Solve 4/1-12/10*(21/9+75/100)+frac{3}{9}

$$\frac{ 4 }{ 1 } - \frac{ 12 }{ 10 } \times ( \frac{ 21 }{ 9 } + \frac{ 75 }{ 100 } )+ \frac{ 3 }{ 9 }$$

Evaluate

$$\frac{19}{30}\approx 0.633333333$$

Solution Steps

Anything divided by one gives itself.

$$4-\frac{12}{10}\left(\frac{21}{9}+\frac{75}{100}\right)+\frac{3}{9}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$4-\frac{6}{5}\left(\frac{21}{9}+\frac{75}{100}\right)+\frac{3}{9}$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$4-\frac{6}{5}\left(\frac{7}{3}+\frac{75}{100}\right)+\frac{3}{9}$$

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$4-\frac{6}{5}\left(\frac{7}{3}+\frac{3}{4}\right)+\frac{3}{9}$$

Least common multiple of 3 and 4 is 12. Convert \frac{7}{3} and \frac{3}{4} to fractions with denominator 12.

$$4-\frac{6}{5}\left(\frac{28}{12}+\frac{9}{12}\right)+\frac{3}{9}$$

Since \frac{28}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$4-\frac{6}{5}\times \frac{28+9}{12}+\frac{3}{9}$$

Add 28 and 9 to get 37.

$$4-\frac{6}{5}\times \frac{37}{12}+\frac{3}{9}$$

Multiply \frac{6}{5} times \frac{37}{12} by multiplying numerator times numerator and denominator times denominator.

$$4-\frac{6\times 37}{5\times 12}+\frac{3}{9}$$

Do the multiplications in the fraction \frac{6\times 37}{5\times 12}.

$$4-\frac{222}{60}+\frac{3}{9}$$

Reduce the fraction \frac{222}{60} to lowest terms by extracting and canceling out 6.

$$4-\frac{37}{10}+\frac{3}{9}$$

Convert 4 to fraction \frac{40}{10}.

$$\frac{40}{10}-\frac{37}{10}+\frac{3}{9}$$

Since \frac{40}{10} and \frac{37}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{40-37}{10}+\frac{3}{9}$$

Subtract 37 from 40 to get 3.

$$\frac{3}{10}+\frac{3}{9}$$

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

$$\frac{3}{10}+\frac{1}{3}$$

Least common multiple of 10 and 3 is 30. Convert \frac{3}{10} and \frac{1}{3} to fractions with denominator 30.

$$\frac{9}{30}+\frac{10}{30}$$

Since \frac{9}{30} and \frac{10}{30} have the same denominator, add them by adding their numerators.

$$\frac{9+10}{30}$$

Add 9 and 10 to get 19.

$$\frac{19}{30}$$

Factor

$$\frac{19}{2 \cdot 3 \cdot 5} = 0.6333333333333333$$