Solve 41/2-32/3+1/4/2-1/5

$$\frac { 4 \frac { 1 } { 2 } - 3 \frac { 2 } { 3 } + 1 / 4 } { 2 - 1 / 5 }$$

Evaluate

$$\frac{65}{108}\approx 0.601851852$$

Solution Steps

Multiply 4 and 2 to get 8.

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

Add 8 and 1 to get 9.

$$\frac{\frac{9}{2}-\frac{3\times 3+2}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{9}{2}-\frac{9+2}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{9}{2}-\frac{11}{3}+\frac{1}{4}}{2-\frac{1}{5}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{11}{3} to fractions with denominator 6.

$$\frac{\frac{27}{6}-\frac{22}{6}+\frac{1}{4}}{2-\frac{1}{5}}$$

Since \frac{27}{6} and \frac{22}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27-22}{6}+\frac{1}{4}}{2-\frac{1}{5}}$$

Subtract 22 from 27 to get 5.

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

Least common multiple of 6 and 4 is 12. Convert \frac{5}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{10}{12}+\frac{3}{12}}{2-\frac{1}{5}}$$

Since \frac{10}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+3}{12}}{2-\frac{1}{5}}$$

Add 10 and 3 to get 13.

$$\frac{\frac{13}{12}}{2-\frac{1}{5}}$$

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{13}{12}}{\frac{10}{5}-\frac{1}{5}}$$

Since \frac{10}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{13}{12}}{\frac{10-1}{5}}$$

Subtract 1 from 10 to get 9.

$$\frac{\frac{13}{12}}{\frac{9}{5}}$$

Divide \frac{13}{12} by \frac{9}{5} by multiplying \frac{13}{12} by the reciprocal of \frac{9}{5}.

$$\frac{13}{12}\times \frac{5}{9}$$

Multiply \frac{13}{12} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 5}{12\times 9}$$

Do the multiplications in the fraction \frac{13\times 5}{12\times 9}.

$$\frac{65}{108}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {2} \cdot 3 ^ {3}} = 0.6018518518518519$$