Solve 3+1/7*4/3/frac{7{3}-5/6}

$$\frac{ 3+ \frac{ 1 }{ 7 } \times \frac{ 4 }{ 3 } }{ \frac{ 7 }{ 3 } - \frac{ 5 }{ 6 } }$$

Evaluate

$$\frac{134}{63}\approx 2.126984127$$

Solution Steps

Multiply \frac{1}{7} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3+\frac{1\times 4}{7\times 3}}{\frac{7}{3}-\frac{5}{6}}$$

Do the multiplications in the fraction \frac{1\times 4}{7\times 3}.

$$\frac{3+\frac{4}{21}}{\frac{7}{3}-\frac{5}{6}}$$

Convert 3 to fraction \frac{63}{21}.

$$\frac{\frac{63}{21}+\frac{4}{21}}{\frac{7}{3}-\frac{5}{6}}$$

Since \frac{63}{21} and \frac{4}{21} have the same denominator, add them by adding their numerators.

$$\frac{\frac{63+4}{21}}{\frac{7}{3}-\frac{5}{6}}$$

Add 63 and 4 to get 67.

$$\frac{\frac{67}{21}}{\frac{7}{3}-\frac{5}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{\frac{67}{21}}{\frac{14}{6}-\frac{5}{6}}$$

Since \frac{14}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{67}{21}}{\frac{14-5}{6}}$$

Subtract 5 from 14 to get 9.

$$\frac{\frac{67}{21}}{\frac{9}{6}}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{67}{21}}{\frac{3}{2}}$$

Divide \frac{67}{21} by \frac{3}{2} by multiplying \frac{67}{21} by the reciprocal of \frac{3}{2}.

$$\frac{67}{21}\times \frac{2}{3}$$

Multiply \frac{67}{21} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{67\times 2}{21\times 3}$$

Do the multiplications in the fraction \frac{67\times 2}{21\times 3}.

$$\frac{134}{63}$$

Factor

$$\frac{2 \cdot 67}{3 ^ {2} \cdot 7} = 2\frac{8}{63} = 2.126984126984127$$