Solve =-27/4(-36)-27/8(18)-135/16(9)

$$= - \frac { 27 } { 4 } ( - 36 ) - \frac { 27 } { 8 } ( 18 ) - \frac { 135 } { 16 } ( 9 )$$

Evaluate

$$\frac{1701}{16}=106.3125$$

Solution Steps

Express -\frac{27}{4}\left(-36\right) as a single fraction.

$$\frac{-27\left(-36\right)}{4}-\frac{27}{8}\times 18-\frac{135}{16}\times 9$$

Multiply -27 and -36 to get 972.

$$\frac{972}{4}-\frac{27}{8}\times 18-\frac{135}{16}\times 9$$

Divide 972 by 4 to get 243.

$$243-\frac{27}{8}\times 18-\frac{135}{16}\times 9$$

Express \frac{27}{8}\times 18 as a single fraction.

$$243-\frac{27\times 18}{8}-\frac{135}{16}\times 9$$

Multiply 27 and 18 to get 486.

$$243-\frac{486}{8}-\frac{135}{16}\times 9$$

Reduce the fraction \frac{486}{8} to lowest terms by extracting and canceling out 2.

$$243-\frac{243}{4}-\frac{135}{16}\times 9$$

Convert 243 to fraction \frac{972}{4}.

$$\frac{972}{4}-\frac{243}{4}-\frac{135}{16}\times 9$$

Since \frac{972}{4} and \frac{243}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{972-243}{4}-\frac{135}{16}\times 9$$

Subtract 243 from 972 to get 729.

$$\frac{729}{4}-\frac{135}{16}\times 9$$

Express \frac{135}{16}\times 9 as a single fraction.

$$\frac{729}{4}-\frac{135\times 9}{16}$$

Multiply 135 and 9 to get 1215.

$$\frac{729}{4}-\frac{1215}{16}$$

Least common multiple of 4 and 16 is 16. Convert \frac{729}{4} and \frac{1215}{16} to fractions with denominator 16.

$$\frac{2916}{16}-\frac{1215}{16}$$

Since \frac{2916}{16} and \frac{1215}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2916-1215}{16}$$

Subtract 1215 from 2916 to get 1701.

$$\frac{1701}{16}$$

Factor

$$\frac{3 ^ {5} \cdot 7}{2 ^ {4}} = 106\frac{5}{16} = 106.3125$$