Solve 5/6*4/35/1+frac{1{3}-2/7}=

$$\frac { \frac { 5 } { 6 } \cdot \frac { 4 } { 35 } } { 1 + \frac { 1 } { 3 } - \frac { 2 } { 7 } } =$$

Evaluate

$$\frac{1}{11}\approx 0.090909091$$

Solution Steps

Multiply \frac{5}{6} times \frac{4}{35} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 4}{6\times 35}}{1+\frac{1}{3}-\frac{2}{7}}$$

Do the multiplications in the fraction \frac{5\times 4}{6\times 35}.

$$\frac{\frac{20}{210}}{1+\frac{1}{3}-\frac{2}{7}}$$

Reduce the fraction \frac{20}{210} to lowest terms by extracting and canceling out 10.

$$\frac{\frac{2}{21}}{1+\frac{1}{3}-\frac{2}{7}}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{2}{21}}{\frac{3}{3}+\frac{1}{3}-\frac{2}{7}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{21}}{\frac{3+1}{3}-\frac{2}{7}}$$

Add 3 and 1 to get 4.

$$\frac{\frac{2}{21}}{\frac{4}{3}-\frac{2}{7}}$$

Least common multiple of 3 and 7 is 21. Convert \frac{4}{3} and \frac{2}{7} to fractions with denominator 21.

$$\frac{\frac{2}{21}}{\frac{28}{21}-\frac{6}{21}}$$

Since \frac{28}{21} and \frac{6}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{21}}{\frac{28-6}{21}}$$

Subtract 6 from 28 to get 22.

$$\frac{\frac{2}{21}}{\frac{22}{21}}$$

Divide \frac{2}{21} by \frac{22}{21} by multiplying \frac{2}{21} by the reciprocal of \frac{22}{21}.

$$\frac{2}{21}\times \frac{21}{22}$$

Multiply \frac{2}{21} times \frac{21}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 21}{21\times 22}$$

Cancel out 21 in both numerator and denominator.

$$\frac{2}{22}$$

Reduce the fraction \frac{2}{22} to lowest terms by extracting and canceling out 2.

$$\frac{1}{11}$$

Factor

$$\frac{1}{11} = 0.09090909090909091$$