Solve 4.73-[22/3-(-2.63)]-1/3

$$4.73 - [ 2 \frac { 2 } { 3 } - ( - 2.63 ) ] - \frac { 1 } { 3 }$$

Evaluate

$$-0.9$$

Solution Steps

Multiply 2 and 3 to get 6.

$$4.73-\left(\frac{6+2}{3}-\left(-2.63\right)\right)-\frac{1}{3}$$

Add 6 and 2 to get 8.

$$4.73-\left(\frac{8}{3}-\left(-2.63\right)\right)-\frac{1}{3}$$

The opposite of -2.63 is 2.63.

$$4.73-\left(\frac{8}{3}+2.63\right)-\frac{1}{3}$$

Convert decimal number 2.63 to fraction \frac{263}{100}.

$$4.73-\left(\frac{8}{3}+\frac{263}{100}\right)-\frac{1}{3}$$

Least common multiple of 3 and 100 is 300. Convert \frac{8}{3} and \frac{263}{100} to fractions with denominator 300.

$$4.73-\left(\frac{800}{300}+\frac{789}{300}\right)-\frac{1}{3}$$

Since \frac{800}{300} and \frac{789}{300} have the same denominator, add them by adding their numerators.

$$4.73-\frac{800+789}{300}-\frac{1}{3}$$

Add 800 and 789 to get 1589.

$$4.73-\frac{1589}{300}-\frac{1}{3}$$

Convert decimal number 4.73 to fraction \frac{473}{100}.

$$\frac{473}{100}-\frac{1589}{300}-\frac{1}{3}$$

Least common multiple of 100 and 300 is 300. Convert \frac{473}{100} and \frac{1589}{300} to fractions with denominator 300.

$$\frac{1419}{300}-\frac{1589}{300}-\frac{1}{3}$$

Since \frac{1419}{300} and \frac{1589}{300} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1419-1589}{300}-\frac{1}{3}$$

Subtract 1589 from 1419 to get -170.

$$\frac{-170}{300}-\frac{1}{3}$$

Reduce the fraction \frac{-170}{300} to lowest terms by extracting and canceling out 10.

$$-\frac{17}{30}-\frac{1}{3}$$

Least common multiple of 30 and 3 is 30. Convert -\frac{17}{30} and \frac{1}{3} to fractions with denominator 30.

$$-\frac{17}{30}-\frac{10}{30}$$

Since -\frac{17}{30} and \frac{10}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-17-10}{30}$$

Subtract 10 from -17 to get -27.

$$\frac{-27}{30}$$

Reduce the fraction \frac{-27}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{9}{10}$$

Factor

$$-0.9$$