Compare the Two Common Fractions 120/160 and 126/168, Which One is Larger? Online Calculator

The operation of comparing fractions:
120/160 and 126/168

Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:


The fraction: 120/160

  • The prime factorizations of the numerator and denominator:
  • 120 = 23 × 3 × 5
  • 160 = 25 × 5
  • 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 (120; 160) = 23 × 5 = 40

120/160 = (120 ÷ 40)/(160 ÷ 40) = 3/4


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


120/160 = (23 × 3 × 5)/(25 × 5) = ((23 × 3 × 5) ÷ (23 × 5))/((25 × 5) ÷ (23 × 5)) = 3/4



The fraction: 126/168

  • 126 = 2 × 32 × 7
  • 168 = 23 × 3 × 7
  • GCF (126; 168) = 2 × 3 × 7 = 42

126/168 = (126 ÷ 42)/(168 ÷ 42) = 3/4


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


126/168 = (2 × 32 × 7)/(23 × 3 × 7) = ((2 × 32 × 7) ÷ (2 × 3 × 7))/((23 × 3 × 7) ÷ (2 × 3 × 7)) = 3/4




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:

The fractions sorted in ascending order:
3/4 = 3/4

The initial fractions sorted in ascending order:
120/160 = 126/168

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.

Other similar operations

Compare and sort the fractions in ascending order:
126/168 and 130/173

» New. All the Calculations Performed by Our Visitors: Common Fractions Compared and Sorted. Data organized on a Monthly Basis

Compare and sort common fractions, online calculator:

Tutoring: Comparing ordinary fractions

How to compare two fractions?

1. Fractions that have different signs:

  • Any positive fraction is larger than any negative fraction:
  • ie: 4/25 > - 19/2

2. A proper and an improper fraction:

  • Any positive improper fraction is larger than any positive proper fraction:
  • ie: 44/25 > 1 > 19/200
  • Any negative improper fraction is smaller than any negative proper fraction:
  • ie: - 44/25 < -1 < - 19/200

3. Fractions that have both like numerators and denominators:

  • The fractions are equal:
  • ie: 89/50 = 89/50

4. Fractions that have unlike (different) numerators but like (equal) denominators.

  • Positive fractions: compare the numerators, the larger fraction is the one with the larger numerator:
  • ie: 24/25 > 19/25
  • Negative fractions: compare the numerators, the larger fraction is the one with the smaller numerator:
  • ie: - 19/25 < - 17/25

5. Fractions that have unlike (different) denominators but like (equal) numerators.

  • Positive fractions: compare the denominators, the larger fraction is the one with the smaller denominator:
  • ie: 24/25 > 24/26
  • Negative fractions: compare the denominators, the larger fraction is the one with the larger denominator:
  • ie: - 17/25 < - 17/29

6. Fractions that have different denominators and numerators (unlike denominators and numerators).

More on ordinary (common) fractions / theory: