# Sort the Common Fractions String ^{42}/_{23}, ^{33}/_{42}, ^{22}/_{36} in Ascending Order. Online Calculator

## The operation of sorting fractions in ascending order:

^{42}/_{23}, ^{33}/_{42}, ^{22}/_{36}

### Analyze the fractions to be compared and ordered, by category:

#### positive proper fractions: ^{33}/_{42}, ^{22}/_{36}

#### 1 positive improper fraction: ^{42}/_{23}

### How to compare and sort the fractions in ascending order, by categories:

#### - any positive proper fraction is smaller than...

#### - any positive improper fraction.

## Sort the positive proper fractions in ascending order:

^{33}/_{42} and ^{22}/_{36}

### Simplify the operation

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

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

^{33}/_{42} = ^{(3 × 11)}/_{(2 × 3 × 7)} = ^{((3 × 11) ÷ 3)}/_{((2 × 3 × 7) ÷ 3)} = ^{11}/_{14}

^{22}/_{36} = ^{(2 × 11)}/_{(22 × 32)} = ^{((2 × 11) ÷ 2)}/_{((22 × 32) ÷ 2)} = ^{11}/_{18}

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

#### This is one of the simplest cases when it comes to comparing and sorting fractions.

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

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

## The fractions sorted in ascending order:

^{11}/_{18} < ^{11}/_{14}

The initial fractions sorted in ascending order:

^{22}/_{36} < ^{33}/_{42}

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

The final answer:

## Sort the positive proper fractions in ascending order:

^{22}/_{36} < ^{33}/_{42}

All the fractions sorted in ascending order:

^{22}/_{36} < ^{33}/_{42} < ^{42}/_{23}

#### 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.

## Compare and sort common fractions, online calculator: