Solve 1/2-2/9*left(41/2-33/5+1frac{7}{20}right)

$$\frac{ 1 }{ 2 } - \frac{ 2 }{ 9 } \times \left( 4 \frac{ 1 }{ 2 } -3 \frac{ 3 }{ 5 } +1 \frac{ 7 }{ 20 } \right)$$

Evaluate

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Solution Steps

Multiply 4 and 2 to get 8.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{8+1}{2}-\frac{3\times 5+3}{5}+\frac{1\times 20+7}{20}\right)$$

Add 8 and 1 to get 9.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{2}-\frac{3\times 5+3}{5}+\frac{1\times 20+7}{20}\right)$$

Multiply 3 and 5 to get 15.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{2}-\frac{15+3}{5}+\frac{1\times 20+7}{20}\right)$$

Add 15 and 3 to get 18.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{2}-\frac{18}{5}+\frac{1\times 20+7}{20}\right)$$

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

$$\frac{1}{2}-\frac{2}{9}\left(\frac{45}{10}-\frac{36}{10}+\frac{1\times 20+7}{20}\right)$$

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

$$\frac{1}{2}-\frac{2}{9}\left(\frac{45-36}{10}+\frac{1\times 20+7}{20}\right)$$

Subtract 36 from 45 to get 9.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{10}+\frac{1\times 20+7}{20}\right)$$

Multiply 1 and 20 to get 20.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{10}+\frac{20+7}{20}\right)$$

Add 20 and 7 to get 27.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{9}{10}+\frac{27}{20}\right)$$

Least common multiple of 10 and 20 is 20. Convert \frac{9}{10} and \frac{27}{20} to fractions with denominator 20.

$$\frac{1}{2}-\frac{2}{9}\left(\frac{18}{20}+\frac{27}{20}\right)$$

Since \frac{18}{20} and \frac{27}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}-\frac{2}{9}\times \frac{18+27}{20}$$

Add 18 and 27 to get 45.

$$\frac{1}{2}-\frac{2}{9}\times \frac{45}{20}$$

Reduce the fraction \frac{45}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}-\frac{2}{9}\times \frac{9}{4}$$

Multiply \frac{2}{9} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{2\times 9}{9\times 4}$$

Cancel out 9 in both numerator and denominator.

$$\frac{1}{2}-\frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}-\frac{1}{2}$$

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

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Factor

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