# Compare and sort in ascending order the two common ordinary fractions, which one is larger: ^{2,910}/_{3,205} and ^{2,917}/_{3,209}. Common ordinary fractions compared and sorted in ascending order, result explained below

## Compare: ^{2,910}/_{3,205} and ^{2,917}/_{3,209}

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

## The operation of comparing fractions:

^{2,910}/_{3,205} and ^{2,917}/_{3,209}

### Simplify the operation

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

#### By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.

#### To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.

^{2,910}/_{3,205} = ^{(2 × 3 × 5 × 97)}/_{(5 × 641)} = ^{((2 × 3 × 5 × 97) ÷ 5)}/_{((5 × 641) ÷ 5)} = ^{582}/_{641}

^{2,917}/_{3,209} is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:

2,917 is a prime number.

3,209 is a prime number.

## To compare and sort the fractions, make their numerators the same.

### To make the fractions' numerators the same - we have to:

#### 1) calculate their common numerator

#### 2) then calculate the expanding number of each fraction

#### 3) then make their numerators the same by expanding the fractions to equivalent forms, which all have equal numerators

### Calculate the common numerator

#### The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.

#### The LCM will be the common numerator of the compared fractions.

#### To calculate the LCM, we need the prime factorization of the numerators:

#### 582 = 2 × 3 × 97

#### 2,917 is a prime number.

#### 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 (582, 2917) = 2 × 3 × 97 × 2,917 = 1,697,694

### Calculate the expanding number of each fraction:

#### Divide the LCM by the numerator of each fraction.

^{582}/_{641} : 1,697,694 ÷ 582 = (2 × 3 × 97 × 2,917) ÷ (2 × 3 × 97) = 2,917

^{2,917}/_{3,209} : 1,697,694 ÷ 2,917 = (2 × 3 × 97 × 2,917) ÷ 2,917 = 582

### Make the fractions' numerators the same:

#### 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 numerator:

^{582}/_{641} = ^{(2,917 × 582)}/_{(2,917 × 641)} = ^{1,697,694}/_{1,869,797}

^{2,917}/_{3,209} = ^{(582 × 2,917)}/_{(582 × 3,209)} = ^{1,697,694}/_{1,867,638}

### The fractions have the same numerator, compare their denominators.

#### The larger the denominator the smaller the positive fraction.

#### The larger the denominator the larger the negative fraction.

## ::: The operation of comparing fractions :::

The final answer:

## The fractions sorted in ascending order:

^{1,697,694}/_{1,869,797} < ^{1,697,694}/_{1,867,638}

The initial fractions sorted in ascending order:

^{2,910}/_{3,205} < ^{2,917}/_{3,209}

#### 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 common ordinary fractions, online calculator: