To reduce a fraction to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF
To calculate the greatest common factor, GCF:
- 1. Factor the numerator and the denominator (into prime factors), build their prime factorizations.
- 2. Multiply all their common prime factors, taken by the lowest exponents.
1. Factor the numerator and the denominator:
To factor a number (into prime factors) - or, in other words, to break it down to prime factors - or, in other words, to build its prime factorization: find the prime numbers that multiply together to get that number.
The prime factorizations:
54,999,989 = 11 × 4,999,999
54,999,989 is a composite number.
29,999,994 = 2 × 3 × 4,999,999
29,999,994 is a composite number.
2. Multiply all the common prime factors:
- Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
GCF (11 × 4,999,999; 2 × 3 × 4,999,999) = 4,999,999
Reduce (simplify) the common ordinary fraction: 54,999,989/29,999,994
Divide the numerator and the denominator by their GCF.
54,999,989/29,999,994 =
(54,999,989 ÷ 4,999,999) / (29,999,994 ÷ 4,999,999) =
11/6
Yet another method to reduce the fraction
To reduce a fraction without calculating the GCF: factor its numerator and denominator, then all the common prime factors are easily identified and crossed out.
54,999,989/29,999,994 =
(11 × 4,999,999)/(2 × 3 × 4,999,999) =
((11 × 4,999,999) ÷ 4,999,999) / ((2 × 3 × 4,999,999) ÷ 4,999,999) =
11/(2 × 3) =
11/6