To reduce, or simplify a fraction, we need to factor the numerator and the denominator.

And if you want to factor a natural number you need to write it as a multiplication of prime numbers. For instance, 14 can be factored as 2x7 (2 and 7 are prime numbers). In the statement 2x7: 2 and 7 are called the factors and 14 is the product.

It is correct if you write 14 as 1x2x7 and 1, 2 and 7 are all factors - but only 2 and 7 are prime numbers because 1 is NOT a prime number.

Two fractions are equivalent if they represent the same value, the same number. When you write an equivalent fraction with the lowest possible denominator you reduce the fraction.

A fraction is reduced to its lowest terms when the numerator and the denominator have no commons factors other than 1.

For example, to reduce the fraction 23/46 remove the commom factor 23 in both numerator and denominator:

Other examples:

You can speed up the process by dividing the denominator and numerator of the fraction by the greatest common factor of them. The greatest common factor of two or more integers is the largest counting number (natural number) that divides all the considered numbers.

• The greatest common factor of 23 and 46 is 23.
• The greatest common factor of 45 and 27 is 9.
• The greatest common factor of 12 and 20 is 4.

		simplifying a fraction
	To reduce a fraction to its lowest terms, divide both the numerator and the denominator by their greatest common factor.