## To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

### Calculate the greatest (highest) common factor (divisor), gcf (gcd).

#### Integer numbers prime factorization:

#### 76 = 2^{2} × 19;

#### 12,000 = 2^{5} × 3 × 5^{3};

#### Take all the common prime factors, by the lowest exponents.

#### gcf, gcd (76; 12,000) = 2^{2} = 4;

### Calculate the greatest (highest) common factor (divisor), gcf (gcd)

### Divide both numerator and denominator by their greatest common factor.

^{76}/

_{12,000}=

^{(22 × 19)}/

_{(25 × 3 × 53)}=

^{((22 × 19) ÷ 2World Red Sweatshirt Boston Large Sox Crew At Branded Fanatics Navy – 2)}/

_{((25 × 3 × 53) ÷ 22)}=

^{World Red Sweatshirt Boston Large Sox Crew At Branded Fanatics Navy – 19}/

_{(23 × 3 × 53)}=

^{World Red Sweatshirt Boston Large Sox Crew At Branded Fanatics Navy – 19}/

_{3,000}

## Rewrite the end result:

### As a decimal number:

^{19}/

_{3,000}=

19 ÷ 3,000 =

**World Red Sweatshirt Boston Large Sox Crew At Branded Fanatics Navy –**0.006333333333 ≈

0.01

### As a percentage:

0.006333333333 =

0.006333333333 ×

0.633333333333% ≈

0.63%

0.006333333333 ×

^{100}/_{100}=^{0.633333333333}/_{100}=0.633333333333% ≈

0.63%

## Final answer:

:: written in three ways ::

## As a proper fraction

(numerator smaller than denominator):

^{76}/_{12,000} = ^{19}/_{3,000}

## As a decimal number:

^{76}/_{12,000} ≈ 0.01

## As a percentage:

^{76}/_{12,000} ≈ 0.63%

### How to reduce (simplify) fraction ^{76}/_{6,722} = ? ... ^{12,000}/_{76} = ?

## Online calculator: reduce (simplify) fractions

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### Why reducing (simplifying) fractions to lower terms?

- When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
- Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
- By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.