Solve 1+(-5/9)*(3/4)-7/11{-frac{21/22}}

$$1+(- \frac{ 5 }{ 9 } ) \times ( \frac{ 3 }{ 4 } )- \frac{ 7 }{ \frac{ 11 }{ - \frac{ 21 }{ 22 } } }$$

Evaluate

$$\frac{1729}{1452}\approx 1.19077135$$

Solution Steps

Multiply -\frac{5}{9} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{-5\times 3}{9\times 4}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Do the multiplications in the fraction \frac{-5\times 3}{9\times 4}.

$$1+\frac{-15}{36}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Reduce the fraction \frac{-15}{36} to lowest terms by extracting and canceling out 3.

$$1-\frac{5}{12}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Convert 1 to fraction \frac{12}{12}.

$$\frac{12}{12}-\frac{5}{12}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Since \frac{12}{12} and \frac{5}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12-5}{12}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Subtract 5 from 12 to get 7.

$$\frac{7}{12}-\frac{7}{\frac{11}{-\frac{21}{22}}}$$

Divide 7 by \frac{11}{-\frac{21}{22}} by multiplying 7 by the reciprocal of \frac{11}{-\frac{21}{22}}.

$$\frac{7}{12}-\frac{7\left(-\frac{21}{22}\right)}{11}$$

Express 7\left(-\frac{21}{22}\right) as a single fraction.

$$\frac{7}{12}-\frac{\frac{7\left(-21\right)}{22}}{11}$$

Multiply 7 and -21 to get -147.

$$\frac{7}{12}-\frac{\frac{-147}{22}}{11}$$

Fraction \frac{-147}{22} can be rewritten as -\frac{147}{22} by extracting the negative sign.

$$\frac{7}{12}-\frac{-\frac{147}{22}}{11}$$

Express \frac{-\frac{147}{22}}{11} as a single fraction.

$$\frac{7}{12}-\frac{-147}{22\times 11}$$

Multiply 22 and 11 to get 242.

$$\frac{7}{12}-\frac{-147}{242}$$

Fraction \frac{-147}{242} can be rewritten as -\frac{147}{242} by extracting the negative sign.

$$\frac{7}{12}-\left(-\frac{147}{242}\right)$$

The opposite of -\frac{147}{242} is \frac{147}{242}.

$$\frac{7}{12}+\frac{147}{242}$$

Least common multiple of 12 and 242 is 1452. Convert \frac{7}{12} and \frac{147}{242} to fractions with denominator 1452.

$$\frac{847}{1452}+\frac{882}{1452}$$

Since \frac{847}{1452} and \frac{882}{1452} have the same denominator, add them by adding their numerators.

$$\frac{847+882}{1452}$$

Add 847 and 882 to get 1729.

$$\frac{1729}{1452}$$

Factor

$$\frac{7 \cdot 13 \cdot 19}{2 ^ {2} \cdot 3 \cdot 11 ^ {2}} = 1\frac{277}{1452} = 1.190771349862259$$