Solve 12/13-[1/5-(-32/5)+7.4]-(-1/13)

$$\frac { 12 } { 13 } - [ \frac { 1 } { 5 } - ( - 3 \frac { 2 } { 5 } ) + 7.4 ] - ( - \frac { 1 } { 13 } )$$

Evaluate

$$-10$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{12}{13}-\left(\frac{1}{5}-\left(-\frac{15+2}{5}\right)+7.4\right)-\left(-\frac{1}{13}\right)$$

Add 15 and 2 to get 17.

$$\frac{12}{13}-\left(\frac{1}{5}-\left(-\frac{17}{5}\right)+7.4\right)-\left(-\frac{1}{13}\right)$$

The opposite of -\frac{17}{5} is \frac{17}{5}.

$$\frac{12}{13}-\left(\frac{1}{5}+\frac{17}{5}+7.4\right)-\left(-\frac{1}{13}\right)$$

Since \frac{1}{5} and \frac{17}{5} have the same denominator, add them by adding their numerators.

$$\frac{12}{13}-\left(\frac{1+17}{5}+7.4\right)-\left(-\frac{1}{13}\right)$$

Add 1 and 17 to get 18.

$$\frac{12}{13}-\left(\frac{18}{5}+7.4\right)-\left(-\frac{1}{13}\right)$$

Convert decimal number 7.4 to fraction \frac{74}{10}. Reduce the fraction \frac{74}{10} to lowest terms by extracting and canceling out 2.

$$\frac{12}{13}-\left(\frac{18}{5}+\frac{37}{5}\right)-\left(-\frac{1}{13}\right)$$

Since \frac{18}{5} and \frac{37}{5} have the same denominator, add them by adding their numerators.

$$\frac{12}{13}-\frac{18+37}{5}-\left(-\frac{1}{13}\right)$$

Add 18 and 37 to get 55.

$$\frac{12}{13}-\frac{55}{5}-\left(-\frac{1}{13}\right)$$

Divide 55 by 5 to get 11.

$$\frac{12}{13}-11-\left(-\frac{1}{13}\right)$$

Convert 11 to fraction \frac{143}{13}.

$$\frac{12}{13}-\frac{143}{13}-\left(-\frac{1}{13}\right)$$

Since \frac{12}{13} and \frac{143}{13} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-143}{13}-\left(-\frac{1}{13}\right)$$

Subtract 143 from 12 to get -131.

$$-\frac{131}{13}-\left(-\frac{1}{13}\right)$$

The opposite of -\frac{1}{13} is \frac{1}{13}.

$$-\frac{131}{13}+\frac{1}{13}$$

Since -\frac{131}{13} and \frac{1}{13} have the same denominator, add them by adding their numerators.

$$\frac{-131+1}{13}$$

Add -131 and 1 to get -130.

$$\frac{-130}{13}$$

Divide -130 by 13 to get -10.

$$-10$$

Factor

$$-10$$