Solve 15/97+15/6/6frac{7{6}3}

$$\frac { 1 \frac { 5 } { 9 } 7 + 1 \frac { 5 } { 6 } } { 6 \frac { 7 } { 6 } 3 }$$

Evaluate

$$\frac{229}{387}\approx 0.591731266$$

Solution Steps

Multiply 1 and 9 to get 9.

$$\frac{\frac{9+5}{9}\times 7+\frac{1\times 6+5}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Add 9 and 5 to get 14.

$$\frac{\frac{14}{9}\times 7+\frac{1\times 6+5}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Express \frac{14}{9}\times 7 as a single fraction.

$$\frac{\frac{14\times 7}{9}+\frac{1\times 6+5}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Multiply 14 and 7 to get 98.

$$\frac{\frac{98}{9}+\frac{1\times 6+5}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Multiply 1 and 6 to get 6.

$$\frac{\frac{98}{9}+\frac{6+5}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Add 6 and 5 to get 11.

$$\frac{\frac{98}{9}+\frac{11}{6}}{\frac{6\times 6+7}{6}\times 3}$$

Least common multiple of 9 and 6 is 18. Convert \frac{98}{9} and \frac{11}{6} to fractions with denominator 18.

$$\frac{\frac{196}{18}+\frac{33}{18}}{\frac{6\times 6+7}{6}\times 3}$$

Since \frac{196}{18} and \frac{33}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{196+33}{18}}{\frac{6\times 6+7}{6}\times 3}$$

Add 196 and 33 to get 229.

$$\frac{\frac{229}{18}}{\frac{6\times 6+7}{6}\times 3}$$

Multiply 6 and 6 to get 36.

$$\frac{\frac{229}{18}}{\frac{36+7}{6}\times 3}$$

Add 36 and 7 to get 43.

$$\frac{\frac{229}{18}}{\frac{43}{6}\times 3}$$

Express \frac{43}{6}\times 3 as a single fraction.

$$\frac{\frac{229}{18}}{\frac{43\times 3}{6}}$$

Multiply 43 and 3 to get 129.

$$\frac{\frac{229}{18}}{\frac{129}{6}}$$

Reduce the fraction \frac{129}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{229}{18}}{\frac{43}{2}}$$

Divide \frac{229}{18} by \frac{43}{2} by multiplying \frac{229}{18} by the reciprocal of \frac{43}{2}.

$$\frac{229}{18}\times \frac{2}{43}$$

Multiply \frac{229}{18} times \frac{2}{43} by multiplying numerator times numerator and denominator times denominator.

$$\frac{229\times 2}{18\times 43}$$

Do the multiplications in the fraction \frac{229\times 2}{18\times 43}.

$$\frac{458}{774}$$

Reduce the fraction \frac{458}{774} to lowest terms by extracting and canceling out 2.

$$\frac{229}{387}$$

Factor

$$\frac{229}{3 ^ {2} \cdot 43} = 0.5917312661498708$$