Solve 2/3+3/4+1/2-11/2=

$$\frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 1 } { 2 } - 1 \frac { 1 } { 2 } =$$

Evaluate

$$\frac{5}{12}\approx 0.416666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{9}{12}+\frac{1}{2}-\frac{1\times 2+1}{2}$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+9}{12}+\frac{1}{2}-\frac{1\times 2+1}{2}$$

Add 8 and 9 to get 17.

$$\frac{17}{12}+\frac{1}{2}-\frac{1\times 2+1}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{17}{12} and \frac{1}{2} to fractions with denominator 12.

$$\frac{17}{12}+\frac{6}{12}-\frac{1\times 2+1}{2}$$

Since \frac{17}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{17+6}{12}-\frac{1\times 2+1}{2}$$

Add 17 and 6 to get 23.

$$\frac{23}{12}-\frac{1\times 2+1}{2}$$

Multiply 1 and 2 to get 2.

$$\frac{23}{12}-\frac{2+1}{2}$$

Add 2 and 1 to get 3.

$$\frac{23}{12}-\frac{3}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{23}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{23}{12}-\frac{18}{12}$$

Since \frac{23}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{23-18}{12}$$

Subtract 18 from 23 to get 5.

$$\frac{5}{12}$$

Factor

$$\frac{5}{2 ^ {2} \cdot 3} = 0.4166666666666667$$