Solve (3/2+4/5-1/10):4+0,5:0,25

$$( \frac { 3 } { 2 } + \frac { 4 } { 5 } - \frac { 1 } { 10 } ) : 4 + 0,5 : 0,25$$

Evaluate

$$2,55$$

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{3}{2} and \frac{4}{5} to fractions with denominator 10.

$$\frac{\frac{15}{10}+\frac{8}{10}-\frac{1}{10}}{4}+\frac{0,5}{0,25}$$

Since \frac{15}{10} and \frac{8}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{15+8}{10}-\frac{1}{10}}{4}+\frac{0,5}{0,25}$$

Add 15 and 8 to get 23.

$$\frac{\frac{23}{10}-\frac{1}{10}}{4}+\frac{0,5}{0,25}$$

Since \frac{23}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{23-1}{10}}{4}+\frac{0,5}{0,25}$$

Subtract 1 from 23 to get 22.

$$\frac{\frac{22}{10}}{4}+\frac{0,5}{0,25}$$

Reduce the fraction \frac{22}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{11}{5}}{4}+\frac{0,5}{0,25}$$

Express \frac{\frac{11}{5}}{4} as a single fraction.

$$\frac{11}{5\times 4}+\frac{0,5}{0,25}$$

Multiply 5 and 4 to get 20.

$$\frac{11}{20}+\frac{0,5}{0,25}$$

Expand \frac{0,5}{0,25} by multiplying both numerator and the denominator by 100.

$$\frac{11}{20}+\frac{50}{25}$$

Divide 50 by 25 to get 2.

$$\frac{11}{20}+2$$

Convert 2 to fraction \frac{40}{20}.

$$\frac{11}{20}+\frac{40}{20}$$

Since \frac{11}{20} and \frac{40}{20} have the same denominator, add them by adding their numerators.

$$\frac{11+40}{20}$$

Add 11 and 40 to get 51.

$$\frac{51}{20}$$

Factor

$$\frac{3 \cdot 17}{5 \cdot 2 ^ {2}} = 2\frac{11}{20} = 2.55$$