Solve (1/4div21/2+33/7*15/9)divfrac{5}{1}-8frac{1}{5}

$$( \frac{ 1 }{ 4 } \div 2 \frac{ 1 }{ 2 } +3 \frac{ 3 }{ 7 } \times 1 \frac{ 5 }{ 9 } ) \div \frac{ 5 }{ 1 } -8 \frac{ 1 }{ 5 }$$

Evaluate

$$-\frac{1067}{150}\approx -7.113333333$$

Solution Steps

Divide \frac{1}{4} by \frac{2\times 2+1}{2} by multiplying \frac{1}{4} by the reciprocal of \frac{2\times 2+1}{2}.

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

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 4 and 5 to get 20.

$$\frac{\frac{2}{20}+\frac{3\times 7+3}{7}\times \frac{1\times 9+5}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{10}+\frac{3\times 7+3}{7}\times \frac{1\times 9+5}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{1}{10}+\frac{21+3}{7}\times \frac{1\times 9+5}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Add 21 and 3 to get 24.

$$\frac{\frac{1}{10}+\frac{24}{7}\times \frac{1\times 9+5}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{1}{10}+\frac{24}{7}\times \frac{9+5}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Add 9 and 5 to get 14.

$$\frac{\frac{1}{10}+\frac{24}{7}\times \frac{14}{9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Multiply \frac{24}{7} times \frac{14}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{10}+\frac{24\times 14}{7\times 9}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Do the multiplications in the fraction \frac{24\times 14}{7\times 9}.

$$\frac{\frac{1}{10}+\frac{336}{63}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Reduce the fraction \frac{336}{63} to lowest terms by extracting and canceling out 21.

$$\frac{\frac{1}{10}+\frac{16}{3}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Least common multiple of 10 and 3 is 30. Convert \frac{1}{10} and \frac{16}{3} to fractions with denominator 30.

$$\frac{\frac{3}{30}+\frac{160}{30}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Since \frac{3}{30} and \frac{160}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+160}{30}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Add 3 and 160 to get 163.

$$\frac{\frac{163}{30}}{\frac{5}{1}}-\frac{8\times 5+1}{5}$$

Anything divided by one gives itself.

$$\frac{\frac{163}{30}}{5}-\frac{8\times 5+1}{5}$$

Express \frac{\frac{163}{30}}{5} as a single fraction.

$$\frac{163}{30\times 5}-\frac{8\times 5+1}{5}$$

Multiply 30 and 5 to get 150.

$$\frac{163}{150}-\frac{8\times 5+1}{5}$$

Multiply 8 and 5 to get 40.

$$\frac{163}{150}-\frac{40+1}{5}$$

Add 40 and 1 to get 41.

$$\frac{163}{150}-\frac{41}{5}$$

Least common multiple of 150 and 5 is 150. Convert \frac{163}{150} and \frac{41}{5} to fractions with denominator 150.

$$\frac{163}{150}-\frac{1230}{150}$$

Since \frac{163}{150} and \frac{1230}{150} have the same denominator, subtract them by subtracting their numerators.

$$\frac{163-1230}{150}$$

Subtract 1230 from 163 to get -1067.

$$-\frac{1067}{150}$$

Factor

$$-\frac{1067}{150} = -7\frac{17}{150} = -7.113333333333333$$