Solve 7.5/0.6-2.5/frac{frac{68div2frac{5{6}-42*0.1}{}1.1}{2/3*0.375+2.68/0.8}}

$$\frac{ \frac{ 7.5 }{ 0.6 } -2.5 }{ \frac{ \frac{ 68 \div 2 \frac{ 5 }{ 6 } -42 \cdot 0.1 }{ } 1.1 }{ \frac{ 2 }{ 3 } \cdot 0.375+ \frac{ 2.68 }{ } 0.8 } }$$

Evaluate

$$\frac{3591}{3982}\approx 0.901808137$$

Solution Steps

Expand \frac{7.5}{0.6} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{75}{6}-2.5}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Reduce the fraction \frac{75}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{25}{2}-2.5}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

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.

$$\frac{\frac{25}{2}-\frac{5}{2}}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Since \frac{25}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-5}{2}}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Subtract 5 from 25 to get 20.

$$\frac{\frac{20}{2}}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Divide 20 by 2 to get 10.

$$\frac{10}{\frac{\frac{\frac{68}{2}\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Divide 68 by 2 to get 34.

$$\frac{10}{\frac{\frac{34\times \frac{5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Express 34\times \frac{5}{6} as a single fraction.

$$\frac{10}{\frac{\frac{\frac{34\times 5}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Multiply 34 and 5 to get 170.

$$\frac{10}{\frac{\frac{\frac{170}{6}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Reduce the fraction \frac{170}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{\frac{\frac{\frac{85}{3}-42\times 0.1}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Multiply 42 and 0.1 to get 4.2.

$$\frac{10}{\frac{\frac{\frac{85}{3}-4.2}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Convert decimal number 4.2 to fraction \frac{42}{10}. Reduce the fraction \frac{42}{10} to lowest terms by extracting and canceling out 2.

$$\frac{10}{\frac{\frac{\frac{85}{3}-\frac{21}{5}}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Least common multiple of 3 and 5 is 15. Convert \frac{85}{3} and \frac{21}{5} to fractions with denominator 15.

$$\frac{10}{\frac{\frac{\frac{425}{15}-\frac{63}{15}}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Since \frac{425}{15} and \frac{63}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{\frac{\frac{\frac{425-63}{15}}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Subtract 63 from 425 to get 362.

$$\frac{10}{\frac{\frac{\frac{362}{15}}{1}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Anything divided by one gives itself.

$$\frac{10}{\frac{\frac{362}{15}\times 1.1}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Convert decimal number 1.1 to fraction \frac{11}{10}.

$$\frac{10}{\frac{\frac{362}{15}\times \frac{11}{10}}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Multiply \frac{362}{15} times \frac{11}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{\frac{\frac{362\times 11}{15\times 10}}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Do the multiplications in the fraction \frac{362\times 11}{15\times 10}.

$$\frac{10}{\frac{\frac{3982}{150}}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Reduce the fraction \frac{3982}{150} to lowest terms by extracting and canceling out 2.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{2}{3}\times 0.375+\frac{2.68}{1}\times 0.8}}$$

Convert decimal number 0.375 to fraction \frac{375}{1000}. Reduce the fraction \frac{375}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{2}{3}\times \frac{3}{8}+\frac{2.68}{1}\times 0.8}}$$

Multiply \frac{2}{3} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{2\times 3}{3\times 8}+\frac{2.68}{1}\times 0.8}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{2}{8}+\frac{2.68}{1}\times 0.8}}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{1}{4}+\frac{2.68}{1}\times 0.8}}$$

Anything divided by one gives itself.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{1}{4}+2.68\times 0.8}}$$

Multiply 2.68 and 0.8 to get 2.144.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{1}{4}+2.144}}$$

Convert decimal number 2.144 to fraction \frac{2144}{1000}. Reduce the fraction \frac{2144}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{1}{4}+\frac{268}{125}}}$$

Least common multiple of 4 and 125 is 500. Convert \frac{1}{4} and \frac{268}{125} to fractions with denominator 500.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{125}{500}+\frac{1072}{500}}}$$

Since \frac{125}{500} and \frac{1072}{500} have the same denominator, add them by adding their numerators.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{125+1072}{500}}}$$

Add 125 and 1072 to get 1197.

$$\frac{10}{\frac{\frac{1991}{75}}{\frac{1197}{500}}}$$

Divide \frac{1991}{75} by \frac{1197}{500} by multiplying \frac{1991}{75} by the reciprocal of \frac{1197}{500}.

$$\frac{10}{\frac{1991}{75}\times \frac{500}{1197}}$$

Multiply \frac{1991}{75} times \frac{500}{1197} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10}{\frac{1991\times 500}{75\times 1197}}$$

Do the multiplications in the fraction \frac{1991\times 500}{75\times 1197}.

$$\frac{10}{\frac{995500}{89775}}$$

Reduce the fraction \frac{995500}{89775} to lowest terms by extracting and canceling out 25.

$$\frac{10}{\frac{39820}{3591}}$$

Divide 10 by \frac{39820}{3591} by multiplying 10 by the reciprocal of \frac{39820}{3591}.

$$10\times \frac{3591}{39820}$$

Express 10\times \frac{3591}{39820} as a single fraction.

$$\frac{10\times 3591}{39820}$$

Multiply 10 and 3591 to get 35910.

$$\frac{35910}{39820}$$

Reduce the fraction \frac{35910}{39820} to lowest terms by extracting and canceling out 10.

$$\frac{3591}{3982}$$

Factor

$$\frac{7 \cdot 19 \cdot 3 ^ {3}}{2 \cdot 11 \cdot 181} = 0.9018081366147664$$