Solve 1.5+23/4-105/12-4.75

$$1.5 + 2 \frac { 3 } { 4 } - 10 \frac { 5 } { 12 } - 4.75$$

Evaluate

$$-\frac{131}{12}\approx -10.916666667$$

Solution Steps

Multiply 2 and 4 to get 8.

$$1.5+\frac{8+3}{4}-\frac{10\times 12+5}{12}-4.75$$

Add 8 and 3 to get 11.

$$1.5+\frac{11}{4}-\frac{10\times 12+5}{12}-4.75$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$\frac{3}{2}+\frac{11}{4}-\frac{10\times 12+5}{12}-4.75$$

Least common multiple of 2 and 4 is 4. Convert \frac{3}{2} and \frac{11}{4} to fractions with denominator 4.

$$\frac{6}{4}+\frac{11}{4}-\frac{10\times 12+5}{12}-4.75$$

Since \frac{6}{4} and \frac{11}{4} have the same denominator, add them by adding their numerators.

$$\frac{6+11}{4}-\frac{10\times 12+5}{12}-4.75$$

Add 6 and 11 to get 17.

$$\frac{17}{4}-\frac{10\times 12+5}{12}-4.75$$

Multiply 10 and 12 to get 120.

$$\frac{17}{4}-\frac{120+5}{12}-4.75$$

Add 120 and 5 to get 125.

$$\frac{17}{4}-\frac{125}{12}-4.75$$

Least common multiple of 4 and 12 is 12. Convert \frac{17}{4} and \frac{125}{12} to fractions with denominator 12.

$$\frac{51}{12}-\frac{125}{12}-4.75$$

Since \frac{51}{12} and \frac{125}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-125}{12}-4.75$$

Subtract 125 from 51 to get -74.

$$\frac{-74}{12}-4.75$$

Reduce the fraction \frac{-74}{12} to lowest terms by extracting and canceling out 2.

$$-\frac{37}{6}-4.75$$

Convert decimal number 4.75 to fraction \frac{475}{100}. Reduce the fraction \frac{475}{100} to lowest terms by extracting and canceling out 25.

$$-\frac{37}{6}-\frac{19}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{37}{6} and \frac{19}{4} to fractions with denominator 12.

$$-\frac{74}{12}-\frac{57}{12}$$

Since -\frac{74}{12} and \frac{57}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-74-57}{12}$$

Subtract 57 from -74 to get -131.

$$-\frac{131}{12}$$

Factor

$$-\frac{131}{12} = -10\frac{11}{12} = -10.916666666666666$$