## Executed (ordinary fractions) operation:

^{3}/_{4} - ^{1}/_{16}

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

#### Fraction: ^{3}/_{4} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

3 is a prime number and 4 = 2^{2};

#### Fraction: - ^{1}/_{16} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

1 cannot be prime factorized and 16 = 2^{4};

### Calculate LCM, the lowest common multiple of the reduced fractions' denominators, this will be the common denominator of fractions, also called LCD, the lowest common denominator:

#### Denominators' prime factorization:

#### 4 = 2^{2};

#### 16 = 2^{4};

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

#### LCM (4; 16) = 2^{4} = 16

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

#### For fraction ^{3}/_{4} is 16 ÷ 4 = 2^{4} ÷ 2^{2} = 4;

#### For fraction - ^{1}/_{16} is 16 ÷ 16 = 1;

### Expand fractions, build up each fraction by multiplying its numerator and denominator by its expanding number so the denominator is built up to the LCM, then work with numerators:

#### ^{3}/_{4} - ^{1}/_{16} =

^{(4 * 3)}/_{(4 * 4)} - ^{(1 * 1)}/_{(1 * 16)} =

^{12}/_{16} - ^{1}/_{16} =

^{(12 - 1)}/_{16} =

^{11}/_{16}

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

#### ^{11}/_{16} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

11 is a prime number and 16 = 2^{4};

### Rewrite result:

#### 11 ÷ 16 = 0.6875 as a decimal number.

## Final answer:

:: written in two ways ::