# Compare and sort in ascending order the two common ordinary fractions, which one is larger: 71 and ^{76}/_{3}. Common ordinary fractions compared and sorted in ascending order, result explained below

## Compare: 71 and ^{76}/_{3}

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

## The operation of comparing fractions:

71 and ^{76}/_{3}

### Simplify the operation

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

^{76}/_{3} is already reduced to the lowest terms.

The numerator and denominator have no common prime factors:

76 = 2^{2} × 19

3 is a prime number.

### To compare and sort the fractions, build them up to the same denominator.

#### Expand the fraction that has 1 as a denominator.

#### Multiply the numerator and denominator by the same number:

#### 71 = ^{(3 × 71)}/_{(3 × 1)} = ^{213}/_{3}

### The fractions have the same denominator, compare their numerators.

#### The larger the numerator the larger the positive fraction.

#### The larger the numerator the smaller the negative fraction.

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

The final answer:

## The fractions sorted in ascending order:

^{76}/_{3} < ^{213}/_{3}

The initial fractions sorted in ascending order:

^{76}/_{3} < 71

#### 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:

## The latest common ordinary fractions compared and sorted in ascending order

** Compare and sort the fractions: 71 and **^{76}/_{3} | *Sep 22 18:51 UTC (GMT) * |

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** See all the common ordinary fractions sorted in ascending order... ** |

## Tutoring: Comparing ordinary fractions

### How to compare two fractions?

#### 1. Fractions that have different signs:

- Any positive fraction is larger than any negative fraction:
- ie:
^{4}/_{25} > - ^{19}/_{2}

#### 2. A proper and an improper fraction:

- Any positive improper fraction is larger than any positive proper fraction:
- ie:
^{44}/_{25} > 1 > ^{19}/_{200} - Any negative improper fraction is smaller than any negative proper fraction:
- ie: -
^{44}/_{25} < -1 < - ^{19}/_{200}

#### 3. Fractions that have both like numerators and denominators:

- The fractions are equal:
- ie:
^{89}/_{50} = ^{89}/_{50}

#### 4. Fractions that have unlike (different) numerators but like (equal) denominators.

**Positive fractions**: compare the numerators, the larger fraction is the one with the larger numerator: - ie:
^{24}/_{25} > ^{19}/_{25} **Negative fractions**: compare the numerators, the larger fraction is the one with the smaller numerator: - ie: -
^{19}/_{25} < - ^{17}/_{25}

#### 5. Fractions that have unlike (different) denominators but like (equal) numerators.

**Positive fractions**: compare the denominators, the larger fraction is the one with the smaller denominator: - ie:
^{24}/_{25} > ^{24}/_{26} **Negative fractions**: compare the denominators, the larger fraction is the one with the larger denominator: - ie: -
^{17}/_{25} < - ^{17}/_{29}

#### 6. Fractions that have different denominators and numerators (unlike denominators and numerators).

- To compare them, fractions should be built up to the same denominator (or if it's easier, to the same numerator).

## More on ordinary (common) fractions / theory: