# Compare, what fraction is larger? ^{1}/_{3} vs. ^{3}/_{8}. Fractions sorted in ascending order: ^{1}/_{3} < ^{3}/_{8}. Ordinary math fractions compared, result explained below

## Comparing fractions operation:

^{1}/_{3} vs. ^{3}/_{8}

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

#### ^{1}/_{3} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

1 cannot be prime factorized and 3 is a prime number;

#### ^{3}/_{8} already reduced to lowest terms, numerator and denominator have no common prime factors, their prime factorization:

3 is a prime number and 8 = 2^{3};

##### To sort fractions, build up their numerators the same.

### Expand the fraction having 1 as a numerator (build up fraction by multiplying its numerator and denominator by the same number), so that the numerators are the same:

#### ^{1}/_{3} = ^{(3 * 1)}/_{(3 * 3)} = ^{3}/_{9};

### Fractions have equal numerators, simply compare their denominators.

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

## ::: Comparing operation :::

Final answer:

## Fractions sorted in ascending order:

^{3}/_{9} < ^{3}/_{8}

Initial fractions in ascending order:

^{1}/_{3} < ^{3}/_{8}

#### Symbols: / fraction line; * multiply; = equal; < less than;

## Compare and sort ordinary fractions, online calculator

## Latest fractions compared or sorted in ascending order

## Tutoring: Comparing ordinary fractions

## How to compare two fractions?

### 1. EQUAL DENOMINATORS but unlike numerators fractions

- a) To compare two positive fractions that have EQUAL DENOMINATORS (like denominators) but different numerators (unlike numerators), simply compare the numerators: the larger fraction is the one with the larger numerator, ie:
^{24}/_{25} > ^{19}/_{25}
- b) To compare two negative fractions that have EQUAL DENOMINATORS (like denominators) but different numerators (unlike numerators), simply compare the numerators: the larger fraction is the one with the smaller numerator, ie: -
^{19}/_{25} < -^{17}/_{25}
- c) To compare two fractions of different signs (one positive and one negative) that have EQUAL DENOMINATORS (like denominators) but different numerators (unlike numerators), the rule is that any positive fraction is larger than any negative fraction, ie:
^{2}/_{25} > -^{1}/_{25}

### 2. EQUAL NUMERATORS but unlike denominators fractions

- a) To compare two positive fractions that have EQUAL NUMERATORS (like numerators) but different denominators (unlike denominators), simply compare the denominators: the larger fraction is the one with the smaller denominator, ie:
^{24}/_{25} > ^{24}/_{26}
- b) To compare two negative fractions that have EQUAL NUMERATORS (like numerators) but different denominators (unlike denominators), simply compare the denominators: the larger fraction is the one with the larger denominator, ie: -
^{17}/_{25} < -^{17}/_{29}
- c) To compare two fractions of different signs (one positive and one negative) that have EQUAL NUMERATORS (like numerators) but different denominators (unlike denominators), the rule is that any negative fraction is smaller than any positive fraction, ie: -
^{1}/_{25} < ^{1}/_{200}

### 3. Different denominators and numerators (unlike denominators and unlike numerators) fractions

- a) To compare two fractions of the same sign (both positive or both negative) that have different denominators and numerators (unlike denominators and unlike numerators), fractions should be brought to the same denominator (or if it's easier, to the same numerators). Please see the next paragraph, 3.a)
- b) To compare two fractions of different signs (one positive and one negative) that have different denominators and numerators (unlike denominators and unlike numerators), the rule is that any negative fraction is smaller than any positive fraction, ie: -
^{11}/_{24} < ^{10}/_{13}

### 3.a) How to compare two fractions of the same sign (both positive or both negative) that have unlike denominators and unlike numerators? Below, we will bring the fractions to the same denominator, but it's also possible to compare fractions by bringing them to the same numerator.

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