Solve (2/3-0.4)div(1/6+0.5)

$$( \frac { 2 } { 3 } - 0.4 ) \div ( \frac { 1 } { 6 } + 0.5 )$$

Evaluate

$$0.4$$

Solution Steps

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2}{3}-\frac{2}{5}}{\frac{1}{6}+0.5}$$

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

$$\frac{\frac{10}{15}-\frac{6}{15}}{\frac{1}{6}+0.5}$$

Since \frac{10}{15} and \frac{6}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-6}{15}}{\frac{1}{6}+0.5}$$

Subtract 6 from 10 to get 4.

$$\frac{\frac{4}{15}}{\frac{1}{6}+0.5}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{4}{15}}{\frac{1}{6}+\frac{1}{2}}$$

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

$$\frac{\frac{4}{15}}{\frac{1}{6}+\frac{3}{6}}$$

Since \frac{1}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{15}}{\frac{1+3}{6}}$$

Add 1 and 3 to get 4.

$$\frac{\frac{4}{15}}{\frac{4}{6}}$$

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

$$\frac{\frac{4}{15}}{\frac{2}{3}}$$

Divide \frac{4}{15} by \frac{2}{3} by multiplying \frac{4}{15} by the reciprocal of \frac{2}{3}.

$$\frac{4}{15}\times \frac{3}{2}$$

Multiply \frac{4}{15} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 3}{15\times 2}$$

Do the multiplications in the fraction \frac{4\times 3}{15\times 2}.

$$\frac{12}{30}$$

Reduce the fraction \frac{12}{30} to lowest terms by extracting and canceling out 6.

$$\frac{2}{5}$$

Factor

$$\frac{2}{5} = 0.4$$