Solve 4.4-[(-0.1)+81/3-(-112/3)]

$$4.4 - [ ( - 0.1 ) + 8 \frac { 1 } { 3 } - ( - 11 \frac { 2 } { 3 } ) ]$$

Evaluate

$$-15.5$$

Solution Steps

Multiply 8 and 3 to get 24.

$$4.4-\left(-0.1+\frac{24+1}{3}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Add 24 and 1 to get 25.

$$4.4-\left(-0.1+\frac{25}{3}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Convert decimal number -0.1 to fraction -\frac{1}{10}.

$$4.4-\left(-\frac{1}{10}+\frac{25}{3}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Least common multiple of 10 and 3 is 30. Convert -\frac{1}{10} and \frac{25}{3} to fractions with denominator 30.

$$4.4-\left(-\frac{3}{30}+\frac{250}{30}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Since -\frac{3}{30} and \frac{250}{30} have the same denominator, add them by adding their numerators.

$$4.4-\left(\frac{-3+250}{30}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Add -3 and 250 to get 247.

$$4.4-\left(\frac{247}{30}-\left(-\frac{11\times 3+2}{3}\right)\right)$$

Multiply 11 and 3 to get 33.

$$4.4-\left(\frac{247}{30}-\left(-\frac{33+2}{3}\right)\right)$$

Add 33 and 2 to get 35.

$$4.4-\left(\frac{247}{30}-\left(-\frac{35}{3}\right)\right)$$

The opposite of -\frac{35}{3} is \frac{35}{3}.

$$4.4-\left(\frac{247}{30}+\frac{35}{3}\right)$$

Least common multiple of 30 and 3 is 30. Convert \frac{247}{30} and \frac{35}{3} to fractions with denominator 30.

$$4.4-\left(\frac{247}{30}+\frac{350}{30}\right)$$

Since \frac{247}{30} and \frac{350}{30} have the same denominator, add them by adding their numerators.

$$4.4-\frac{247+350}{30}$$

Add 247 and 350 to get 597.

$$4.4-\frac{597}{30}$$

Reduce the fraction \frac{597}{30} to lowest terms by extracting and canceling out 3.

$$4.4-\frac{199}{10}$$

Convert decimal number 4.4 to fraction \frac{44}{10}. Reduce the fraction \frac{44}{10} to lowest terms by extracting and canceling out 2.

$$\frac{22}{5}-\frac{199}{10}$$

Least common multiple of 5 and 10 is 10. Convert \frac{22}{5} and \frac{199}{10} to fractions with denominator 10.

$$\frac{44}{10}-\frac{199}{10}$$

Since \frac{44}{10} and \frac{199}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{44-199}{10}$$

Subtract 199 from 44 to get -155.

$$\frac{-155}{10}$$

Reduce the fraction \frac{-155}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{31}{2}$$

Factor

$$-15.5$$