Solve (51/3-11/4)div75/12

$$( 5 \frac { 1 } { 3 } - 1 \frac { 1 } { 4 } ) \div 7 \frac { 5 } { 12 }$$

Evaluate

$$\frac{49}{89}\approx 0.550561798$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{\frac{15+1}{3}-\frac{1\times 4+1}{4}}{\frac{7\times 12+5}{12}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{16}{3}-\frac{1\times 4+1}{4}}{\frac{7\times 12+5}{12}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{16}{3}-\frac{4+1}{4}}{\frac{7\times 12+5}{12}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{16}{3}-\frac{5}{4}}{\frac{7\times 12+5}{12}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{16}{3} and \frac{5}{4} to fractions with denominator 12.

$$\frac{\frac{64}{12}-\frac{15}{12}}{\frac{7\times 12+5}{12}}$$

Since \frac{64}{12} and \frac{15}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{64-15}{12}}{\frac{7\times 12+5}{12}}$$

Subtract 15 from 64 to get 49.

$$\frac{\frac{49}{12}}{\frac{7\times 12+5}{12}}$$

Multiply 7 and 12 to get 84.

$$\frac{\frac{49}{12}}{\frac{84+5}{12}}$$

Add 84 and 5 to get 89.

$$\frac{\frac{49}{12}}{\frac{89}{12}}$$

Divide \frac{49}{12} by \frac{89}{12} by multiplying \frac{49}{12} by the reciprocal of \frac{89}{12}.

$$\frac{49}{12}\times \frac{12}{89}$$

Multiply \frac{49}{12} times \frac{12}{89} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 12}{12\times 89}$$

Cancel out 12 in both numerator and denominator.

$$\frac{49}{89}$$

Factor

$$\frac{7 ^ {2}}{89} = 0.550561797752809$$