Solve ((4/10)div(1/5)-21/3)+((5/3)-3frac{1}{2})

$$(( \frac{ 4 }{ 10 } ) \div ( \frac{ 1 }{ 5 } )-2 \frac{ 1 }{ 3 } )+(( \frac{ 5 }{ 3 } )-3 \frac{ 1 }{ 2 } )$$

Evaluate

$$-\frac{13}{6}\approx -2.166666667$$

Solution Steps

Divide \frac{4}{10} by \frac{1}{5} by multiplying \frac{4}{10} by the reciprocal of \frac{1}{5}.

$$\frac{4\times 5}{10}-\frac{2\times 3+1}{3}+\frac{5}{3}-\frac{3\times 2+1}{2}$$

Multiply 4 and 5 to get 20.

$$\frac{20}{10}-\frac{2\times 3+1}{3}+\frac{5}{3}-\frac{3\times 2+1}{2}$$

Divide 20 by 10 to get 2.

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

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

$$2-\frac{7}{3}+\frac{5}{3}-\frac{3\times 2+1}{2}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{7}{3}+\frac{5}{3}-\frac{3\times 2+1}{2}$$

Since \frac{6}{3} and \frac{7}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-7}{3}+\frac{5}{3}-\frac{3\times 2+1}{2}$$

Subtract 7 from 6 to get -1.

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

Since -\frac{1}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

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

Add -1 and 5 to get 4.

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

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{4}{3}-\frac{7}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{8}{6}-\frac{21}{6}$$

Since \frac{8}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-21}{6}$$

Subtract 21 from 8 to get -13.

$$-\frac{13}{6}$$

Factor

$$-\frac{13}{6} = -2\frac{1}{6} = -2.1666666666666665$$