Solve 3-|5/3+4/2+frac{1{4}}+2|

$$3 - | \frac { 5 } { 3 } + \frac { 4 } { 2 + \frac { 1 } { 4 } } + 2 |$$

Evaluate

$$-\frac{22}{9}\approx -2.444444444$$

Solution Steps

Convert 2 to fraction \frac{8}{4}.

$$3-|\frac{5}{3}+\frac{4}{\frac{8}{4}+\frac{1}{4}}+2|$$

Since \frac{8}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$3-|\frac{5}{3}+\frac{4}{\frac{8+1}{4}}+2|$$

Add 8 and 1 to get 9.

$$3-|\frac{5}{3}+\frac{4}{\frac{9}{4}}+2|$$

Divide 4 by \frac{9}{4} by multiplying 4 by the reciprocal of \frac{9}{4}.

$$3-|\frac{5}{3}+4\times \frac{4}{9}+2|$$

Express 4\times \frac{4}{9} as a single fraction.

$$3-|\frac{5}{3}+\frac{4\times 4}{9}+2|$$

Multiply 4 and 4 to get 16.

$$3-|\frac{5}{3}+\frac{16}{9}+2|$$

Least common multiple of 3 and 9 is 9. Convert \frac{5}{3} and \frac{16}{9} to fractions with denominator 9.

$$3-|\frac{15}{9}+\frac{16}{9}+2|$$

Since \frac{15}{9} and \frac{16}{9} have the same denominator, add them by adding their numerators.

$$3-|\frac{15+16}{9}+2|$$

Add 15 and 16 to get 31.

$$3-|\frac{31}{9}+2|$$

Convert 2 to fraction \frac{18}{9}.

$$3-|\frac{31}{9}+\frac{18}{9}|$$

Since \frac{31}{9} and \frac{18}{9} have the same denominator, add them by adding their numerators.

$$3-|\frac{31+18}{9}|$$

Add 31 and 18 to get 49.

$$3-|\frac{49}{9}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{49}{9} is \frac{49}{9}.

$$3-\frac{49}{9}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{27}{9}-\frac{49}{9}$$

Since \frac{27}{9} and \frac{49}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-49}{9}$$

Subtract 49 from 27 to get -22.

$$-\frac{22}{9}$$

Factor

$$-\frac{22}{9} = -2\frac{4}{9} = -2.4444444444444446$$