Compare and sort in ascending order the two common ordinary fractions, which one is larger: - 202/122 and - 205/126. Common ordinary fractions compared and sorted in ascending order, result explained below

Compare: - 202/122 and - 205/126

To compare and sort multiple fractions, they should either have the same denominator or the same numerator.

The operation of comparing fractions:
- 202/122 and - 205/126

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

- 202/122 = - (2 × 101)/(2 × 61) = - ((2 × 101) ÷ 2)/((2 × 61) ÷ 2) = - 101/61


- 205/126 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
205 = 5 × 41
126 = 2 × 32 × 7




To compare and sort the fractions, build them up to the same denominator.

To build the fractions up to the same denominator we have to:

1) calculate their common denominator


2) then calculate the expanding number of each fraction


3) then build up their denominators the same by expanding the fractions to equivalent forms, which all have equal denominators

Calculate the common denominator

The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.


The LCM will be the common denominator of the compared fractions.


To calculate the LCM, we need the prime factorization of the denominators:


61 is a prime number.


126 = 2 × 32 × 7


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 (61, 126) = 2 × 32 × 7 × 61 = 7,686


External link > Calculate LCM, the least common multiple of numbers, online calculator


Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.


- 101/61 : 7,686 ÷ 61 = (2 × 32 × 7 × 61) ÷ 61 = 126


- 205/126 : 7,686 ÷ 126 = (2 × 32 × 7 × 61) ÷ (2 × 32 × 7) = 61



Build up the fractions to the same common denominator:

Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.


This way all the fractions will have the same denominator:


- 101/61 = - (126 × 101)/(126 × 61) = - 12,726/7,686


- 205/126 = - (61 × 205)/(61 × 126) = - 12,505/7,686



The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.


The larger the numerator the larger the positive fraction.


::: The operation of comparing fractions :::
The final answer:

The fractions sorted in ascending order:
- 12,726/7,686 < - 12,505/7,686

The initial fractions sorted in ascending order:
- 202/122 < - 205/126

How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

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Compare and sort common ordinary fractions, online calculator:

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) fractions / theory:

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


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


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


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers