Solve 3/6+3/4-1/9:3/1+frac{4}{22}

$$\frac { 3 } { 6 } + \frac { 3 } { 4 } - \frac { 1 } { 9 } : \frac { 3 } { 1 } + \frac { 4 } { 22 }$$

Evaluate

$$\frac{1657}{1188}\approx 1.394781145$$

Solution Steps

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

$$\frac{1}{2}+\frac{3}{4}-\frac{\frac{1}{9}}{\frac{3}{1}}+\frac{4}{22}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{3}{4}-\frac{\frac{1}{9}}{\frac{3}{1}}+\frac{4}{22}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}-\frac{\frac{1}{9}}{\frac{3}{1}}+\frac{4}{22}$$

Add 2 and 3 to get 5.

$$\frac{5}{4}-\frac{\frac{1}{9}}{\frac{3}{1}}+\frac{4}{22}$$

Divide \frac{1}{9} by \frac{3}{1} by multiplying \frac{1}{9} by the reciprocal of \frac{3}{1}.

$$\frac{5}{4}-\frac{1}{9\times 3}+\frac{4}{22}$$

Multiply 9 and 3 to get 27.

$$\frac{5}{4}-\frac{1}{27}+\frac{4}{22}$$

Least common multiple of 4 and 27 is 108. Convert \frac{5}{4} and \frac{1}{27} to fractions with denominator 108.

$$\frac{135}{108}-\frac{4}{108}+\frac{4}{22}$$

Since \frac{135}{108} and \frac{4}{108} have the same denominator, subtract them by subtracting their numerators.

$$\frac{135-4}{108}+\frac{4}{22}$$

Subtract 4 from 135 to get 131.

$$\frac{131}{108}+\frac{4}{22}$$

Reduce the fraction \frac{4}{22} to lowest terms by extracting and canceling out 2.

$$\frac{131}{108}+\frac{2}{11}$$

Least common multiple of 108 and 11 is 1188. Convert \frac{131}{108} and \frac{2}{11} to fractions with denominator 1188.

$$\frac{1441}{1188}+\frac{216}{1188}$$

Since \frac{1441}{1188} and \frac{216}{1188} have the same denominator, add them by adding their numerators.

$$\frac{1441+216}{1188}$$

Add 1441 and 216 to get 1657.

$$\frac{1657}{1188}$$

Factor

$$\frac{1657}{2 ^ {2} \cdot 3 ^ {3} \cdot 11} = 1\frac{469}{1188} = 1.3947811447811447$$