Solve (6/5-1+12/5)(1/5-1/4+frac{7}{2}-frac{8}{3})

$$( \frac { 6 } { 5 } - 1 + \frac { 12 } { 5 } ) ( \frac { 1 } { 5 } - \frac { 1 } { 4 } + \frac { 7 } { 2 } - \frac { 8 } { 3 } )$$

Evaluate

$$\frac{611}{300}\approx 2.036666667$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\left(\frac{6}{5}-\frac{5}{5}+\frac{12}{5}\right)\left(\frac{1}{5}-\frac{1}{4}+\frac{7}{2}-\frac{8}{3}\right)$$

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

$$\left(\frac{6-5}{5}+\frac{12}{5}\right)\left(\frac{1}{5}-\frac{1}{4}+\frac{7}{2}-\frac{8}{3}\right)$$

Subtract 5 from 6 to get 1.

$$\left(\frac{1}{5}+\frac{12}{5}\right)\left(\frac{1}{5}-\frac{1}{4}+\frac{7}{2}-\frac{8}{3}\right)$$

Since \frac{1}{5} and \frac{12}{5} have the same denominator, add them by adding their numerators.

$$\frac{1+12}{5}\left(\frac{1}{5}-\frac{1}{4}+\frac{7}{2}-\frac{8}{3}\right)$$

Add 1 and 12 to get 13.

$$\frac{13}{5}\left(\frac{1}{5}-\frac{1}{4}+\frac{7}{2}-\frac{8}{3}\right)$$

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

$$\frac{13}{5}\left(\frac{4}{20}-\frac{5}{20}+\frac{7}{2}-\frac{8}{3}\right)$$

Since \frac{4}{20} and \frac{5}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{5}\left(\frac{4-5}{20}+\frac{7}{2}-\frac{8}{3}\right)$$

Subtract 5 from 4 to get -1.

$$\frac{13}{5}\left(-\frac{1}{20}+\frac{7}{2}-\frac{8}{3}\right)$$

Least common multiple of 20 and 2 is 20. Convert -\frac{1}{20} and \frac{7}{2} to fractions with denominator 20.

$$\frac{13}{5}\left(-\frac{1}{20}+\frac{70}{20}-\frac{8}{3}\right)$$

Since -\frac{1}{20} and \frac{70}{20} have the same denominator, add them by adding their numerators.

$$\frac{13}{5}\left(\frac{-1+70}{20}-\frac{8}{3}\right)$$

Add -1 and 70 to get 69.

$$\frac{13}{5}\left(\frac{69}{20}-\frac{8}{3}\right)$$

Least common multiple of 20 and 3 is 60. Convert \frac{69}{20} and \frac{8}{3} to fractions with denominator 60.

$$\frac{13}{5}\left(\frac{207}{60}-\frac{160}{60}\right)$$

Since \frac{207}{60} and \frac{160}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{5}\times \frac{207-160}{60}$$

Subtract 160 from 207 to get 47.

$$\frac{13}{5}\times \frac{47}{60}$$

Multiply \frac{13}{5} times \frac{47}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 47}{5\times 60}$$

Do the multiplications in the fraction \frac{13\times 47}{5\times 60}.

$$\frac{611}{300}$$

Factor

$$\frac{13 \cdot 47}{2 ^ {2} \cdot 3 \cdot 5 ^ {2}} = 2\frac{11}{300} = 2.0366666666666666$$