Solve 45/8-27/12/5frac{1{3}-11/4}

$$\frac { 4 \frac { 5 } { 8 } - 2 \frac { 7 } { 12 } } { 5 \frac { 1 } { 3 } - \frac { 11 } { 4 } }$$

Evaluate

$$\frac{49}{62}\approx 0.790322581$$

Solution Steps

Multiply 4 and 8 to get 32.

$$\frac{\frac{32+5}{8}-\frac{2\times 12+7}{12}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Add 32 and 5 to get 37.

$$\frac{\frac{37}{8}-\frac{2\times 12+7}{12}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Multiply 2 and 12 to get 24.

$$\frac{\frac{37}{8}-\frac{24+7}{12}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Add 24 and 7 to get 31.

$$\frac{\frac{37}{8}-\frac{31}{12}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Least common multiple of 8 and 12 is 24. Convert \frac{37}{8} and \frac{31}{12} to fractions with denominator 24.

$$\frac{\frac{111}{24}-\frac{62}{24}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Since \frac{111}{24} and \frac{62}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{111-62}{24}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Subtract 62 from 111 to get 49.

$$\frac{\frac{49}{24}}{\frac{5\times 3+1}{3}-\frac{11}{4}}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{49}{24}}{\frac{15+1}{3}-\frac{11}{4}}$$

Add 15 and 1 to get 16.

$$\frac{\frac{49}{24}}{\frac{16}{3}-\frac{11}{4}}$$

Least common multiple of 3 and 4 is 12. Convert \frac{16}{3} and \frac{11}{4} to fractions with denominator 12.

$$\frac{\frac{49}{24}}{\frac{64}{12}-\frac{33}{12}}$$

Since \frac{64}{12} and \frac{33}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{49}{24}}{\frac{64-33}{12}}$$

Subtract 33 from 64 to get 31.

$$\frac{\frac{49}{24}}{\frac{31}{12}}$$

Divide \frac{49}{24} by \frac{31}{12} by multiplying \frac{49}{24} by the reciprocal of \frac{31}{12}.

$$\frac{49}{24}\times \frac{12}{31}$$

Multiply \frac{49}{24} times \frac{12}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{49\times 12}{24\times 31}$$

Do the multiplications in the fraction \frac{49\times 12}{24\times 31}.

$$\frac{588}{744}$$

Reduce the fraction \frac{588}{744} to lowest terms by extracting and canceling out 12.

$$\frac{49}{62}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 31} = 0.7903225806451613$$