Solve 35/9+(-21/4)-(-45/6)-52/3

$$3 \frac { 5 } { 9 } +(- 2 \frac { 1 } { 4 } )-( -4 \frac { 5 } { 6 } )- 5 \frac { 2 } { 3 }$$

Evaluate

$$\frac{17}{36}\approx 0.472222222$$

Solution Steps

Multiply 3 and 9 to get 27.

$$\frac{27+5}{9}-\frac{2\times 4+1}{4}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Add 27 and 5 to get 32.

$$\frac{32}{9}-\frac{2\times 4+1}{4}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Multiply 2 and 4 to get 8.

$$\frac{32}{9}-\frac{8+1}{4}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Add 8 and 1 to get 9.

$$\frac{32}{9}-\frac{9}{4}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Least common multiple of 9 and 4 is 36. Convert \frac{32}{9} and \frac{9}{4} to fractions with denominator 36.

$$\frac{128}{36}-\frac{81}{36}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Since \frac{128}{36} and \frac{81}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{128-81}{36}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Subtract 81 from 128 to get 47.

$$\frac{47}{36}-\left(-\frac{4\times 6+5}{6}\right)-\frac{5\times 3+2}{3}$$

Multiply 4 and 6 to get 24.

$$\frac{47}{36}-\left(-\frac{24+5}{6}\right)-\frac{5\times 3+2}{3}$$

Add 24 and 5 to get 29.

$$\frac{47}{36}-\left(-\frac{29}{6}\right)-\frac{5\times 3+2}{3}$$

The opposite of -\frac{29}{6} is \frac{29}{6}.

$$\frac{47}{36}+\frac{29}{6}-\frac{5\times 3+2}{3}$$

Least common multiple of 36 and 6 is 36. Convert \frac{47}{36} and \frac{29}{6} to fractions with denominator 36.

$$\frac{47}{36}+\frac{174}{36}-\frac{5\times 3+2}{3}$$

Since \frac{47}{36} and \frac{174}{36} have the same denominator, add them by adding their numerators.

$$\frac{47+174}{36}-\frac{5\times 3+2}{3}$$

Add 47 and 174 to get 221.

$$\frac{221}{36}-\frac{5\times 3+2}{3}$$

Multiply 5 and 3 to get 15.

$$\frac{221}{36}-\frac{15+2}{3}$$

Add 15 and 2 to get 17.

$$\frac{221}{36}-\frac{17}{3}$$

Least common multiple of 36 and 3 is 36. Convert \frac{221}{36} and \frac{17}{3} to fractions with denominator 36.

$$\frac{221}{36}-\frac{204}{36}$$

Since \frac{221}{36} and \frac{204}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{221-204}{36}$$

Subtract 204 from 221 to get 17.

$$\frac{17}{36}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3 ^ {2}} = 0.4722222222222222$$