Solve (23/4:1,1+31/3)*12/7/2,5-0,4*3frac{1{8}}

$$\frac { ( 2 \frac { 3 } { 4 } : 1,1 + 3 \frac { 1 } { 3 } ) \cdot 1 \frac { 2 } { 7 } } { 2,5 - 0,4 \cdot 3 \frac { 1 } { 8 } }$$

Evaluate

$$6$$

Solution Steps

Express \frac{\frac{2\times 4+3}{4}}{1,1} as a single fraction.

$$\frac{\left(\frac{2\times 4+3}{4\times 1,1}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply 2 and 4 to get 8.

$$\frac{\left(\frac{8+3}{4\times 1,1}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Add 8 and 3 to get 11.

$$\frac{\left(\frac{11}{4\times 1,1}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply 4 and 1,1 to get 4,4.

$$\frac{\left(\frac{11}{4,4}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Expand \frac{11}{4,4} by multiplying both numerator and the denominator by 10.

$$\frac{\left(\frac{110}{44}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Reduce the fraction \frac{110}{44} to lowest terms by extracting and canceling out 22.

$$\frac{\left(\frac{5}{2}+\frac{3\times 3+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply 3 and 3 to get 9.

$$\frac{\left(\frac{5}{2}+\frac{9+1}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Add 9 and 1 to get 10.

$$\frac{\left(\frac{5}{2}+\frac{10}{3}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{10}{3} to fractions with denominator 6.

$$\frac{\left(\frac{15}{6}+\frac{20}{6}\right)\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Since \frac{15}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+20}{6}\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Add 15 and 20 to get 35.

$$\frac{\frac{35}{6}\times \frac{1\times 7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply 1 and 7 to get 7.

$$\frac{\frac{35}{6}\times \frac{7+2}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Add 7 and 2 to get 9.

$$\frac{\frac{35}{6}\times \frac{9}{7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply \frac{35}{6} times \frac{9}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{35\times 9}{6\times 7}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Do the multiplications in the fraction \frac{35\times 9}{6\times 7}.

$$\frac{\frac{315}{42}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Reduce the fraction \frac{315}{42} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{15}{2}}{2,5-0,4\times \frac{3\times 8+1}{8}}$$

Multiply 3 and 8 to get 24.

$$\frac{\frac{15}{2}}{2,5-0,4\times \frac{24+1}{8}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{15}{2}}{2,5-0,4\times \frac{25}{8}}$$

Convert decimal number 0,4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{15}{2}}{2,5-\frac{2}{5}\times \frac{25}{8}}$$

Multiply \frac{2}{5} times \frac{25}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15}{2}}{2,5-\frac{2\times 25}{5\times 8}}$$

Do the multiplications in the fraction \frac{2\times 25}{5\times 8}.

$$\frac{\frac{15}{2}}{2,5-\frac{50}{40}}$$

Reduce the fraction \frac{50}{40} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{15}{2}}{2,5-\frac{5}{4}}$$

Convert decimal number 2,5 to fraction \frac{25}{10}. Reduce the fraction \frac{25}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{15}{2}}{\frac{5}{2}-\frac{5}{4}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{5}{4} to fractions with denominator 4.

$$\frac{\frac{15}{2}}{\frac{10}{4}-\frac{5}{4}}$$

Since \frac{10}{4} and \frac{5}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15}{2}}{\frac{10-5}{4}}$$

Subtract 5 from 10 to get 5.

$$\frac{\frac{15}{2}}{\frac{5}{4}}$$

Divide \frac{15}{2} by \frac{5}{4} by multiplying \frac{15}{2} by the reciprocal of \frac{5}{4}.

$$\frac{15}{2}\times \frac{4}{5}$$

Multiply \frac{15}{2} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 4}{2\times 5}$$

Do the multiplications in the fraction \frac{15\times 4}{2\times 5}.

$$\frac{60}{10}$$

Divide 60 by 10 to get 6.

$$6$$

Factor

$$2\times 3$$