Solve {l}{(-4/15+5/9):(-26/45)}{-12:(-21/13)+1frac{1}{4}:(-frac{15}{46})}

$$\left. \begin{array} { l } { ( - \frac { 4 } { 15 } + \frac { 5 } { 9 } ) : ( - \frac { 26 } { 45 } ) } \\ { - 12 : ( - 2 \frac { 1 } { 13 } ) + 1 \frac { 1 } { 4 } : ( - \frac { 15 } { 46 } ) } \end{array} \right.$$

Evaluate

$$\frac{13}{9}\approx 1.444444444$$

Solution Steps

Least common multiple of 15 and 9 is 45. Convert -\frac{4}{15} and \frac{5}{9} to fractions with denominator 45.

$$\frac{-\frac{12}{45}+\frac{25}{45}}{-\frac{26}{45}}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Since -\frac{12}{45} and \frac{25}{45} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-12+25}{45}}{-\frac{26}{45}}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Add -12 and 25 to get 13.

$$\frac{\frac{13}{45}}{-\frac{26}{45}}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Divide \frac{13}{45} by -\frac{26}{45} by multiplying \frac{13}{45} by the reciprocal of -\frac{26}{45}.

$$\frac{13}{45}\left(-\frac{45}{26}\right)-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Multiply \frac{13}{45} times -\frac{45}{26} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\left(-45\right)}{45\times 26}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Do the multiplications in the fraction \frac{13\left(-45\right)}{45\times 26}.

$$\frac{-585}{1170}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Reduce the fraction \frac{-585}{1170} to lowest terms by extracting and canceling out 585.

$$-\frac{1}{2}-\frac{12}{-\frac{2\times 13+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Multiply 2 and 13 to get 26.

$$-\frac{1}{2}-\frac{12}{-\frac{26+1}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Add 26 and 1 to get 27.

$$-\frac{1}{2}-\frac{12}{-\frac{27}{13}}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Divide 12 by -\frac{27}{13} by multiplying 12 by the reciprocal of -\frac{27}{13}.

$$-\frac{1}{2}-12\left(-\frac{13}{27}\right)+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Express 12\left(-\frac{13}{27}\right) as a single fraction.

$$-\frac{1}{2}-\frac{12\left(-13\right)}{27}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Multiply 12 and -13 to get -156.

$$-\frac{1}{2}-\frac{-156}{27}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Reduce the fraction \frac{-156}{27} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{2}-\left(-\frac{52}{9}\right)+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

The opposite of -\frac{52}{9} is \frac{52}{9}.

$$-\frac{1}{2}+\frac{52}{9}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Least common multiple of 2 and 9 is 18. Convert -\frac{1}{2} and \frac{52}{9} to fractions with denominator 18.

$$-\frac{9}{18}+\frac{104}{18}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Since -\frac{9}{18} and \frac{104}{18} have the same denominator, add them by adding their numerators.

$$\frac{-9+104}{18}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Add -9 and 104 to get 95.

$$\frac{95}{18}+\frac{\frac{1\times 4+1}{4}}{-\frac{15}{46}}$$

Divide \frac{1\times 4+1}{4} by -\frac{15}{46} by multiplying \frac{1\times 4+1}{4} by the reciprocal of -\frac{15}{46}.

$$\frac{95}{18}+\frac{\left(1\times 4+1\right)\times 46}{4\left(-15\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{95}{18}+\frac{23\left(1+4\right)}{-15\times 2}$$

Add 1 and 4 to get 5.

$$\frac{95}{18}+\frac{23\times 5}{-15\times 2}$$

Multiply 23 and 5 to get 115.

$$\frac{95}{18}+\frac{115}{-15\times 2}$$

Multiply -15 and 2 to get -30.

$$\frac{95}{18}+\frac{115}{-30}$$

Reduce the fraction \frac{115}{-30} to lowest terms by extracting and canceling out 5.

$$\frac{95}{18}-\frac{23}{6}$$

Least common multiple of 18 and 6 is 18. Convert \frac{95}{18} and \frac{23}{6} to fractions with denominator 18.

$$\frac{95}{18}-\frac{69}{18}$$

Since \frac{95}{18} and \frac{69}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{95-69}{18}$$

Subtract 69 from 95 to get 26.

$$\frac{26}{18}$$

Reduce the fraction \frac{26}{18} to lowest terms by extracting and canceling out 2.

$$\frac{13}{9}$$

Factor

$$\frac{13}{3 ^ {2}} = 1\frac{4}{9} = 1.4444444444444444$$