Fractions as Numbers

Pre-Algebra · Axiom Academy

A fraction is a number with its own place on the number line — the denominator splits the unit into equal parts, and the numerator counts them. 1. Fractions Live on the Number Line Whole numbers leave gaps between them. Fractions are numbers too, and they fill those gaps — each one a precise point, not just a symbol. Watch the spaces between 0 , 1 , and 2 fill in. 2. Building a Fraction: the Case of 3/4 Watch the unit from 0 to 1 divide into four equal parts, then count along — one, two, three: How many equal parts we count along. How many equal parts the unit is split into. 3. Proper Fractions: Between 0 and 1 A proper fraction has a numerator smaller than its denominator. Because we count fewer parts than the whole is split into, we never reach 1 — so a proper fraction always lands between 0 and 1 . Watch three of them get located by the same split-and-count. 4. Improper Fractions: Walking Past 1 What if we keep counting parts even after we reach a whole? An improper fraction has a numerator greater than or equal to its denominator. Take : split each unit into fourths and count seven of them. The fourth step reaches 1 , and the count keeps walking past it. 5. Mixed Numbers: the Same Point, Two Names Take : count seven thirds. The first three fill up to 1 , the next three fill up to 2 — that is 2 whole units — and the last single third is the leftover. So . You've seen that a fraction is a number with a place — built by splitting the unit and counting along.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.