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

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

Evaluate

$$\frac{49}{40}=1.225$$

Solution Steps

Convert 1 to fraction \frac{3}{3}.

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

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

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

Add -1 and 3 to get 2.

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

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.

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

Since \frac{2}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

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

Least common multiple of 3 and 8 is 24. Convert \frac{2}{3} and \frac{1}{8} to fractions with denominator 24.

$$\frac{3}{5}-3\left(\frac{16}{24}-\frac{3}{24}-\frac{3}{4}\right)$$

Since \frac{16}{24} and \frac{3}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}-3\left(\frac{16-3}{24}-\frac{3}{4}\right)$$

Subtract 3 from 16 to get 13.

$$\frac{3}{5}-3\left(\frac{13}{24}-\frac{3}{4}\right)$$

Least common multiple of 24 and 4 is 24. Convert \frac{13}{24} and \frac{3}{4} to fractions with denominator 24.

$$\frac{3}{5}-3\left(\frac{13}{24}-\frac{18}{24}\right)$$

Since \frac{13}{24} and \frac{18}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}-3\times \frac{13-18}{24}$$

Subtract 18 from 13 to get -5.

$$\frac{3}{5}-3\left(-\frac{5}{24}\right)$$

Express -3\left(-\frac{5}{24}\right) as a single fraction.

$$\frac{3}{5}+\frac{-3\left(-5\right)}{24}$$

Multiply -3 and -5 to get 15.

$$\frac{3}{5}+\frac{15}{24}$$

Reduce the fraction \frac{15}{24} to lowest terms by extracting and canceling out 3.

$$\frac{3}{5}+\frac{5}{8}$$

Least common multiple of 5 and 8 is 40. Convert \frac{3}{5} and \frac{5}{8} to fractions with denominator 40.

$$\frac{24}{40}+\frac{25}{40}$$

Since \frac{24}{40} and \frac{25}{40} have the same denominator, add them by adding their numerators.

$$\frac{24+25}{40}$$

Add 24 and 25 to get 49.

$$\frac{49}{40}$$

Factor

$$\frac{7 ^ {2}}{2 ^ {3} \cdot 5} = 1\frac{9}{40} = 1.225$$