Solve -3/4div1/36-7/9/frac{1{36}}+frac{7}{12}+frac{1}{36}

$$- \frac{ 3 }{ 4 } \div \frac{ 1 }{ 36 } - \frac{ \frac{ 7 }{ 9 } }{ \frac{ 1 }{ 36 } } + \frac{ 7 }{ 12 } + \frac{ 1 }{ 36 }$$

Evaluate

$$-\frac{979}{18}\approx -54.388888889$$

Solution Steps

Divide -\frac{3}{4} by \frac{1}{36} by multiplying -\frac{3}{4} by the reciprocal of \frac{1}{36}.

$$-\frac{3}{4}\times 36-\frac{\frac{7}{9}}{\frac{1}{36}}+\frac{7}{12}+\frac{1}{36}$$

Express -\frac{3}{4}\times 36 as a single fraction.

$$\frac{-3\times 36}{4}-\frac{\frac{7}{9}}{\frac{1}{36}}+\frac{7}{12}+\frac{1}{36}$$

Multiply -3 and 36 to get -108.

$$\frac{-108}{4}-\frac{\frac{7}{9}}{\frac{1}{36}}+\frac{7}{12}+\frac{1}{36}$$

Divide -108 by 4 to get -27.

$$-27-\frac{\frac{7}{9}}{\frac{1}{36}}+\frac{7}{12}+\frac{1}{36}$$

Divide \frac{7}{9} by \frac{1}{36} by multiplying \frac{7}{9} by the reciprocal of \frac{1}{36}.

$$-27-\frac{7}{9}\times 36+\frac{7}{12}+\frac{1}{36}$$

Express \frac{7}{9}\times 36 as a single fraction.

$$-27-\frac{7\times 36}{9}+\frac{7}{12}+\frac{1}{36}$$

Multiply 7 and 36 to get 252.

$$-27-\frac{252}{9}+\frac{7}{12}+\frac{1}{36}$$

Divide 252 by 9 to get 28.

$$-27-28+\frac{7}{12}+\frac{1}{36}$$

Subtract 28 from -27 to get -55.

$$-55+\frac{7}{12}+\frac{1}{36}$$

Convert -55 to fraction -\frac{660}{12}.

$$-\frac{660}{12}+\frac{7}{12}+\frac{1}{36}$$

Since -\frac{660}{12} and \frac{7}{12} have the same denominator, add them by adding their numerators.

$$\frac{-660+7}{12}+\frac{1}{36}$$

Add -660 and 7 to get -653.

$$-\frac{653}{12}+\frac{1}{36}$$

Least common multiple of 12 and 36 is 36. Convert -\frac{653}{12} and \frac{1}{36} to fractions with denominator 36.

$$-\frac{1959}{36}+\frac{1}{36}$$

Since -\frac{1959}{36} and \frac{1}{36} have the same denominator, add them by adding their numerators.

$$\frac{-1959+1}{36}$$

Add -1959 and 1 to get -1958.

$$\frac{-1958}{36}$$

Reduce the fraction \frac{-1958}{36} to lowest terms by extracting and canceling out 2.

$$-\frac{979}{18}$$

Factor

$$-\frac{979}{18} = -54\frac{7}{18} = -54.388888888888886$$