Solve 58/10div(13/6-25/90+7/90-frac{3}{90})+(frac{26}{10}+frac{2}{9}*frac{36}{10})divfrac{34}{90}=

$$\frac{ 58 }{ 10 } \div ( \frac{ 13 }{ 6 } - \frac{ 25 }{ 90 } + \frac{ 7 }{ 90 } - \frac{ 3 }{ 90 } )+( \frac{ 26 }{ 10 } + \frac{ 2 }{ 9 } \times \frac{ 36 }{ 10 } ) \div \frac{ 34 }{ 90 } =$$

Evaluate

$$12$$

Solution Steps

Reduce the fraction \frac{58}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{5}}{\frac{13}{6}-\frac{25}{90}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{25}{90} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{29}{5}}{\frac{13}{6}-\frac{5}{18}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Least common multiple of 6 and 18 is 18. Convert \frac{13}{6} and \frac{5}{18} to fractions with denominator 18.

$$\frac{\frac{29}{5}}{\frac{39}{18}-\frac{5}{18}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Since \frac{39}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29}{5}}{\frac{39-5}{18}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Subtract 5 from 39 to get 34.

$$\frac{\frac{29}{5}}{\frac{34}{18}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{34}{18} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{5}}{\frac{17}{9}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Least common multiple of 9 and 90 is 90. Convert \frac{17}{9} and \frac{7}{90} to fractions with denominator 90.

$$\frac{\frac{29}{5}}{\frac{170}{90}+\frac{7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Since \frac{170}{90} and \frac{7}{90} have the same denominator, add them by adding their numerators.

$$\frac{\frac{29}{5}}{\frac{170+7}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Add 170 and 7 to get 177.

$$\frac{\frac{29}{5}}{\frac{177}{90}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{177}{90} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{29}{5}}{\frac{59}{30}-\frac{3}{90}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{3}{90} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{29}{5}}{\frac{59}{30}-\frac{1}{30}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Since \frac{59}{30} and \frac{1}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{29}{5}}{\frac{59-1}{30}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Subtract 1 from 59 to get 58.

$$\frac{\frac{29}{5}}{\frac{58}{30}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{58}{30} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{29}{5}}{\frac{29}{15}}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Divide \frac{29}{5} by \frac{29}{15} by multiplying \frac{29}{5} by the reciprocal of \frac{29}{15}.

$$\frac{29}{5}\times \frac{15}{29}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Multiply \frac{29}{5} times \frac{15}{29} by multiplying numerator times numerator and denominator times denominator.

$$\frac{29\times 15}{5\times 29}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Cancel out 29 in both numerator and denominator.

$$\frac{15}{5}+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Divide 15 by 5 to get 3.

$$3+\frac{\frac{26}{10}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$3+\frac{\frac{13}{5}+\frac{2}{9}\times \frac{36}{10}}{\frac{34}{90}}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$3+\frac{\frac{13}{5}+\frac{2}{9}\times \frac{18}{5}}{\frac{34}{90}}$$

Multiply \frac{2}{9} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{\frac{13}{5}+\frac{2\times 18}{9\times 5}}{\frac{34}{90}}$$

Do the multiplications in the fraction \frac{2\times 18}{9\times 5}.

$$3+\frac{\frac{13}{5}+\frac{36}{45}}{\frac{34}{90}}$$

Reduce the fraction \frac{36}{45} to lowest terms by extracting and canceling out 9.

$$3+\frac{\frac{13}{5}+\frac{4}{5}}{\frac{34}{90}}$$

Since \frac{13}{5} and \frac{4}{5} have the same denominator, add them by adding their numerators.

$$3+\frac{\frac{13+4}{5}}{\frac{34}{90}}$$

Add 13 and 4 to get 17.

$$3+\frac{\frac{17}{5}}{\frac{34}{90}}$$

Reduce the fraction \frac{34}{90} to lowest terms by extracting and canceling out 2.

$$3+\frac{\frac{17}{5}}{\frac{17}{45}}$$

Divide \frac{17}{5} by \frac{17}{45} by multiplying \frac{17}{5} by the reciprocal of \frac{17}{45}.

$$3+\frac{17}{5}\times \frac{45}{17}$$

Multiply \frac{17}{5} times \frac{45}{17} by multiplying numerator times numerator and denominator times denominator.

$$3+\frac{17\times 45}{5\times 17}$$

Cancel out 17 in both numerator and denominator.

$$3+\frac{45}{5}$$

Divide 45 by 5 to get 9.

$$3+9$$

Add 3 and 9 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$