Solve 1/2(1+1/2-1/9-1/10)

$$\frac { 1 } { 2 } ( 1 + \frac { 1 } { 2 } - \frac { 1 } { 9 } - \frac { 1 } { 10 } )$$

Evaluate

$$\frac{29}{45}\approx 0.644444444$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{2}\left(\frac{2}{2}+\frac{1}{2}-\frac{1}{9}-\frac{1}{10}\right)$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\left(\frac{2+1}{2}-\frac{1}{9}-\frac{1}{10}\right)$$

Add 2 and 1 to get 3.

$$\frac{1}{2}\left(\frac{3}{2}-\frac{1}{9}-\frac{1}{10}\right)$$

Least common multiple of 2 and 9 is 18. Convert \frac{3}{2} and \frac{1}{9} to fractions with denominator 18.

$$\frac{1}{2}\left(\frac{27}{18}-\frac{2}{18}-\frac{1}{10}\right)$$

Since \frac{27}{18} and \frac{2}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\left(\frac{27-2}{18}-\frac{1}{10}\right)$$

Subtract 2 from 27 to get 25.

$$\frac{1}{2}\left(\frac{25}{18}-\frac{1}{10}\right)$$

Least common multiple of 18 and 10 is 90. Convert \frac{25}{18} and \frac{1}{10} to fractions with denominator 90.

$$\frac{1}{2}\left(\frac{125}{90}-\frac{9}{90}\right)$$

Since \frac{125}{90} and \frac{9}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{125-9}{90}$$

Subtract 9 from 125 to get 116.

$$\frac{1}{2}\times \frac{116}{90}$$

Reduce the fraction \frac{116}{90} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}\times \frac{58}{45}$$

Multiply \frac{1}{2} times \frac{58}{45} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 58}{2\times 45}$$

Do the multiplications in the fraction \frac{1\times 58}{2\times 45}.

$$\frac{58}{90}$$

Reduce the fraction \frac{58}{90} to lowest terms by extracting and canceling out 2.

$$\frac{29}{45}$$

Factor

$$\frac{29}{3 ^ {2} \cdot 5} = 0.6444444444444445$$