Question

Which are larger: proper fractions, or improper fractions?

Answer 1

Improper fractions are larger.

Explanation:

By definition, an improper fraction is a fraction where the numerator (top number) is at least as large as the denominator (bottom number). Because of this, an improper fraction will always be at least 1 (or at most -1, if it's negative). Examples: `14/5, 4/3, -7/4, 6/6.`

A proper fraction is a fraction where the numerator is smaller than the denominator. It is proper because it represents what most people associate with a fraction; that is, a few pieces of a whole. As such, a proper fraction will always be smaller than 1 (or greater than -1, if it's negative). Examples: `6/11, 5/7, -1/2.`

A fraction equivalent to 0 is neither proper nor improper.

Since (positive) improper fractions are greater than 1, and (positive) proper fractions are less than 1, improper fractions will always be greater than proper ones.

This inequality is true for positive fractions:

`0 < color(white)[color(black)(("proper"),("fractions"))] < 1 <= color(white)[color(black)(("improper"),("fractions"))]`