Solve 13/5-2/3/frac{12{13}}+7/5frac{1}{3}

$$1 \frac{ 3 }{ 5 } - \frac{ \frac{ 2 }{ 3 } }{ \frac{ 12 }{ 13 } } + \frac{ 7 }{ 5 } \frac{ 1 }{ 3 }$$

Evaluate

$$\frac{121}{90}\approx 1.344444444$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{5+3}{5}-\frac{\frac{2}{3}}{\frac{12}{13}}+\frac{7}{5}\times \frac{1}{3}$$

Add 5 and 3 to get 8.

$$\frac{8}{5}-\frac{\frac{2}{3}}{\frac{12}{13}}+\frac{7}{5}\times \frac{1}{3}$$

Divide \frac{2}{3} by \frac{12}{13} by multiplying \frac{2}{3} by the reciprocal of \frac{12}{13}.

$$\frac{8}{5}-\frac{2}{3}\times \frac{13}{12}+\frac{7}{5}\times \frac{1}{3}$$

Multiply \frac{2}{3} times \frac{13}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8}{5}-\frac{2\times 13}{3\times 12}+\frac{7}{5}\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{2\times 13}{3\times 12}.

$$\frac{8}{5}-\frac{26}{36}+\frac{7}{5}\times \frac{1}{3}$$

Reduce the fraction \frac{26}{36} to lowest terms by extracting and canceling out 2.

$$\frac{8}{5}-\frac{13}{18}+\frac{7}{5}\times \frac{1}{3}$$

Least common multiple of 5 and 18 is 90. Convert \frac{8}{5} and \frac{13}{18} to fractions with denominator 90.

$$\frac{144}{90}-\frac{65}{90}+\frac{7}{5}\times \frac{1}{3}$$

Since \frac{144}{90} and \frac{65}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{144-65}{90}+\frac{7}{5}\times \frac{1}{3}$$

Subtract 65 from 144 to get 79.

$$\frac{79}{90}+\frac{7}{5}\times \frac{1}{3}$$

Multiply \frac{7}{5} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{79}{90}+\frac{7\times 1}{5\times 3}$$

Do the multiplications in the fraction \frac{7\times 1}{5\times 3}.

$$\frac{79}{90}+\frac{7}{15}$$

Least common multiple of 90 and 15 is 90. Convert \frac{79}{90} and \frac{7}{15} to fractions with denominator 90.

$$\frac{79}{90}+\frac{42}{90}$$

Since \frac{79}{90} and \frac{42}{90} have the same denominator, add them by adding their numerators.

$$\frac{79+42}{90}$$

Add 79 and 42 to get 121.

$$\frac{121}{90}$$

Factor

$$\frac{11 ^ {2}}{2 \cdot 3 ^ {2} \cdot 5} = 1\frac{31}{90} = 1.3444444444444446$$