Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
The fraction: 62/93
- The prime factorizations of the numerator and denominator:
- 62 = 2 × 31
- 93 = 3 × 31
- 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 (62; 93) = 31
62/93 = (62 ÷ 31)/(93 ÷ 31) = 2/3
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
62/93 = (2 × 31)/(3 × 31) = ((2 × 31) ÷ 31)/((3 × 31) ÷ 31) = 2/3
The fraction: 66/99
- 66 = 2 × 3 × 11
- 99 = 32 × 11
- GCF (66; 99) = 3 × 11 = 33
66/99 = (66 ÷ 33)/(99 ÷ 33) = 2/3
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
66/99 = (2 × 3 × 11)/(32 × 11) = ((2 × 3 × 11) ÷ (3 × 11))/((32 × 11) ÷ (3 × 11)) = 2/3
The fractions are equal.
This is one of the simplest cases when comparing two fractions.
Not only are the numerators of the fractions equal but their denominators are also equal.
::: The operation of comparing fractions :::
The final answer: