Compare and sort in ascending order the two common ordinary fractions, which one is larger: ^{- 8}/₄₅ and ^{- 13}/₅₄. Common ordinary fractions compared and sorted in ascending order, result explained below

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

By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.

To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.

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

- ⁸/₄₅ is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
8 = 2³
45 = 3² × 5

- ¹³/₅₄ is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
13 is a prime number.
54 = 2 × 3³

1) calculate their common numerator

2) then calculate the expanding number of each fraction

3) then make 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:

8 = 2³

13 is a prime number.

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).

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

LCM (8, 13) = 2³ × 13 = 104

Divide the LCM by the numerator of each fraction.

- ⁸/₄₅ : 104 ÷ 8 = (2³ × 13) ÷ 2³ = 13

- ¹³/₅₄ : 104 ÷ 13 = (2³ × 13) ÷ 13 = 8

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:

- ⁸/₄₅ = - ^{(13 × 8)}/_{(13 × 45)} = - ¹⁰⁴/₅₈₅

- ¹³/₅₄ = - ^{(8 × 13)}/_{(8 × 54)} = - ¹⁰⁴/₄₃₂

The larger the denominator the larger the negative fraction.

The larger the denominator the smaller the positive fraction.

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