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: - 99/44
- The prime factorizations of the numerator and denominator:
- 99 = 32 × 11
- 44 = 22 × 11
- 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 (99; 44) = 11
- 99/44 = - (99 ÷ 11)/(44 ÷ 11) = - 9/4
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
- 99/44 = - (32 × 11)/(22 × 11) = - ((32 × 11) ÷ 11)/((22 × 11) ÷ 11) = - 9/4
The fraction: - 108/48
- 108 = 22 × 33
- 48 = 24 × 3
- GCF (108; 48) = 22 × 3 = 12
- 108/48 = - (108 ÷ 12)/(48 ÷ 12) = - 9/4
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
- 108/48 = - (22 × 33)/(24 × 3) = - ((22 × 33) ÷ (22 × 3))/((24 × 3) ÷ (22 × 3)) = - 9/4
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: