Solve [(8/14+3/35:9/25)*7/2]+frac{1}{6}

$$[ ( \frac { 8 } { 14 } + \frac { 3 } { 35 } : \frac { 9 } { 25 } ) \cdot \frac { 7 } { 2 } ] + \frac { 1 } { 6 }$$

Evaluate

$$3$$

Solution Steps

Reduce the fraction \frac{8}{14} to lowest terms by extracting and canceling out 2.

$$\left(\frac{4}{7}+\frac{\frac{3}{35}}{\frac{9}{25}}\right)\times \frac{7}{2}+\frac{1}{6}$$

Divide \frac{3}{35} by \frac{9}{25} by multiplying \frac{3}{35} by the reciprocal of \frac{9}{25}.

$$\left(\frac{4}{7}+\frac{3}{35}\times \frac{25}{9}\right)\times \frac{7}{2}+\frac{1}{6}$$

Multiply \frac{3}{35} times \frac{25}{9} by multiplying numerator times numerator and denominator times denominator.

$$\left(\frac{4}{7}+\frac{3\times 25}{35\times 9}\right)\times \frac{7}{2}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{3\times 25}{35\times 9}.

$$\left(\frac{4}{7}+\frac{75}{315}\right)\times \frac{7}{2}+\frac{1}{6}$$

Reduce the fraction \frac{75}{315} to lowest terms by extracting and canceling out 15.

$$\left(\frac{4}{7}+\frac{5}{21}\right)\times \frac{7}{2}+\frac{1}{6}$$

Least common multiple of 7 and 21 is 21. Convert \frac{4}{7} and \frac{5}{21} to fractions with denominator 21.

$$\left(\frac{12}{21}+\frac{5}{21}\right)\times \frac{7}{2}+\frac{1}{6}$$

Since \frac{12}{21} and \frac{5}{21} have the same denominator, add them by adding their numerators.

$$\frac{12+5}{21}\times \frac{7}{2}+\frac{1}{6}$$

Add 12 and 5 to get 17.

$$\frac{17}{21}\times \frac{7}{2}+\frac{1}{6}$$

Multiply \frac{17}{21} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 7}{21\times 2}+\frac{1}{6}$$

Do the multiplications in the fraction \frac{17\times 7}{21\times 2}.

$$\frac{119}{42}+\frac{1}{6}$$

Reduce the fraction \frac{119}{42} to lowest terms by extracting and canceling out 7.

$$\frac{17}{6}+\frac{1}{6}$$

Since \frac{17}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{17+1}{6}$$

Add 17 and 1 to get 18.

$$\frac{18}{6}$$

Divide 18 by 6 to get 3.

$$3$$

Factor

$$3$$