Solve 12/5-(31/3-25/6*25/100)div5frac{1}{4}

$$1 \frac{ 2 }{ 5 } -(3 \frac{ 1 }{ 3 } -2 \frac{ 5 }{ 6 } \times \frac{ 25 }{ 100 } ) \div 5 \frac{ 1 }{ 4 }$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{5+2}{5}-\frac{\frac{3\times 3+1}{3}-\frac{2\times 6+5}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Add 5 and 2 to get 7.

$$\frac{7}{5}-\frac{\frac{3\times 3+1}{3}-\frac{2\times 6+5}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{7}{5}-\frac{\frac{9+1}{3}-\frac{2\times 6+5}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Add 9 and 1 to get 10.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{2\times 6+5}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Multiply 2 and 6 to get 12.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{12+5}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Add 12 and 5 to get 17.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{17}{6}\times \frac{25}{100}}{\frac{5\times 4+1}{4}}$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{17}{6}\times \frac{1}{4}}{\frac{5\times 4+1}{4}}$$

Multiply \frac{17}{6} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{17\times 1}{6\times 4}}{\frac{5\times 4+1}{4}}$$

Do the multiplications in the fraction \frac{17\times 1}{6\times 4}.

$$\frac{7}{5}-\frac{\frac{10}{3}-\frac{17}{24}}{\frac{5\times 4+1}{4}}$$

Least common multiple of 3 and 24 is 24. Convert \frac{10}{3} and \frac{17}{24} to fractions with denominator 24.

$$\frac{7}{5}-\frac{\frac{80}{24}-\frac{17}{24}}{\frac{5\times 4+1}{4}}$$

Since \frac{80}{24} and \frac{17}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{5}-\frac{\frac{80-17}{24}}{\frac{5\times 4+1}{4}}$$

Subtract 17 from 80 to get 63.

$$\frac{7}{5}-\frac{\frac{63}{24}}{\frac{5\times 4+1}{4}}$$

Reduce the fraction \frac{63}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{5}-\frac{\frac{21}{8}}{\frac{5\times 4+1}{4}}$$

Multiply 5 and 4 to get 20.

$$\frac{7}{5}-\frac{\frac{21}{8}}{\frac{20+1}{4}}$$

Add 20 and 1 to get 21.

$$\frac{7}{5}-\frac{\frac{21}{8}}{\frac{21}{4}}$$

Divide \frac{21}{8} by \frac{21}{4} by multiplying \frac{21}{8} by the reciprocal of \frac{21}{4}.

$$\frac{7}{5}-\frac{21}{8}\times \frac{4}{21}$$

Multiply \frac{21}{8} times \frac{4}{21} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{5}-\frac{21\times 4}{8\times 21}$$

Cancel out 21 in both numerator and denominator.

$$\frac{7}{5}-\frac{4}{8}$$

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{7}{5}-\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{7}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{14}{10}-\frac{5}{10}$$

Since \frac{14}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-5}{10}$$

Subtract 5 from 14 to get 9.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$