Compare the Two Common Fractions 123/109 and 130/111, Which One is Larger? Online Calculator
Fractions 123/109 and 130/111 are compared by building equivalent fractions, which have either equal denominators or equal numerators
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
123/109 and 130/111
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: 123/109
123/109 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 123 = 3 × 41
- 109 is a prime number.
- GCF (123; 109) = 1
The fraction: 130/111
130/111 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 130 = 2 × 5 × 13
- 111 = 3 × 37
- GCF (130; 111) = 1
To compare and sort the fractions, make their denominators the same.
To make the fractions' denominators the same - we have to:
- 1) calculate their common denominator
- 2) then calculate the expanding number of each fraction
- 3) expand the fractions to equivalent forms having the same denominator
Calculate the common denominator
The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
To calculate the LCM, we need the prime factorization of the denominators:
109 is a prime number.
111 = 3 × 37
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 (109, 111) = 3 × 37 × 109 = 12,099
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
123/109 ⟶ 12,099 ÷ 109 = (3 × 37 × 109) ÷ 109 = 111
130/111 ⟶ 12,099 ÷ 111 = (3 × 37 × 109) ÷ (3 × 37) = 109
Make the denominators of the fractions the same:
- Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated above.
- This way all the fractions will have the same denominator:
123/109 = (111 × 123)/(111 × 109) = 13,653/12,099
130/111 = (109 × 130)/(109 × 111) = 14,170/12,099
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
The larger the numerator the smaller the negative fraction.
::: The operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
13,653/12,099 < 14,170/12,099
The initial fractions sorted in ascending order:
123/109 < 130/111
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.
Compare and sort common fractions, online calculator: