# Compare and sort in ascending order the two common ordinary fractions, which one is larger: ^{25}/_{45} and ^{29}/_{49}. Common ordinary fractions compared and sorted in ascending order, result explained below

## Compare: ^{25}/_{45} and ^{29}/_{49}

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

## The operation of comparing fractions:

^{25}/_{45} and ^{29}/_{49}

### 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.

^{25}/_{45} = ^{52}/_{(32 × 5)} = ^{(52 ÷ 5)}/_{((32 × 5) ÷ 5)} = ^{5}/_{9}

^{29}/_{49} is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:

29 is a prime number.

49 = 7^{2}

## 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:

#### 5 is a prime number.

#### 29 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 (5, 29) = 5 × 29 = 145

### Calculate the expanding number of each fraction:

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

^{5}/_{9} : 145 ÷ 5 = (5 × 29) ÷ 5 = 29

^{29}/_{49} : 145 ÷ 29 = (5 × 29) ÷ 29 = 5

### 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:

^{5}/_{9} = ^{(29 × 5)}/_{(29 × 9)} = ^{145}/_{261}

^{29}/_{49} = ^{(5 × 29)}/_{(5 × 49)} = ^{145}/_{245}

### 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:

^{145}/_{261} < ^{145}/_{245}

The initial fractions sorted in ascending order:

^{25}/_{45} < ^{29}/_{49}

#### 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: