Solve 5/3+4/37/5/frac{14{4}divfrac{6}{5}}

$$\frac{ \frac{ 5 }{ 3 } + \frac{ 4 }{ 3 } \frac{ 7 }{ 5 } }{ \frac{ 14 }{ 4 } \div \frac{ 6 }{ 5 } }$$

Evaluate

$$\frac{212}{175}\approx 1.211428571$$

Solution Steps

Multiply \frac{4}{3} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{3}+\frac{4\times 7}{3\times 5}}{\frac{\frac{14}{4}}{\frac{6}{5}}}$$

Do the multiplications in the fraction \frac{4\times 7}{3\times 5}.

$$\frac{\frac{5}{3}+\frac{28}{15}}{\frac{\frac{14}{4}}{\frac{6}{5}}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{5}{3} and \frac{28}{15} to fractions with denominator 15.

$$\frac{\frac{25}{15}+\frac{28}{15}}{\frac{\frac{14}{4}}{\frac{6}{5}}}$$

Since \frac{25}{15} and \frac{28}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+28}{15}}{\frac{\frac{14}{4}}{\frac{6}{5}}}$$

Add 25 and 28 to get 53.

$$\frac{\frac{53}{15}}{\frac{\frac{14}{4}}{\frac{6}{5}}}$$

Divide \frac{14}{4} by \frac{6}{5} by multiplying \frac{14}{4} by the reciprocal of \frac{6}{5}.

$$\frac{\frac{53}{15}}{\frac{14\times 5}{4\times 6}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\frac{53}{15}}{\frac{5\times 7}{2\times 6}}$$

Multiply 5 and 7 to get 35.

$$\frac{\frac{53}{15}}{\frac{35}{2\times 6}}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{53}{15}}{\frac{35}{12}}$$

Divide \frac{53}{15} by \frac{35}{12} by multiplying \frac{53}{15} by the reciprocal of \frac{35}{12}.

$$\frac{53}{15}\times \frac{12}{35}$$

Multiply \frac{53}{15} times \frac{12}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{53\times 12}{15\times 35}$$

Do the multiplications in the fraction \frac{53\times 12}{15\times 35}.

$$\frac{636}{525}$$

Reduce the fraction \frac{636}{525} to lowest terms by extracting and canceling out 3.

$$\frac{212}{175}$$

Factor

$$\frac{2 ^ {2} \cdot 53}{5 ^ {2} \cdot 7} = 1\frac{37}{175} = 1.2114285714285715$$