Solve 1/2-2/9x(41/2-33/5+1frac{1}{12})

$$\frac { 1 } { 2 } - \frac { 2 } { 9 } x ( 4 \frac { 1 } { 2 } - 3 \frac { 3 } { 5 } + 1 \frac { 1 } { 12 } )$$

Evaluate

$$-\frac{119x}{270}+\frac{1}{2}$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{8+1}{2}-\frac{3\times 5+3}{5}+\frac{1\times 12+1}{12}\right)$$

Add 8 and 1 to get 9.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{3\times 5+3}{5}+\frac{1\times 12+1}{12}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{15+3}{5}+\frac{1\times 12+1}{12}\right)$$

Add 15 and 3 to get 18.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{18}{5}+\frac{1\times 12+1}{12}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{18}{5} to fractions with denominator 10.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{45}{10}-\frac{36}{10}+\frac{1\times 12+1}{12}\right)$$

Since \frac{45}{10} and \frac{36}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{45-36}{10}+\frac{1\times 12+1}{12}\right)$$

Subtract 36 from 45 to get 9.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{1\times 12+1}{12}\right)$$

Multiply 1 and 12 to get 12.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{12+1}{12}\right)$$

Add 12 and 1 to get 13.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{13}{12}\right)$$

Least common multiple of 10 and 12 is 60. Convert \frac{9}{10} and \frac{13}{12} to fractions with denominator 60.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{54}{60}+\frac{65}{60}\right)$$

Since \frac{54}{60} and \frac{65}{60} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{2}{9}x\times \frac{54+65}{60}$$

Add 54 and 65 to get 119.

$$\frac{1}{2}-\frac{2}{9}x\times \frac{119}{60}$$

Multiply \frac{2}{9} times \frac{119}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{2\times 119}{9\times 60}x$$

Do the multiplications in the fraction \frac{2\times 119}{9\times 60}.

$$\frac{1}{2}-\frac{238}{540}x$$

Reduce the fraction \frac{238}{540} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}-\frac{119}{270}x$$

Expand

$$-\frac{119x}{270}+\frac{1}{2}$$

Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{8+1}{2}-\frac{3\times 5+3}{5}+\frac{1\times 12+1}{12}\right)$$

Add 8 and 1 to get 9.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{3\times 5+3}{5}+\frac{1\times 12+1}{12}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{15+3}{5}+\frac{1\times 12+1}{12}\right)$$

Add 15 and 3 to get 18.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{2}-\frac{18}{5}+\frac{1\times 12+1}{12}\right)$$

Least common multiple of 2 and 5 is 10. Convert \frac{9}{2} and \frac{18}{5} to fractions with denominator 10.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{45}{10}-\frac{36}{10}+\frac{1\times 12+1}{12}\right)$$

Since \frac{45}{10} and \frac{36}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{45-36}{10}+\frac{1\times 12+1}{12}\right)$$

Subtract 36 from 45 to get 9.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{1\times 12+1}{12}\right)$$

Multiply 1 and 12 to get 12.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{12+1}{12}\right)$$

Add 12 and 1 to get 13.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{9}{10}+\frac{13}{12}\right)$$

Least common multiple of 10 and 12 is 60. Convert \frac{9}{10} and \frac{13}{12} to fractions with denominator 60.

$$\frac{1}{2}-\frac{2}{9}x\left(\frac{54}{60}+\frac{65}{60}\right)$$

Since \frac{54}{60} and \frac{65}{60} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{2}{9}x\times \frac{54+65}{60}$$

Add 54 and 65 to get 119.

$$\frac{1}{2}-\frac{2}{9}x\times \frac{119}{60}$$

Multiply \frac{2}{9} times \frac{119}{60} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{2\times 119}{9\times 60}x$$

Do the multiplications in the fraction \frac{2\times 119}{9\times 60}.

$$\frac{1}{2}-\frac{238}{540}x$$

Reduce the fraction \frac{238}{540} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}-\frac{119}{270}x$$