Solve 5/8-{1/3*[(-1/4+3/5)-(frac{1}{3}+3frac{1}{2})]}

$$\frac { 5 } { 8 } - \{ \frac { 1 } { 3 } \times [ ( - \frac { 1 } { 4 } + \frac { 3 } { 5 } ) - ( \frac { 1 } { 3 } + 3 \frac { 1 } { 2 } ) ] \}$$

Evaluate

$$\frac{643}{360}\approx 1.786111111$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert -\frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{5}{8}-\frac{1}{3}\left(-\frac{5}{20}+\frac{12}{20}-\left(\frac{1}{3}+\frac{3\times 2+1}{2}\right)\right)$$

Since -\frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{-5+12}{20}-\left(\frac{1}{3}+\frac{3\times 2+1}{2}\right)\right)$$

Add -5 and 12 to get 7.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\left(\frac{1}{3}+\frac{3\times 2+1}{2}\right)\right)$$

Multiply 3 and 2 to get 6.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\left(\frac{1}{3}+\frac{6+1}{2}\right)\right)$$

Add 6 and 1 to get 7.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\left(\frac{1}{3}+\frac{7}{2}\right)\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\left(\frac{2}{6}+\frac{21}{6}\right)\right)$$

Since \frac{2}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\frac{2+21}{6}\right)$$

Add 2 and 21 to get 23.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{7}{20}-\frac{23}{6}\right)$$

Least common multiple of 20 and 6 is 60. Convert \frac{7}{20} and \frac{23}{6} to fractions with denominator 60.

$$\frac{5}{8}-\frac{1}{3}\left(\frac{21}{60}-\frac{230}{60}\right)$$

Since \frac{21}{60} and \frac{230}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{8}-\frac{1}{3}\times \frac{21-230}{60}$$

Subtract 230 from 21 to get -209.

$$\frac{5}{8}-\frac{1}{3}\left(-\frac{209}{60}\right)$$

Multiply \frac{1}{3} times -\frac{209}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}-\frac{1\left(-209\right)}{3\times 60}$$

Do the multiplications in the fraction \frac{1\left(-209\right)}{3\times 60}.

$$\frac{5}{8}-\frac{-209}{180}$$

Fraction \frac{-209}{180} can be rewritten as -\frac{209}{180} by extracting the negative sign.

$$\frac{5}{8}-\left(-\frac{209}{180}\right)$$

The opposite of -\frac{209}{180} is \frac{209}{180}.

$$\frac{5}{8}+\frac{209}{180}$$

Least common multiple of 8 and 180 is 360. Convert \frac{5}{8} and \frac{209}{180} to fractions with denominator 360.

$$\frac{225}{360}+\frac{418}{360}$$

Since \frac{225}{360} and \frac{418}{360} have the same denominator, add them by adding their numerators.

$$\frac{225+418}{360}$$

Add 225 and 418 to get 643.

$$\frac{643}{360}$$

Factor

$$\frac{643}{2 ^ {3} \cdot 3 ^ {2} \cdot 5} = 1\frac{283}{360} = 1.7861111111111112$$