Solve (2/4+1/6):(5/9-2/15)*frac{38}{7}-frac{30}{7})*7

$$( \frac { 2 } { 4 } + \frac { 1 } { 6 } ) : ( \frac { 5 } { 9 } - \frac { 2 } { 15 } ) \times \frac { 38 } { 7 } - \frac { 30 } { 7 } ) \times 7$$

Evaluate

$$\frac{30}{7}\approx 4.285714286$$

Solution Steps

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

$$\frac{\frac{1}{2}+\frac{1}{6}}{\frac{5}{9}-\frac{2}{15}}\times \frac{38}{7}-\frac{30}{7}$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{3}{6}+\frac{1}{6}}{\frac{5}{9}-\frac{2}{15}}\times \frac{38}{7}-\frac{30}{7}$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+1}{6}}{\frac{5}{9}-\frac{2}{15}}\times \frac{38}{7}-\frac{30}{7}$$

Add 3 and 1 to get 4.

$$\frac{\frac{4}{6}}{\frac{5}{9}-\frac{2}{15}}\times \frac{38}{7}-\frac{30}{7}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}}{\frac{5}{9}-\frac{2}{15}}\times \frac{38}{7}-\frac{30}{7}$$

Least common multiple of 9 and 15 is 45. Convert \frac{5}{9} and \frac{2}{15} to fractions with denominator 45.

$$\frac{\frac{2}{3}}{\frac{25}{45}-\frac{6}{45}}\times \frac{38}{7}-\frac{30}{7}$$

Since \frac{25}{45} and \frac{6}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2}{3}}{\frac{25-6}{45}}\times \frac{38}{7}-\frac{30}{7}$$

Subtract 6 from 25 to get 19.

$$\frac{\frac{2}{3}}{\frac{19}{45}}\times \frac{38}{7}-\frac{30}{7}$$

Divide \frac{2}{3} by \frac{19}{45} by multiplying \frac{2}{3} by the reciprocal of \frac{19}{45}.

$$\frac{2}{3}\times \frac{45}{19}\times \frac{38}{7}-\frac{30}{7}$$

Multiply \frac{2}{3} times \frac{45}{19} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 45}{3\times 19}\times \frac{38}{7}-\frac{30}{7}$$

Do the multiplications in the fraction \frac{2\times 45}{3\times 19}.

$$\frac{90}{57}\times \frac{38}{7}-\frac{30}{7}$$

Reduce the fraction \frac{90}{57} to lowest terms by extracting and canceling out 3.

$$\frac{30}{19}\times \frac{38}{7}-\frac{30}{7}$$

Multiply \frac{30}{19} times \frac{38}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{30\times 38}{19\times 7}-\frac{30}{7}$$

Do the multiplications in the fraction \frac{30\times 38}{19\times 7}.

$$\frac{1140}{133}-\frac{30}{7}$$

Reduce the fraction \frac{1140}{133} to lowest terms by extracting and canceling out 19.

$$\frac{60}{7}-\frac{30}{7}$$

Since \frac{60}{7} and \frac{30}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{60-30}{7}$$

Subtract 30 from 60 to get 30.

$$\frac{30}{7}$$

Factor

$$\frac{2 \cdot 3 \cdot 5}{7} = 4\frac{2}{7} = 4.285714285714286$$