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.

• External link > 1) Calculate all the factors (divisors) of a number, or 2) Find all the common factors of two numbers, online calculator.

• 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 (simplify) common ordinary fractions to the lowest terms, to the simplest equivalent form, irreducible, with the smallest possible numerator and denominator. Online calculator

Read the rest of the article > How to reduce (simplify) common ordinary fractions to the lowest terms, to the simplest equivalent form, irreducible

(1) What is a fraction? Fractions types. How do they compare?

(2) Changing the form of fractions, by expanding or reducing (simplifying)

(3) How to reduce fractions (simplifying). The greatest common factor, GCF

(4) How to compare two fractions with unlike (different) numerators and denominators

(5) How to sort out fractions in ascending order

(6) Adding common (ordinary) fractions

(7) Subtracting common (ordinary) fractions

(8) Multiplying common (ordinary) fractions

(9) Fractions as rational numbers