How to sort multiple fractions?

• To sort fractions easier, first, we must place them into categories: positive and negative fractions, improper and proper fractions.
• As a general rule:
  • any positive improper fraction is larger...
  • ... than any positive proper fraction, which is larger...
  • ... than zero, which is larger...
  • ... than any negative proper fraction, which is larger...
  • ... than any negative improper fraction.
• If the fractions to be compared and sorted are all from different categories, then our work is very easy, just follow the rule above.
• If we have more than one fraction in each category, first, we must compare the fractions in each category, then sort them by following the rule above.
• Below we will sort in ascending order three positive proper fractions.

Learn how to compare ordinary fractions. Steps. Examples.

An example of sorting three positive proper fractions that have unlike denominators and numerators, with explanations:

• ¹/₂ vs. ¹⁶/₂₄ vs. ⁴⁵/₇₅

• Reduce (simplify) each fraction to the lowest terms:

  • Factor the numerator and the denominator of each fraction, break them down to prime factors.
  • Factor numbers, break them down to prime factors, online.
  • Divide the numerator and denominator of each fraction by the GCF, the greatest common factor. GCF is the product of all the common prime factors of the numerator and the denominator, multiplied by the smallest exponents - this is the greatest common factor, GCF;
  • Calculate the greatest common factor (GCF), online.
  • Reduce fraction ¹/₂ - the numerator and the denominator are coprime numbers, they don't have any common prime factors and as a result the fraction cannot be reduced (simplified), it's irreducible.
  • Reduce fraction ¹⁶/₂₄ = ²⁴ / _{(2³ × 3)} = ^{(24 ÷ 23)} / _{((2³ × 3) ÷ 2³)} = ²/₃
  • Reduce fraction ⁴⁵/₇₅ = ^{(32 × 5)} / _{(3 × 5²)} = ^{((32 × 5) ÷ (3 × 5))} / _{((3 × 5²) ÷ (3 × 5))} = ³/₅
  • At this point, the three fractions are reduced to the lowest terms (simplified):
  • ¹/₂, ¹⁶/₂₄ = ²/₃, ⁴⁵/₇₅ = ³/₅
  • Reduce (simplify) ordinary fractions, online.

The entire article: How to sort in ascending order fractions with unlike (different) numerators and denominators?

(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