How to compare two fractions?

1. Fractions that have different signs:

• Any positive fraction is larger than any negative fraction:
• ie: ⁴/₂₅ > - ¹⁹/₂

2. A proper and an improper fraction:

• Any positive improper fraction is larger than any positive proper fraction:
• ie: ⁴⁴/₂₅ > 1 > ¹⁹/₂₀₀
• Any negative improper fraction is smaller than any negative proper fraction:
• ie: - ⁴⁴/₂₅ < -1 < - ¹⁹/₂₀₀

3. Fractions that have both like numerators and denominators:

• The fractions are equal:
• ie: ⁸⁹/₅₀ = ⁸⁹/₅₀

4. Fractions that have unlike (different) numerators but like (equal) denominators.

• Positive fractions: compare the numerators, the larger fraction is the one with the larger numerator:
• ie: ²⁴/₂₅ > ¹⁹/₂₅
• Negative fractions: compare the numerators, the larger fraction is the one with the smaller numerator:
• ie: - ¹⁹/₂₅ < - ¹⁷/₂₅

5. Fractions that have unlike (different) denominators but like (equal) numerators.

• Positive fractions: compare the denominators, the larger fraction is the one with the smaller denominator:
• ie: ²⁴/₂₅ > ²⁴/₂₆
• Negative fractions: compare the denominators, the larger fraction is the one with the larger denominator:
• ie: - ¹⁷/₂₅ < - ¹⁷/₂₉

6. Fractions that have different denominators and numerators (unlike denominators and numerators).

• To compare them, fractions should be built up to the same denominator (or if it's easier, to the same numerator).

• ... Read the rest of this article, here: how to, comparing two fractions with unlike (different) numerators and denominators.

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

(2) Fractions changing form, expand and reduce (simplify) fractions

(3) Reducing fractions. The greatest common factor, GCF

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

(5) Sorting fractions in ascending order

(6) Adding ordinary (common, simple) fractions

(7) Subtracting ordinary (common, simple) fractions

(8) Multiplying ordinary (common, simple) fractions

(9) Fractions, theory: rational numbers