Compare and sort in ascending order the two ordinary fractions, which one is larger: 39/90 and 45/98. Ordinary fractions compared and sorted in ascending order, result explained below

Compare: 39/90 and 45/98

The operation of comparing fractions:
39/90 and 45/98

Reduce (simplify) fractions to their lowest terms equivalents:

39/90 = (3 × 13)/(2 × 32 × 5) = ((3 × 13) ÷ 3)/((2 × 32 × 5) ÷ 3) = 13/30


45/98 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
45 = 32 × 5;
98 = 2 × 72;


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


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

Calculate LCM, the least common multiple of the fractions' numerators

LCM will be the common numerator of the compared fractions.

The prime factorization of the numerators:


13 is a prime number


45 = 32 × 5


Multiply all the unique prime factors, by the largest exponents:


LCM (13, 45) = 32 × 5 × 13 = 585

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the numerator of each fraction:


For fraction: 13/30 is 585 ÷ 13 = (32 × 5 × 13) ÷ 13 = 45


For fraction: 45/98 is 585 ÷ 45 = (32 × 5 × 13) ÷ (32 × 5) = 13



Expand the fractions

Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and denominators by their expanding number:

13/30 = (45 × 13)/(45 × 30) = 585/1,350


45/98 = (13 × 45)/(13 × 98) = 585/1,274



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:
585/1,350 < 585/1,274

The initial fractions in ascending order:
39/90 < 45/98

More operations of this kind:

Compare and sort the fractions in ascending order:
45/98 and 53/103


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