Solve 5/7-9/14*4/27/frac{5{6}+1}

$$\frac { \frac { 5 } { 7 } - \frac { 9 } { 14 } \times \frac { 4 } { 27 } } { \frac { 5 } { 6 } + 1 }$$

Evaluate

$$\frac{26}{77}\approx 0.337662338$$

Solution Steps

Multiply \frac{9}{14} times \frac{4}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{7}-\frac{9\times 4}{14\times 27}}{\frac{5}{6}+1}$$

Do the multiplications in the fraction \frac{9\times 4}{14\times 27}.

$$\frac{\frac{5}{7}-\frac{36}{378}}{\frac{5}{6}+1}$$

Reduce the fraction \frac{36}{378} to lowest terms by extracting and canceling out 18.

$$\frac{\frac{5}{7}-\frac{2}{21}}{\frac{5}{6}+1}$$

Least common multiple of 7 and 21 is 21. Convert \frac{5}{7} and \frac{2}{21} to fractions with denominator 21.

$$\frac{\frac{15}{21}-\frac{2}{21}}{\frac{5}{6}+1}$$

Since \frac{15}{21} and \frac{2}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{15-2}{21}}{\frac{5}{6}+1}$$

Subtract 2 from 15 to get 13.

$$\frac{\frac{13}{21}}{\frac{5}{6}+1}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{13}{21}}{\frac{5}{6}+\frac{6}{6}}$$

Since \frac{5}{6} and \frac{6}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{21}}{\frac{5+6}{6}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{13}{21}}{\frac{11}{6}}$$

Divide \frac{13}{21} by \frac{11}{6} by multiplying \frac{13}{21} by the reciprocal of \frac{11}{6}.

$$\frac{13}{21}\times \frac{6}{11}$$

Multiply \frac{13}{21} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 6}{21\times 11}$$

Do the multiplications in the fraction \frac{13\times 6}{21\times 11}.

$$\frac{78}{231}$$

Reduce the fraction \frac{78}{231} to lowest terms by extracting and canceling out 3.

$$\frac{26}{77}$$

Factor

$$\frac{2 \cdot 13}{7 \cdot 11} = 0.33766233766233766$$