Solve 1/2+1/3div1/4-1/5

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

Evaluate

$$\frac{49}{30}\approx 1.633333333$$

Solution Steps

Divide \frac{1}{3} by \frac{1}{4} by multiplying \frac{1}{3} by the reciprocal of \frac{1}{4}.

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

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

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

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{3}{6}+\frac{8}{6}-\frac{1}{5}$$

Since \frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{3+8}{6}-\frac{1}{5}$$

Add 3 and 8 to get 11.

$$\frac{11}{6}-\frac{1}{5}$$

Least common multiple of 6 and 5 is 30. Convert \frac{11}{6} and \frac{1}{5} to fractions with denominator 30.

$$\frac{55}{30}-\frac{6}{30}$$

Since \frac{55}{30} and \frac{6}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{55-6}{30}$$

Subtract 6 from 55 to get 49.

$$\frac{49}{30}$$

Factor

$$\frac{7 ^ {2}}{2 \cdot 3 \cdot 5} = 1\frac{19}{30} = 1.6333333333333333$$