Solve 5.2/3frac{1{5}}-12/30.7

$$\frac{ 5.2 }{ 3 \frac{ 1 }{ 5 } } -1 \frac{ 2 }{ 3 } 0.7$$

Evaluate

$$\frac{11}{24}\approx 0.458333333$$

Solution Steps

Divide 5.2 by \frac{3\times 5+1}{5} by multiplying 5.2 by the reciprocal of \frac{3\times 5+1}{5}.

$$\frac{5.2\times 5}{3\times 5+1}-\frac{1\times 3+2}{3}\times 0.7$$

Multiply 5.2 and 5 to get 26.

$$\frac{26}{3\times 5+1}-\frac{1\times 3+2}{3}\times 0.7$$

Multiply 3 and 5 to get 15.

$$\frac{26}{15+1}-\frac{1\times 3+2}{3}\times 0.7$$

Add 15 and 1 to get 16.

$$\frac{26}{16}-\frac{1\times 3+2}{3}\times 0.7$$

Reduce the fraction \frac{26}{16} to lowest terms by extracting and canceling out 2.

$$\frac{13}{8}-\frac{1\times 3+2}{3}\times 0.7$$

Multiply 1 and 3 to get 3.

$$\frac{13}{8}-\frac{3+2}{3}\times 0.7$$

Add 3 and 2 to get 5.

$$\frac{13}{8}-\frac{5}{3}\times 0.7$$

Convert decimal number 0.7 to fraction \frac{7}{10}.

$$\frac{13}{8}-\frac{5}{3}\times \frac{7}{10}$$

Multiply \frac{5}{3} times \frac{7}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{8}-\frac{5\times 7}{3\times 10}$$

Do the multiplications in the fraction \frac{5\times 7}{3\times 10}.

$$\frac{13}{8}-\frac{35}{30}$$

Reduce the fraction \frac{35}{30} to lowest terms by extracting and canceling out 5.

$$\frac{13}{8}-\frac{7}{6}$$

Least common multiple of 8 and 6 is 24. Convert \frac{13}{8} and \frac{7}{6} to fractions with denominator 24.

$$\frac{39}{24}-\frac{28}{24}$$

Since \frac{39}{24} and \frac{28}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{39-28}{24}$$

Subtract 28 from 39 to get 11.

$$\frac{11}{24}$$

Factor

$$\frac{11}{3 \cdot 2 ^ {3}} = 0.4583333333333333$$