Solve -{5/7-1/9}*7/5-5/7+(-frac{2}{9}+sqrt{16})*frac{1}{9}

$$- \{ \frac { 5 } { 7 } - \frac { 1 } { 9 } \} \cdot \frac { 7 } { 5 } - \frac { 5 } { 7 } + ( - \frac { 2 } { 9 } + \sqrt { 16 } ) \cdot \frac { 1 } { 9 }$$

Evaluate

$$-\frac{3229}{2835}\approx -1.138977072$$

Solution Steps

Least common multiple of 7 and 9 is 63. Convert \frac{5}{7} and \frac{1}{9} to fractions with denominator 63.

$$\left(-\left(\frac{45}{63}-\frac{7}{63}\right)\right)\times \frac{7}{5}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Since \frac{45}{63} and \frac{7}{63} have the same denominator, subtract them by subtracting their numerators.

$$\left(-\frac{45-7}{63}\right)\times \frac{7}{5}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Subtract 7 from 45 to get 38.

$$-\frac{38}{63}\times \frac{7}{5}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Multiply -\frac{38}{63} times \frac{7}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-38\times 7}{63\times 5}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Do the multiplications in the fraction \frac{-38\times 7}{63\times 5}.

$$\frac{-266}{315}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Reduce the fraction \frac{-266}{315} to lowest terms by extracting and canceling out 7.

$$-\frac{38}{45}-\frac{5}{7}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Least common multiple of 45 and 7 is 315. Convert -\frac{38}{45} and \frac{5}{7} to fractions with denominator 315.

$$-\frac{266}{315}-\frac{225}{315}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Since -\frac{266}{315} and \frac{225}{315} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-266-225}{315}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Subtract 225 from -266 to get -491.

$$-\frac{491}{315}+\left(-\frac{2}{9}+\sqrt{16}\right)\times \frac{1}{9}$$

Calculate the square root of 16 and get 4.

$$-\frac{491}{315}+\left(-\frac{2}{9}+4\right)\times \frac{1}{9}$$

Convert 4 to fraction \frac{36}{9}.

$$-\frac{491}{315}+\left(-\frac{2}{9}+\frac{36}{9}\right)\times \frac{1}{9}$$

Since -\frac{2}{9} and \frac{36}{9} have the same denominator, add them by adding their numerators.

$$-\frac{491}{315}+\frac{-2+36}{9}\times \frac{1}{9}$$

Add -2 and 36 to get 34.

$$-\frac{491}{315}+\frac{34}{9}\times \frac{1}{9}$$

Multiply \frac{34}{9} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{491}{315}+\frac{34\times 1}{9\times 9}$$

Do the multiplications in the fraction \frac{34\times 1}{9\times 9}.

$$-\frac{491}{315}+\frac{34}{81}$$

Least common multiple of 315 and 81 is 2835. Convert -\frac{491}{315} and \frac{34}{81} to fractions with denominator 2835.

$$-\frac{4419}{2835}+\frac{1190}{2835}$$

Since -\frac{4419}{2835} and \frac{1190}{2835} have the same denominator, add them by adding their numerators.

$$\frac{-4419+1190}{2835}$$

Add -4419 and 1190 to get -3229.

$$-\frac{3229}{2835}$$

Factor

$$-\frac{3229}{2835} = -1\frac{394}{2835} = -1.1389770723104056$$