Solve 1/2-1/3div3/4+2/5

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

Evaluate

$$\frac{41}{90}\approx 0.455555556$$

Solution Steps

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

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

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

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

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

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

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{9}{18}-\frac{8}{18}+\frac{2}{5}$$

Since \frac{9}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-8}{18}+\frac{2}{5}$$

Subtract 8 from 9 to get 1.

$$\frac{1}{18}+\frac{2}{5}$$

Least common multiple of 18 and 5 is 90. Convert \frac{1}{18} and \frac{2}{5} to fractions with denominator 90.

$$\frac{5}{90}+\frac{36}{90}$$

Since \frac{5}{90} and \frac{36}{90} have the same denominator, add them by adding their numerators.

$$\frac{5+36}{90}$$

Add 5 and 36 to get 41.

$$\frac{41}{90}$$

Factor

$$\frac{41}{2 \cdot 3 ^ {2} \cdot 5} = 0.45555555555555555$$