Solve 5371-20/13(4/9-7/3+25/2)=

$$5371 - \frac { 20 } { 13 } ( \frac { 4 } { 9 } - \frac { 7 } { 3 } + \frac { 25 } { 2 } ) =$$

Evaluate

$$\frac{626497}{117}\approx 5354.675213675$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert \frac{4}{9} and \frac{7}{3} to fractions with denominator 9.

$$5371-\frac{20}{13}\left(\frac{4}{9}-\frac{21}{9}+\frac{25}{2}\right)$$

Since \frac{4}{9} and \frac{21}{9} have the same denominator, subtract them by subtracting their numerators.

$$5371-\frac{20}{13}\left(\frac{4-21}{9}+\frac{25}{2}\right)$$

Subtract 21 from 4 to get -17.

$$5371-\frac{20}{13}\left(-\frac{17}{9}+\frac{25}{2}\right)$$

Least common multiple of 9 and 2 is 18. Convert -\frac{17}{9} and \frac{25}{2} to fractions with denominator 18.

$$5371-\frac{20}{13}\left(-\frac{34}{18}+\frac{225}{18}\right)$$

Since -\frac{34}{18} and \frac{225}{18} have the same denominator, add them by adding their numerators.

$$5371-\frac{20}{13}\times \frac{-34+225}{18}$$

Add -34 and 225 to get 191.

$$5371-\frac{20}{13}\times \frac{191}{18}$$

Multiply \frac{20}{13} times \frac{191}{18} by multiplying numerator times numerator and denominator times denominator.

$$5371-\frac{20\times 191}{13\times 18}$$

Do the multiplications in the fraction \frac{20\times 191}{13\times 18}.

$$5371-\frac{3820}{234}$$

Reduce the fraction \frac{3820}{234} to lowest terms by extracting and canceling out 2.

$$5371-\frac{1910}{117}$$

Convert 5371 to fraction \frac{628407}{117}.

$$\frac{628407}{117}-\frac{1910}{117}$$

Since \frac{628407}{117} and \frac{1910}{117} have the same denominator, subtract them by subtracting their numerators.

$$\frac{628407-1910}{117}$$

Subtract 1910 from 628407 to get 626497.

$$\frac{626497}{117}$$

Factor

$$\frac{23 \cdot 27239}{3 ^ {2} \cdot 13} = 5354\frac{79}{117} = 5354.675213675214$$