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.