Solve 192/3-331/2-263/4+455/6

$$19 \frac { 2 } { 3 } - 33 \frac { 1 } { 2 } - 26 \frac { 3 } { 4 } + 45 \frac { 5 } { 6 }$$

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Multiply 19 and 3 to get 57.

$$\frac{57+2}{3}-\frac{33\times 2+1}{2}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Add 57 and 2 to get 59.

$$\frac{59}{3}-\frac{33\times 2+1}{2}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Multiply 33 and 2 to get 66.

$$\frac{59}{3}-\frac{66+1}{2}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Add 66 and 1 to get 67.

$$\frac{59}{3}-\frac{67}{2}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Least common multiple of 3 and 2 is 6. Convert \frac{59}{3} and \frac{67}{2} to fractions with denominator 6.

$$\frac{118}{6}-\frac{201}{6}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Since \frac{118}{6} and \frac{201}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{118-201}{6}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Subtract 201 from 118 to get -83.

$$-\frac{83}{6}-\frac{26\times 4+3}{4}+\frac{45\times 6+5}{6}$$

Multiply 26 and 4 to get 104.

$$-\frac{83}{6}-\frac{104+3}{4}+\frac{45\times 6+5}{6}$$

Add 104 and 3 to get 107.

$$-\frac{83}{6}-\frac{107}{4}+\frac{45\times 6+5}{6}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{83}{6} and \frac{107}{4} to fractions with denominator 12.

$$-\frac{166}{12}-\frac{321}{12}+\frac{45\times 6+5}{6}$$

Since -\frac{166}{12} and \frac{321}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-166-321}{12}+\frac{45\times 6+5}{6}$$

Subtract 321 from -166 to get -487.

$$-\frac{487}{12}+\frac{45\times 6+5}{6}$$

Multiply 45 and 6 to get 270.

$$-\frac{487}{12}+\frac{270+5}{6}$$

Add 270 and 5 to get 275.

$$-\frac{487}{12}+\frac{275}{6}$$

Least common multiple of 12 and 6 is 12. Convert -\frac{487}{12} and \frac{275}{6} to fractions with denominator 12.

$$-\frac{487}{12}+\frac{550}{12}$$

Since -\frac{487}{12} and \frac{550}{12} have the same denominator, add them by adding their numerators.

$$\frac{-487+550}{12}$$

Add -487 and 550 to get 63.

$$\frac{63}{12}$$

Reduce the fraction \frac{63}{12} to lowest terms by extracting and canceling out 3.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$