right] ^{2}[/tex]

[tex]\left[ \frac{8}{20}\right] ^{2} = \frac{64}{400} = \frac{32}{200} = \frac{16}{100} = \frac{8}{50} = \frac{4}{25}[/tex]

Rešenje:
Najpre mešovite brojeve pretvaramo u neprave razlomke.

[tex]3\frac{1}{2} = 3+\frac{1}{2} = \frac{7}{2}[/tex]

[tex]2\frac{3}{4} = 2+\frac{3}{4} = \frac{11}{4}[/tex]

[tex]\frac{\left( 3\frac{1}{2}-2\right) }{\left( 2\frac{3}{4}+1\right) } = \frac{\left( \frac{7}{2}-2\right) }{\left( \frac{11}{4}+1\right) } = \frac{\left( \frac{7-4}{2}\right) }{\left( \frac{11+4}{4}\right) } = \frac{\frac{3}{2}}{\frac{15}{4}} = \frac{12}{30} = \frac{6}{15} = \frac{2}{5}[/tex]

Rešenje:
[tex](2{,}5+1{,}8+3{,}4): \left( 2{,}35-1{,}25\right) =7{,}7: 1{,}1=7[/tex]

Rešenje:
Najpre [tex]2\frac{3}{4}[/tex] pretvaramo u nepravi razlomak.

[tex]2\frac{3}{4} = 2+\frac{3}{4} = \frac{11}{4}[/tex]

[tex]\frac{\left[ \left( \frac{3}{2}+\frac{1}{3}\right) \cdot \left( \frac{2}{5}+\frac{1}{4}\right) \right] }{\frac{11}{4}} = \frac{\left[ \left( \frac{9+2}{6}\right) \cdot \left( \frac{8+5}{20}\right) \right] }{\frac{11}{4}}[/tex]

NZS[tex](4; 5) = 20[/tex]     NZS[tex](2; 3) = 6[/tex]

[tex]\frac{\left[ \left( \frac{9+2}{6}\right) \cdot \left( \frac{8+5}{20}\right) \right] }{\frac{11}{4}} = \frac{\left[ \left( \frac{11}{6}\right) \cdot \left( \frac{13}{20}\right) \right] }{\frac{11}{4}} = \frac{\frac{143}{120}}{\frac{11}{4}} = \frac{572}{1320} = \frac{286}{660} = \frac{143}{330}[/tex]

Rešenje:
Najpre [tex]2\frac{1}{4}[/tex] pretvaramo u decimalni broj.

[tex]2\frac{1}{4} = \frac{9}{4} = 2{,}25[/tex]

[tex](4{,}7-1{,}6+2{,}3)\cdot 2\frac{1}{4} = (4{,}7-1{,}6+2{,}3)\cdot 2{,}25[/tex]

[tex](4{,}7-1{,}6+2{,}3)\cdot 2{,}25 = 5{,}4\cdot 2{,}25 = 12{,}15[/tex]

Rešenje:
[tex]3\frac{1}{4}=\frac{13}{4}[/tex]

[tex]2\frac{3}{5}=\frac{13}{5}[/tex]

[tex]5\frac{2}{3}=\frac{17}{3}[/tex]

[tex]1\frac{1}{2}=\frac{3}{2}[/tex]

[tex](3\frac{1}{4}-2\frac{3}{5}): (5\frac{2}{3}+1\frac{1}{2})=(\frac{13}{4}-\frac{13}{5}): (\frac{17}{3}+\frac{3}{2})[/tex]

[tex](\frac{13}{4}-\frac{13}{5}): (\frac{17}{3}+\frac{3}{2})=(\frac{65-52}{20}): (\frac{34+9}{6})=(\frac{13}{20}): (\frac{43}{6})=\frac{13\cdot 6}{43\cdot 20}=\frac{78}{860}=\frac{39}{430}[/tex]

Rešenje:
Prvo da pretvorimo razlomke u decimale.

[tex]\frac{7}{4}=1{,}75\qquad 2\frac{1}{4}=2{,}25[/tex]

[tex](\frac{7}{4}+2\frac{1}{4}+5{,}25)^{2}=(1{,}75+2{,}25+5{,}25)^{2}=(9{,}25)^{2}=85{,}56[/tex]

Rešenje:
[tex]3\frac{3}{2}=\frac{9}{2}=4{,}5[/tex]

[tex](3\frac{3}{2})^{2}: (7{,}20-2{,}35)=(4{,}5)^{2}: (4{,}85)[/tex]

[tex](4{,}5)^{2}: (4{,}85)=20{,}25: 4{,}85=4{,}18[/tex]

Rešenje:
[tex](\frac{4}{3}-\frac{2}{5}+1) : (\frac{3}{2}+3) = (\frac{20-6+15}{15}) : (\frac{3+6}{2})[/tex]

NZS[tex](3; 5; 1) = 15[/tex]     NZS[tex](2; 1) = 2[/tex]

[tex](\frac{20-6+15}{15}) : (\frac{3+6}{2}) = \frac{29}{15} : \frac{9}{2} = \frac{58}{135}[/tex]

Rešenje:
[tex]2\frac{1}{4}=\frac{9}{4}=2{,}25[/tex]

[tex](5{,}24-2{,}49+2{,}25)^{2}=5^{2}=25[/tex]