Solve 7/3*3/2div((5/4+2/5)*1/3+1)

$$7 / 3 \times 3 / 2 \div ( ( 5 / 4 + 2 / 5 ) \times 1 / 3 + 1 )$$

Evaluate

$$\frac{70}{31}\approx 2.258064516$$

Solution Steps

Multiply \frac{7}{3} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Least common multiple of 4 and 5 is 20. Convert \frac{5}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{\frac{7}{2}}{\left(\frac{25}{20}+\frac{8}{20}\right)\times \frac{1}{3}+1}$$

Since \frac{25}{20} and \frac{8}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{2}}{\frac{25+8}{20}\times \frac{1}{3}+1}$$

Add 25 and 8 to get 33.

$$\frac{\frac{7}{2}}{\frac{33}{20}\times \frac{1}{3}+1}$$

Multiply \frac{33}{20} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{2}}{\frac{33\times 1}{20\times 3}+1}$$

Do the multiplications in the fraction \frac{33\times 1}{20\times 3}.

$$\frac{\frac{7}{2}}{\frac{33}{60}+1}$$

Reduce the fraction \frac{33}{60} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{7}{2}}{\frac{11}{20}+1}$$

Convert 1 to fraction \frac{20}{20}.

$$\frac{\frac{7}{2}}{\frac{11}{20}+\frac{20}{20}}$$

Since \frac{11}{20} and \frac{20}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{2}}{\frac{11+20}{20}}$$

Add 11 and 20 to get 31.

$$\frac{\frac{7}{2}}{\frac{31}{20}}$$

Divide \frac{7}{2} by \frac{31}{20} by multiplying \frac{7}{2} by the reciprocal of \frac{31}{20}.

$$\frac{7}{2}\times \frac{20}{31}$$

Multiply \frac{7}{2} times \frac{20}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 20}{2\times 31}$$

Do the multiplications in the fraction \frac{7\times 20}{2\times 31}.

$$\frac{140}{62}$$

Reduce the fraction \frac{140}{62} to lowest terms by extracting and canceling out 2.

$$\frac{70}{31}$$

Factor

$$\frac{2 \cdot 5 \cdot 7}{31} = 2\frac{8}{31} = 2.2580645161290325$$