Solve 10,1-(2,1:7-0,05):2=

$$10,1 - ( 2,1 : 7 - 0,05 ) : 2 =$$

Evaluate

$$9,975$$

Solution Steps

Expand \frac{2,1}{7} by multiplying both numerator and the denominator by 10.

$$10,1-\frac{\frac{21}{70}-0,05}{2}$$

Reduce the fraction \frac{21}{70} to lowest terms by extracting and canceling out 7.

$$10,1-\frac{\frac{3}{10}-0,05}{2}$$

Convert decimal number 0,05 to fraction \frac{5}{100}. Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$10,1-\frac{\frac{3}{10}-\frac{1}{20}}{2}$$

Least common multiple of 10 and 20 is 20. Convert \frac{3}{10} and \frac{1}{20} to fractions with denominator 20.

$$10,1-\frac{\frac{6}{20}-\frac{1}{20}}{2}$$

Since \frac{6}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$10,1-\frac{\frac{6-1}{20}}{2}$$

Subtract 1 from 6 to get 5.

$$10,1-\frac{\frac{5}{20}}{2}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$10,1-\frac{\frac{1}{4}}{2}$$

Express \frac{\frac{1}{4}}{2} as a single fraction.

$$10,1-\frac{1}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$10,1-\frac{1}{8}$$

Convert decimal number 10,1 to fraction \frac{101}{10}.

$$\frac{101}{10}-\frac{1}{8}$$

Least common multiple of 10 and 8 is 40. Convert \frac{101}{10} and \frac{1}{8} to fractions with denominator 40.

$$\frac{404}{40}-\frac{5}{40}$$

Since \frac{404}{40} and \frac{5}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{404-5}{40}$$

Subtract 5 from 404 to get 399.

$$\frac{399}{40}$$

Factor

$$\frac{3 \cdot 7 \cdot 19}{5 \cdot 2 ^ {3}} = 9\frac{39}{40} = 9.975$$