Solve (1/2+1/3)div11/4-1/5

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

Evaluate

$$\frac{7}{15}\approx 0.466666667$$

Solution Steps

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

$$\frac{\frac{3}{6}+\frac{2}{6}}{\frac{1\times 4+1}{4}}-\frac{1}{5}$$

Since \frac{3}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3+2}{6}}{\frac{1\times 4+1}{4}}-\frac{1}{5}$$

Add 3 and 2 to get 5.

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

Multiply 1 and 4 to get 4.

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

Add 4 and 1 to get 5.

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

Divide \frac{5}{6} by \frac{5}{4} by multiplying \frac{5}{6} by the reciprocal of \frac{5}{4}.

$$\frac{5}{6}\times \frac{4}{5}-\frac{1}{5}$$

Multiply \frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{6\times 5}-\frac{1}{5}$$

Cancel out 5 in both numerator and denominator.

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

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{10}{15}-\frac{3}{15}$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-3}{15}$$

Subtract 3 from 10 to get 7.

$$\frac{7}{15}$$

Factor

$$\frac{7}{3 \cdot 5} = 0.4666666666666667$$