Solve 2/4+4/3*1/3div1/4-frac{1}{5}

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

Evaluate

$$\frac{187}{90}\approx 2.077777778$$

Solution Steps

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

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

Multiply \frac{4}{3} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{4\times 1}{3\times 3}.

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

Divide \frac{4}{9} by \frac{1}{4} by multiplying \frac{4}{9} by the reciprocal of \frac{1}{4}.

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

Express \frac{4}{9}\times 4 as a single fraction.

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

Multiply 4 and 4 to get 16.

$$\frac{1}{2}+\frac{16}{9}-\frac{1}{5}$$

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{16}{9} to fractions with denominator 18.

$$\frac{9}{18}+\frac{32}{18}-\frac{1}{5}$$

Since \frac{9}{18} and \frac{32}{18} have the same denominator, add them by adding their numerators.

$$\frac{9+32}{18}-\frac{1}{5}$$

Add 9 and 32 to get 41.

$$\frac{41}{18}-\frac{1}{5}$$

Least common multiple of 18 and 5 is 90. Convert \frac{41}{18} and \frac{1}{5} to fractions with denominator 90.

$$\frac{205}{90}-\frac{18}{90}$$

Since \frac{205}{90} and \frac{18}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{205-18}{90}$$

Subtract 18 from 205 to get 187.

$$\frac{187}{90}$$

Factor

$$\frac{11 \cdot 17}{2 \cdot 3 ^ {2} \cdot 5} = 2\frac{7}{90} = 2.077777777777778$$