Solve 6/11-3/4+5/11quad5/9-(frac{1}{18}-frac{4}{9})

$$\frac { 6 } { 11 } - \frac { 3 } { 4 } + \frac { 5 } { 11 } \quad \frac { 5 } { 9 } - ( \frac { 1 } { 18 } - \frac { 4 } { 9 } )$$

Evaluate

$$\frac{173}{396}\approx 0.436868687$$

Solution Steps

Least common multiple of 11 and 4 is 44. Convert \frac{6}{11} and \frac{3}{4} to fractions with denominator 44.

$$\frac{24}{44}-\frac{33}{44}+\frac{5}{11}\times \frac{5}{9}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Since \frac{24}{44} and \frac{33}{44} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24-33}{44}+\frac{5}{11}\times \frac{5}{9}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Subtract 33 from 24 to get -9.

$$-\frac{9}{44}+\frac{5}{11}\times \frac{5}{9}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Multiply \frac{5}{11} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{9}{44}+\frac{5\times 5}{11\times 9}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Do the multiplications in the fraction \frac{5\times 5}{11\times 9}.

$$-\frac{9}{44}+\frac{25}{99}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Least common multiple of 44 and 99 is 396. Convert -\frac{9}{44} and \frac{25}{99} to fractions with denominator 396.

$$-\frac{81}{396}+\frac{100}{396}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Since -\frac{81}{396} and \frac{100}{396} have the same denominator, add them by adding their numerators.

$$\frac{-81+100}{396}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Add -81 and 100 to get 19.

$$\frac{19}{396}-\left(\frac{1}{18}-\frac{4}{9}\right)$$

Least common multiple of 18 and 9 is 18. Convert \frac{1}{18} and \frac{4}{9} to fractions with denominator 18.

$$\frac{19}{396}-\left(\frac{1}{18}-\frac{8}{18}\right)$$

Since \frac{1}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19}{396}-\frac{1-8}{18}$$

Subtract 8 from 1 to get -7.

$$\frac{19}{396}-\left(-\frac{7}{18}\right)$$

The opposite of -\frac{7}{18} is \frac{7}{18}.

$$\frac{19}{396}+\frac{7}{18}$$

Least common multiple of 396 and 18 is 396. Convert \frac{19}{396} and \frac{7}{18} to fractions with denominator 396.

$$\frac{19}{396}+\frac{154}{396}$$

Since \frac{19}{396} and \frac{154}{396} have the same denominator, add them by adding their numerators.

$$\frac{19+154}{396}$$

Add 19 and 154 to get 173.

$$\frac{173}{396}$$

Factor

$$\frac{173}{2 ^ {2} \cdot 3 ^ {2} \cdot 11} = 0.43686868686868685$$