Solve 1/6-46/27div(5/3+1/4)

$$\frac { 1 } { 6 } - \frac { 46 } { 27 } \div ( \frac { 5 } { 3 } + \frac { 1 } { 4 } )$$

Evaluate

$$-\frac{13}{18}\approx -0.722222222$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{6}-\frac{\frac{46}{27}}{\frac{20}{12}+\frac{3}{12}}$$

Since \frac{20}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}-\frac{\frac{46}{27}}{\frac{20+3}{12}}$$

Add 20 and 3 to get 23.

$$\frac{1}{6}-\frac{\frac{46}{27}}{\frac{23}{12}}$$

Divide \frac{46}{27} by \frac{23}{12} by multiplying \frac{46}{27} by the reciprocal of \frac{23}{12}.

$$\frac{1}{6}-\frac{46}{27}\times \frac{12}{23}$$

Multiply \frac{46}{27} times \frac{12}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{6}-\frac{46\times 12}{27\times 23}$$

Do the multiplications in the fraction \frac{46\times 12}{27\times 23}.

$$\frac{1}{6}-\frac{552}{621}$$

Reduce the fraction \frac{552}{621} to lowest terms by extracting and canceling out 69.

$$\frac{1}{6}-\frac{8}{9}$$

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{8}{9} to fractions with denominator 18.

$$\frac{3}{18}-\frac{16}{18}$$

Since \frac{3}{18} and \frac{16}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-16}{18}$$

Subtract 16 from 3 to get -13.

$$-\frac{13}{18}$$

Factor

$$-\frac{13}{18} = -0.7222222222222222$$