Solve 6/7+21/23*5/42div15/7-frac{1}{6}

$$\frac { 6 } { 7 } + \frac { 21 } { 23 } \times \frac { 5 } { 42 } \div \frac { 15 } { 7 } - \frac { 1 } { 6 }$$

Evaluate

$$\frac{358}{483}\approx 0.741200828$$

Solution Steps

Multiply \frac{21}{23} times \frac{5}{42} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{7}+\frac{\frac{21\times 5}{23\times 42}}{\frac{15}{7}}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{21\times 5}{23\times 42}.

$$\frac{6}{7}+\frac{\frac{105}{966}}{\frac{15}{7}}-\frac{1}{6}$$

Reduce the fraction \frac{105}{966} to lowest terms by extracting and canceling out 21.

$$\frac{6}{7}+\frac{\frac{5}{46}}{\frac{15}{7}}-\frac{1}{6}$$

Divide \frac{5}{46} by \frac{15}{7} by multiplying \frac{5}{46} by the reciprocal of \frac{15}{7}.

$$\frac{6}{7}+\frac{5}{46}\times \frac{7}{15}-\frac{1}{6}$$

Multiply \frac{5}{46} times \frac{7}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{7}+\frac{5\times 7}{46\times 15}-\frac{1}{6}$$

Do the multiplications in the fraction \frac{5\times 7}{46\times 15}.

$$\frac{6}{7}+\frac{35}{690}-\frac{1}{6}$$

Reduce the fraction \frac{35}{690} to lowest terms by extracting and canceling out 5.

$$\frac{6}{7}+\frac{7}{138}-\frac{1}{6}$$

Least common multiple of 7 and 138 is 966. Convert \frac{6}{7} and \frac{7}{138} to fractions with denominator 966.

$$\frac{828}{966}+\frac{49}{966}-\frac{1}{6}$$

Since \frac{828}{966} and \frac{49}{966} have the same denominator, add them by adding their numerators.

$$\frac{828+49}{966}-\frac{1}{6}$$

Add 828 and 49 to get 877.

$$\frac{877}{966}-\frac{1}{6}$$

Least common multiple of 966 and 6 is 966. Convert \frac{877}{966} and \frac{1}{6} to fractions with denominator 966.

$$\frac{877}{966}-\frac{161}{966}$$

Since \frac{877}{966} and \frac{161}{966} have the same denominator, subtract them by subtracting their numerators.

$$\frac{877-161}{966}$$

Subtract 161 from 877 to get 716.

$$\frac{716}{966}$$

Reduce the fraction \frac{716}{966} to lowest terms by extracting and canceling out 2.

$$\frac{358}{483}$$

Factor

$$\frac{2 \cdot 179}{3 \cdot 7 \cdot 23} = 0.7412008281573499$$