Compare and sort in ascending order the two ordinary fractions, which one is larger: 127/1,000 and 1/8. Ordinary fractions compared and sorted in ascending order, result explained below

Compare: 127/1,000 and 1/8

The operation of comparing fractions:
127/1,000 and 1/8

Reduce (simplify) fractions to their lowest terms equivalents:

127/1,000 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
127 is a prime number;
1,000 = 23 × 53;


1/8 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
1 cannot be factored into other prime factors;
8 = 23;


>> Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions, build them up to the same numerator.

Expand the fraction that has 1 as a numerator.


Multiply the numerator and denominator by the same number:


1/8 = (127 × 1)/(127 × 8) = 127/1,016


The fractions have the same numerator, compare their denominators.

The larger the denominator the smaller the positive fraction.

::: Comparing operation :::
The final answer:

The fractions sorted in ascending order:
127/1,016 < 127/1,000

The initial fractions in ascending order:
1/8 < 127/1,000

More operations of this kind:

Compare and sort the fractions in ascending order:
127/1,000 and 130/1,007


Writing numbers: comma ',' used as a thousands separator;

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than;

Compare and sort ordinary fractions, online calculator

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see more... compared fractions
see more... sorted fractions

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) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers