Solve 31/4:(7/8-2/3)-2*11/4

$$3 \frac { 1 } { 4 } : ( \frac { 7 } { 8 } - \frac { 2 } { 3 } ) - 2 \cdot 1 \frac { 1 } { 4 }$$

Evaluate

$$\frac{131}{10}=13.1$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+1}{4}}{\frac{7}{8}-\frac{2}{3}}-2\times \frac{1\times 4+1}{4}$$

Add 12 and 1 to get 13.

$$\frac{\frac{13}{4}}{\frac{7}{8}-\frac{2}{3}}-2\times \frac{1\times 4+1}{4}$$

Least common multiple of 8 and 3 is 24. Convert \frac{7}{8} and \frac{2}{3} to fractions with denominator 24.

$$\frac{\frac{13}{4}}{\frac{21}{24}-\frac{16}{24}}-2\times \frac{1\times 4+1}{4}$$

Since \frac{21}{24} and \frac{16}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{4}}{\frac{21-16}{24}}-2\times \frac{1\times 4+1}{4}$$

Subtract 16 from 21 to get 5.

$$\frac{\frac{13}{4}}{\frac{5}{24}}-2\times \frac{1\times 4+1}{4}$$

Divide \frac{13}{4} by \frac{5}{24} by multiplying \frac{13}{4} by the reciprocal of \frac{5}{24}.

$$\frac{13}{4}\times \frac{24}{5}-2\times \frac{1\times 4+1}{4}$$

Multiply \frac{13}{4} times \frac{24}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 24}{4\times 5}-2\times \frac{1\times 4+1}{4}$$

Do the multiplications in the fraction \frac{13\times 24}{4\times 5}.

$$\frac{312}{20}-2\times \frac{1\times 4+1}{4}$$

Reduce the fraction \frac{312}{20} to lowest terms by extracting and canceling out 4.

$$\frac{78}{5}-2\times \frac{1\times 4+1}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{78}{5}-2\times \frac{4+1}{4}$$

Add 4 and 1 to get 5.

$$\frac{78}{5}-2\times \frac{5}{4}$$

Express 2\times \frac{5}{4} as a single fraction.

$$\frac{78}{5}-\frac{2\times 5}{4}$$

Multiply 2 and 5 to get 10.

$$\frac{78}{5}-\frac{10}{4}$$

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

$$\frac{78}{5}-\frac{5}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{78}{5} and \frac{5}{2} to fractions with denominator 10.

$$\frac{156}{10}-\frac{25}{10}$$

Since \frac{156}{10} and \frac{25}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{156-25}{10}$$

Subtract 25 from 156 to get 131.

$$\frac{131}{10}$$

Factor

$$\frac{131}{2 \cdot 5} = 13\frac{1}{10} = 13.1$$