Lahenda {left(5/10+3/9right)}^2div{left(15/9right)}^2+lceil(7/10divfrac{84}{90}+frac{24}{9}divfrac{4}{9})*frac{2}{27}+frac{5}{12}rceil=

$${ \left( \frac{ 5 }{ 10 } + \frac{ 3 }{ 9 } \right) }^{ 2 } \div { \left( \frac{ 15 }{ 9 } \right) }^{ 2 } + \lceil ( \frac{ 7 }{ 10 } \div \frac{ 84 }{ 90 } + \frac{ 24 }{ 9 } \div \frac{ 4 }{ 9 } ) \times \frac{ 2 }{ 27 } + \frac{ 5 }{ 12 } \rceil =$$

Arvuta

$$\frac{5}{4}=1,25$$

Lahenduse etapid

Taandage murd \frac{5}{10} vähimale ühiskordsele, eraldades ja taandades arvu 5.

$$\frac{\left(\frac{1}{2}+\frac{3}{9}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Taandage murd \frac{3}{9} vähimale ühiskordsele, eraldades ja taandades arvu 3.

$$\frac{\left(\frac{1}{2}+\frac{1}{3}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Liitke \frac{1}{2} ja \frac{1}{3}, et leida \frac{5}{6}.

$$\frac{\left(\frac{5}{6}\right)^{2}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Arvutage 2 aste \frac{5}{6} ja leidke \frac{25}{36}.

$$\frac{\frac{25}{36}}{\left(\frac{15}{9}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Taandage murd \frac{15}{9} vähimale ühiskordsele, eraldades ja taandades arvu 3.

$$\frac{\frac{25}{36}}{\left(\frac{5}{3}\right)^{2}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Arvutage 2 aste \frac{5}{3} ja leidke \frac{25}{9}.

$$\frac{\frac{25}{36}}{\frac{25}{9}}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Jagage \frac{25}{36} väärtusega \frac{25}{9}, korrutades \frac{25}{36} väärtuse \frac{25}{9} pöördväärtusega.

$$\frac{25}{36}\times \frac{9}{25}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Korrutage \frac{25}{36} ja \frac{9}{25}, et leida \frac{1}{4}.

$$\frac{1}{4}+\lceil \left(\frac{\frac{7}{10}}{\frac{84}{90}}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Jagage \frac{7}{10} väärtusega \frac{84}{90}, korrutades \frac{7}{10} väärtuse \frac{84}{90} pöördväärtusega.

$$\frac{1}{4}+\lceil \left(\frac{7\times 90}{10\times 84}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Taandage 3\times 7\times 10 nii lugejas kui ka nimetajas.

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+\frac{\frac{24}{9}}{\frac{4}{9}}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Jagage \frac{24}{9} väärtusega \frac{4}{9}, korrutades \frac{24}{9} väärtuse \frac{4}{9} pöördväärtusega.

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+\frac{24\times 9}{9\times 4}\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Taandage 3\times 3\times 4 nii lugejas kui ka nimetajas.

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+2\times 3\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Korrutage 2 ja 3, et leida 6.

$$\frac{1}{4}+\lceil \left(\frac{3}{4}+6\right)\times \frac{2}{27}+\frac{5}{12}\rceil$$

Liitke \frac{3}{4} ja 6, et leida \frac{27}{4}.

$$\frac{1}{4}+\lceil \frac{27}{4}\times \frac{2}{27}+\frac{5}{12}\rceil$$

Korrutage \frac{27}{4} ja \frac{2}{27}, et leida \frac{1}{2}.

$$\frac{1}{4}+\lceil \frac{1}{2}+\frac{5}{12}\rceil$$

Liitke \frac{1}{2} ja \frac{5}{12}, et leida \frac{11}{12}.

$$\frac{1}{4}+\lceil \frac{11}{12}\rceil$$

11 jagamisel 12-ga saadakse 0 ja jääk 11. Kirjutage \frac{11}{12} ümber kujul 0+\frac{11}{12}.

$$\frac{1}{4}+\lceil 0+\frac{11}{12}\rceil$$

Reaalarvu a ülemine täisosa on väikseim täisarv, mis on suurem kui a või sellega võrdne. 0+\frac{11}{12} ülemine täisosa on 1.

$$\frac{1}{4}+1$$

Liitke \frac{1}{4} ja 1, et leida \frac{5}{4}.

$$\frac{5}{4}$$

Lahuta teguriteks

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1,25$$