Compare and sort in ascending order the two ordinary fractions, which one is larger: - 44/137 and - 52/142. Ordinary fractions compared and sorted in ascending order, result explained below

Compare: - 44/137 and - 52/142

The operation of comparing fractions:
- 44/137 and - 52/142

Reduce (simplify) fractions to their lowest terms equivalents:

- 44/137 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
44 = 22 × 11;
137 is a prime number;


- 52/142 = - (22 × 13)/(2 × 71) = - ((22 × 13) ÷ 2)/((2 × 71) ÷ 2) = - 26/71


>> 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:


44 = 22 × 11


26 = 2 × 13


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


LCM (44, 26) = 22 × 11 × 13 = 572

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: - 44/137 is 572 ÷ 44 = (22 × 11 × 13) ÷ (22 × 11) = 13


For fraction: - 26/71 is 572 ÷ 26 = (22 × 11 × 13) ÷ (2 × 13) = 22



Expand the fractions

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

- 44/137 = - (13 × 44)/(13 × 137) = - 572/1,781


- 26/71 = - (22 × 26)/(22 × 71) = - 572/1,562



The fractions have the same numerator, compare their denominators.

The larger the denominator the larger the negative fraction.

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

The fractions sorted in ascending order:
- 572/1,562 < - 572/1,781

The initial fractions in ascending order:
- 52/142 < - 44/137

More operations of this kind:

Compare and sort the fractions in ascending order:
- 52/142 and - 56/150


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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Tutoring: Comparing ordinary fractions

How to compare two fractions?

1. Fractions that have different signs:

2. A proper and an improper fraction:

3. Fractions that have both like numerators and denominators:

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

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

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