Solve 23/4:(11/2-2/5)-3*21/6

$$2 \frac { 3 } { 4 } : ( 1 \frac { 1 } { 2 } - \frac { 2 } { 5 } ) - 3 \cdot 2 \frac { 1 } { 6 }$$

Evaluate

$$-4$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{\frac{8+3}{4}}{\frac{1\times 2+1}{2}-\frac{2}{5}}-3\times \frac{2\times 6+1}{6}$$

Add 8 and 3 to get 11.

$$\frac{\frac{11}{4}}{\frac{1\times 2+1}{2}-\frac{2}{5}}-3\times \frac{2\times 6+1}{6}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{11}{4}}{\frac{2+1}{2}-\frac{2}{5}}-3\times \frac{2\times 6+1}{6}$$

Add 2 and 1 to get 3.

$$\frac{\frac{11}{4}}{\frac{3}{2}-\frac{2}{5}}-3\times \frac{2\times 6+1}{6}$$

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{\frac{11}{4}}{\frac{15}{10}-\frac{4}{10}}-3\times \frac{2\times 6+1}{6}$$

Since \frac{15}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11}{4}}{\frac{15-4}{10}}-3\times \frac{2\times 6+1}{6}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{11}{4}}{\frac{11}{10}}-3\times \frac{2\times 6+1}{6}$$

Divide \frac{11}{4} by \frac{11}{10} by multiplying \frac{11}{4} by the reciprocal of \frac{11}{10}.

$$\frac{11}{4}\times \frac{10}{11}-3\times \frac{2\times 6+1}{6}$$

Multiply \frac{11}{4} times \frac{10}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 10}{4\times 11}-3\times \frac{2\times 6+1}{6}$$

Cancel out 11 in both numerator and denominator.

$$\frac{10}{4}-3\times \frac{2\times 6+1}{6}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{5}{2}-3\times \frac{2\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$\frac{5}{2}-3\times \frac{12+1}{6}$$

Add 12 and 1 to get 13.

$$\frac{5}{2}-3\times \frac{13}{6}$$

Express 3\times \frac{13}{6} as a single fraction.

$$\frac{5}{2}-\frac{3\times 13}{6}$$

Multiply 3 and 13 to get 39.

$$\frac{5}{2}-\frac{39}{6}$$

Reduce the fraction \frac{39}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}-\frac{13}{2}$$

Since \frac{5}{2} and \frac{13}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-13}{2}$$

Subtract 13 from 5 to get -8.

$$\frac{-8}{2}$$

Divide -8 by 2 to get -4.

$$-4$$

Factor

$$-4$$