## 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).
#### ... Read the rest of this article, here: how to, comparing two fractions with unlike (different) numerators and denominators.