## Fractions reducing to lower terms (simplifying). Equivalent fractions

### Let's learn by an example, let's simplify the fraction: ^{12}/_{16}

**Numerator of the fraction.**The number that is above the fraction bar, 12, is called the numerator of the fraction;**Denominator of the fraction.**The number that is below the fraction bar, 16, is called the denominator of the fraction;**The value of the fraction.**Fraction^{12}/_{16}shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:- 12 ÷ 16 = 0.75
- We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
^{12}/_{16}=^{(12 ÷ 2)}/_{(16 ÷ 2)}=^{6}/_{8}- The value of the fraction
^{6}/_{8}is calculated as: - 6 ÷ 8 = 0.75
- We notice that the value of the fraction
^{6}/_{8}is equal to that of the fraction^{12}/_{16}, namely 0.75 **Reduced (simplified) fraction**,**Equivalent fraction.**The new fraction,^{6}/_{8}, is equivalent to the original one,^{12}/_{16}, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.**Common factor (divisor).**The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.- Find all the divisors of a number or all the common factors of two numbers, online.
- The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
- We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
^{6}/_{8}=^{(6 ÷ 2)}/_{(8 ÷ 2)}=^{3}/_{4}- The value of the fraction
^{3}/_{4}is calculated as: - 3 ÷ 4 = 0.75
- The new fraction,
^{3}/_{4}, is a reduced fraction (a simplified fraction) and an equivalent of the fractions^{12}/_{16}and^{6}/_{8} **Irreducible fraction.**Fraction^{3}/_{4}is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.### Reduce fractions to lower terms (simplify), online, with explanations.