Solve 3/2-(5/6-0.5)+4/15+0.4

$$\frac{ 3 }{ 2 } -( \frac{ 5 }{ 6 } -0.5)+ \frac{ 4 }{ 15 } +0.4$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

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.

$$\frac{3}{2}-\left(\frac{5}{6}-\frac{1}{2}\right)+\frac{4}{15}+0.4$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{3}{2}-\left(\frac{5}{6}-\frac{3}{6}\right)+\frac{4}{15}+0.4$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}-\frac{5-3}{6}+\frac{4}{15}+0.4$$

Subtract 3 from 5 to get 2.

$$\frac{3}{2}-\frac{2}{6}+\frac{4}{15}+0.4$$

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

$$\frac{3}{2}-\frac{1}{3}+\frac{4}{15}+0.4$$

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

$$\frac{9}{6}-\frac{2}{6}+\frac{4}{15}+0.4$$

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-2}{6}+\frac{4}{15}+0.4$$

Subtract 2 from 9 to get 7.

$$\frac{7}{6}+\frac{4}{15}+0.4$$

Least common multiple of 6 and 15 is 30. Convert \frac{7}{6} and \frac{4}{15} to fractions with denominator 30.

$$\frac{35}{30}+\frac{8}{30}+0.4$$

Since \frac{35}{30} and \frac{8}{30} have the same denominator, add them by adding their numerators.

$$\frac{35+8}{30}+0.4$$

Add 35 and 8 to get 43.

$$\frac{43}{30}+0.4$$

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.

$$\frac{43}{30}+\frac{2}{5}$$

Least common multiple of 30 and 5 is 30. Convert \frac{43}{30} and \frac{2}{5} to fractions with denominator 30.

$$\frac{43}{30}+\frac{12}{30}$$

Since \frac{43}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$\frac{43+12}{30}$$

Add 43 and 12 to get 55.

$$\frac{55}{30}$$

Reduce the fraction \frac{55}{30} to lowest terms by extracting and canceling out 5.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$