Solve 311/18-(61/6-311/21)

$$3 \frac{ 11 }{ 18 } -(6 \frac{ 1 }{ 6 } -3 \frac{ 11 }{ 21 } )$$

Evaluate

$$\frac{61}{63}\approx 0.968253968$$

Solution Steps

Multiply 3 and 18 to get 54.

$$\frac{54+11}{18}-\left(\frac{6\times 6+1}{6}-\frac{3\times 21+11}{21}\right)$$

Add 54 and 11 to get 65.

$$\frac{65}{18}-\left(\frac{6\times 6+1}{6}-\frac{3\times 21+11}{21}\right)$$

Multiply 6 and 6 to get 36.

$$\frac{65}{18}-\left(\frac{36+1}{6}-\frac{3\times 21+11}{21}\right)$$

Add 36 and 1 to get 37.

$$\frac{65}{18}-\left(\frac{37}{6}-\frac{3\times 21+11}{21}\right)$$

Multiply 3 and 21 to get 63.

$$\frac{65}{18}-\left(\frac{37}{6}-\frac{63+11}{21}\right)$$

Add 63 and 11 to get 74.

$$\frac{65}{18}-\left(\frac{37}{6}-\frac{74}{21}\right)$$

Least common multiple of 6 and 21 is 42. Convert \frac{37}{6} and \frac{74}{21} to fractions with denominator 42.

$$\frac{65}{18}-\left(\frac{259}{42}-\frac{148}{42}\right)$$

Since \frac{259}{42} and \frac{148}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65}{18}-\frac{259-148}{42}$$

Subtract 148 from 259 to get 111.

$$\frac{65}{18}-\frac{111}{42}$$

Reduce the fraction \frac{111}{42} to lowest terms by extracting and canceling out 3.

$$\frac{65}{18}-\frac{37}{14}$$

Least common multiple of 18 and 14 is 126. Convert \frac{65}{18} and \frac{37}{14} to fractions with denominator 126.

$$\frac{455}{126}-\frac{333}{126}$$

Since \frac{455}{126} and \frac{333}{126} have the same denominator, subtract them by subtracting their numerators.

$$\frac{455-333}{126}$$

Subtract 333 from 455 to get 122.

$$\frac{122}{126}$$

Reduce the fraction \frac{122}{126} to lowest terms by extracting and canceling out 2.

$$\frac{61}{63}$$

Factor

$$\frac{61}{3 ^ {2} \cdot 7} = 0.9682539682539683$$