Solve 1/2(1/2)-2(1/frac{5{2}})-1/2(frac{1}{3})-2(frac{1}{3})

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

Evaluate

$$-\frac{83}{60}\approx -1.383333333$$

Solution Steps

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

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

Divide 1 by \frac{5}{2} by multiplying 1 by the reciprocal of \frac{5}{2}.

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

Multiply 1 and \frac{2}{5} to get \frac{2}{5}.

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

Express 2\times \frac{2}{5} as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{4}{5} to fractions with denominator 20.

$$\frac{5}{20}-\frac{16}{20}-\frac{1}{2}\times \frac{1}{3}-2\times \frac{1}{3}$$

Since \frac{5}{20} and \frac{16}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-16}{20}-\frac{1}{2}\times \frac{1}{3}-2\times \frac{1}{3}$$

Subtract 16 from 5 to get -11.

$$-\frac{11}{20}-\frac{1}{2}\times \frac{1}{3}-2\times \frac{1}{3}$$

Multiply \frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{11}{20}-\frac{1\times 1}{2\times 3}-2\times \frac{1}{3}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 3}.

$$-\frac{11}{20}-\frac{1}{6}-2\times \frac{1}{3}$$

Least common multiple of 20 and 6 is 60. Convert -\frac{11}{20} and \frac{1}{6} to fractions with denominator 60.

$$-\frac{33}{60}-\frac{10}{60}-2\times \frac{1}{3}$$

Since -\frac{33}{60} and \frac{10}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-33-10}{60}-2\times \frac{1}{3}$$

Subtract 10 from -33 to get -43.

$$-\frac{43}{60}-2\times \frac{1}{3}$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$-\frac{43}{60}-\frac{2}{3}$$

Least common multiple of 60 and 3 is 60. Convert -\frac{43}{60} and \frac{2}{3} to fractions with denominator 60.

$$-\frac{43}{60}-\frac{40}{60}$$

Since -\frac{43}{60} and \frac{40}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-43-40}{60}$$

Subtract 40 from -43 to get -83.

$$-\frac{83}{60}$$

Factor

$$-\frac{83}{60} = -1\frac{23}{60} = -1.3833333333333333$$