To compare and sort multiple fractions, they should either have the same denominator or the same numerator.

³⁶⁶/₈₉₇ = ^{(2 × 3 × 61)}/_{(3 × 13 × 23)} = ^{((2 × 3 × 61) ÷ 3)}/_{((3 × 13 × 23) ÷ 3)} = ¹²²/₂₉₉

³⁷⁴/₉₀₁ = ^{(2 × 11 × 17)}/_{(17 × 53)} = ^{((2 × 11 × 17) ÷ 17)}/_{((17 × 53) ÷ 17)} = ²²/₅₃

Internal link > Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator

1) calculate their common numerator

2) then calculate the expanding number of each fraction

3) then build up their numerators the same by expanding the fractions to equivalent forms, which all have equal numerators

The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.

The LCM will be the common numerator of the compared fractions.

To calculate the LCM, we need the prime factorization of the numerators:

122 = 2 × 61

22 = 2 × 11

Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).

LCM (122, 22) = 2 × 11 × 61 = 1,342

External link > Calculate LCM, the least common multiple of numbers, online calculator

Divide the LCM by the numerator of each fraction.

¹²²/₂₉₉ : 1,342 ÷ 122 = (2 × 11 × 61) ÷ (2 × 61) = 11

²²/₅₃ : 1,342 ÷ 22 = (2 × 11 × 61) ÷ (2 × 11) = 61

Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.

This way all the fractions will have the same numerator:

¹²²/₂₉₉ = ^{(11 × 122)}/_{(11 × 299)} = ^1,342/_3,289

²²/₅₃ = ^{(61 × 22)}/_{(61 × 53)} = ^1,342/_3,233

The larger the denominator the smaller the positive fraction.

The larger the denominator the larger the negative fraction.

How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.