# Compare and sort in ascending order the two common ordinary fractions, which one is larger: ^{46}/_{60} and ^{53}/_{67}. Common ordinary fractions compared and sorted in ascending order, result explained below

## Compare: ^{46}/_{60} and ^{53}/_{67}

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

## The operation of comparing fractions:

^{46}/_{60} and ^{53}/_{67}

### 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.

^{46}/_{60} = ^{(2 × 23)}/_{(22 × 3 × 5)} = ^{((2 × 23) ÷ 2)}/_{((22 × 3 × 5) ÷ 2)} = ^{23}/_{30}

^{53}/_{67} is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:

53 is a prime number.

67 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:

#### 23 is a prime number.

#### 53 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 (23, 53) = 23 × 53 = 1,219

### Calculate the expanding number of each fraction:

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

^{23}/_{30} : 1,219 ÷ 23 = (23 × 53) ÷ 23 = 53

^{53}/_{67} : 1,219 ÷ 53 = (23 × 53) ÷ 53 = 23

### 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:

^{23}/_{30} = ^{(53 × 23)}/_{(53 × 30)} = ^{1,219}/_{1,590}

^{53}/_{67} = ^{(23 × 53)}/_{(23 × 67)} = ^{1,219}/_{1,541}

### 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:

^{1,219}/_{1,590} < ^{1,219}/_{1,541}

The initial fractions sorted in ascending order:

^{46}/_{60} < ^{53}/_{67}

#### 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: