Solve [(3/20+6/9):46-4/90+135-13/100*frac{5}{9}]:frac{25-2}{10}

$$[ ( \frac { 3 } { 20 } + \frac { 6 } { 9 } ) : \frac { 46 - 4 } { 90 } + \frac { 135 - 13 } { 100 } \times \frac { 5 } { 9 } ] : \frac { 25 - 2 } { 10 }$$

Evaluate

$$\frac{19}{18}\approx 1.055555556$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{\frac{3}{20}+\frac{2}{3}}{\frac{46-4}{90}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Least common multiple of 20 and 3 is 60. Convert \frac{3}{20} and \frac{2}{3} to fractions with denominator 60.

$$\frac{\frac{\frac{9}{60}+\frac{40}{60}}{\frac{46-4}{90}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Since \frac{9}{60} and \frac{40}{60} have the same denominator, add them by adding their numerators.

$$\frac{\frac{\frac{9+40}{60}}{\frac{46-4}{90}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Add 9 and 40 to get 49.

$$\frac{\frac{\frac{49}{60}}{\frac{46-4}{90}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Subtract 4 from 46 to get 42.

$$\frac{\frac{\frac{49}{60}}{\frac{42}{90}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Reduce the fraction \frac{42}{90} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{\frac{49}{60}}{\frac{7}{15}}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Divide \frac{49}{60} by \frac{7}{15} by multiplying \frac{49}{60} by the reciprocal of \frac{7}{15}.

$$\frac{\frac{49}{60}\times \frac{15}{7}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Multiply \frac{49}{60} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{49\times 15}{60\times 7}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Do the multiplications in the fraction \frac{49\times 15}{60\times 7}.

$$\frac{\frac{735}{420}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Reduce the fraction \frac{735}{420} to lowest terms by extracting and canceling out 105.

$$\frac{\frac{7}{4}+\frac{135-13}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Subtract 13 from 135 to get 122.

$$\frac{\frac{7}{4}+\frac{122}{100}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Reduce the fraction \frac{122}{100} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{4}+\frac{61}{50}\times \frac{5}{9}}{\frac{25-2}{10}}$$

Multiply \frac{61}{50} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{7}{4}+\frac{61\times 5}{50\times 9}}{\frac{25-2}{10}}$$

Do the multiplications in the fraction \frac{61\times 5}{50\times 9}.

$$\frac{\frac{7}{4}+\frac{305}{450}}{\frac{25-2}{10}}$$

Reduce the fraction \frac{305}{450} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{7}{4}+\frac{61}{90}}{\frac{25-2}{10}}$$

Least common multiple of 4 and 90 is 180. Convert \frac{7}{4} and \frac{61}{90} to fractions with denominator 180.

$$\frac{\frac{315}{180}+\frac{122}{180}}{\frac{25-2}{10}}$$

Since \frac{315}{180} and \frac{122}{180} have the same denominator, add them by adding their numerators.

$$\frac{\frac{315+122}{180}}{\frac{25-2}{10}}$$

Add 315 and 122 to get 437.

$$\frac{\frac{437}{180}}{\frac{25-2}{10}}$$

Subtract 2 from 25 to get 23.

$$\frac{\frac{437}{180}}{\frac{23}{10}}$$

Divide \frac{437}{180} by \frac{23}{10} by multiplying \frac{437}{180} by the reciprocal of \frac{23}{10}.

$$\frac{437}{180}\times \frac{10}{23}$$

Multiply \frac{437}{180} times \frac{10}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{437\times 10}{180\times 23}$$

Do the multiplications in the fraction \frac{437\times 10}{180\times 23}.

$$\frac{4370}{4140}$$

Reduce the fraction \frac{4370}{4140} to lowest terms by extracting and canceling out 230.

$$\frac{19}{18}$$

Factor

$$\frac{19}{2 \cdot 3 ^ {2}} = 1\frac{1}{18} = 1.0555555555555556$$