## Executed (ordinary fractions) operation:

^{2}/_{5} - ^{3}/_{10}

### Reduce (simplify) fractions to their lowest terms equivalents:

#### Fraction: ^{2}/_{5} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

2 is a prime number and 5 is a prime number;

#### Fraction: - ^{3}/_{10} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

3 is a prime number and 10 = 2 * 5;

### LCM (lowest common multiple) of the reduced fractions' denominators will be the common denominator of the fractions we work with:

#### Denominators' prime factorization:

#### 5 is a prime number;

#### 10 = 2 * 5;

#### For LCM, take all the unique prime factors, by the largest exponents:

#### LCM (5; 10) = 2 * 5 = 10

### Each fraction's expanding number (divide LCM by each fraction's denominator):

#### For fraction ^{2}/_{5} is 10 ÷ 5 = (2 * 5) ÷ 5 = 2;

#### For fraction - ^{3}/_{10} is 10 ÷ 10 = 1;

### Expand fractions to make the denominators the same, then work with numerators:

#### ^{2}/_{5} - ^{3}/_{10} =

^{(2 * 2)}/_{(2 * 5)} - ^{(1 * 3)}/_{(1 * 10)} =

^{4}/_{10} - ^{3}/_{10} =

^{(4 - 3)}/_{10} =

^{1}/_{10}

### Reduce (simplify) fraction to its lowest terms equivalent:

#### ^{1}/_{10} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

1 cannot be prime factorized and 10 = 2 * 5;

### Rewrite result:

#### 1 ÷ 10 = 0.1 as a decimal number.

## Final answer:

:: written in two ways ::