Solve (1/1-3/5)-(2/10-4/1)

$$( \frac{ 1 }{ 1 } - \frac{ 3 }{ 5 } )-( \frac{ 2 }{ 10 } - \frac{ 4 }{ 1 } )$$

Evaluate

$$\frac{21}{5}=4.2$$

Solution Steps

Divide 1 by 1 to get 1.

$$1-\frac{3}{5}-\left(\frac{2}{10}-\frac{4}{1}\right)$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{5}-\frac{3}{5}-\left(\frac{2}{10}-\frac{4}{1}\right)$$

Since \frac{5}{5} and \frac{3}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-3}{5}-\left(\frac{2}{10}-\frac{4}{1}\right)$$

Subtract 3 from 5 to get 2.

$$\frac{2}{5}-\left(\frac{2}{10}-\frac{4}{1}\right)$$

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

$$\frac{2}{5}-\left(\frac{1}{5}-\frac{4}{1}\right)$$

Anything divided by one gives itself.

$$\frac{2}{5}-\left(\frac{1}{5}-4\right)$$

Convert 4 to fraction \frac{20}{5}.

$$\frac{2}{5}-\left(\frac{1}{5}-\frac{20}{5}\right)$$

Since \frac{1}{5} and \frac{20}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 20 from 1 to get -19.

$$\frac{2}{5}-\left(-\frac{19}{5}\right)$$

The opposite of -\frac{19}{5} is \frac{19}{5}.

$$\frac{2}{5}+\frac{19}{5}$$

Since \frac{2}{5} and \frac{19}{5} have the same denominator, add them by adding their numerators.

$$\frac{2+19}{5}$$

Add 2 and 19 to get 21.

$$\frac{21}{5}$$

Factor

$$\frac{3 \cdot 7}{5} = 4\frac{1}{5} = 4.2$$