## 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}