Fractions with Variables

Algebra 1 · Axiom Academy

A fraction with letters in it follows the exact rules you already know for numbers — factor the top and bottom, then cancel what they share. You already simplify fractions. Watch why it works. Reducing a fraction like 12/18 isn't a magic trick — every time you do it, you're crossing out a factor that the top and bottom both contain. Pin down exactly what's happening here, and the whole idea of "fractions with variables" turns out to be the same move with a letter in place of a number. Press play: 12 and 18 each split into their prime factors. The 2 and the 3 they share light up — that shared part is the common factor — and canceling it from both the top and the bottom leaves the simplified fraction 2/3. Simplifying a fraction = deleting the factor the numerator and denominator have in common. Now slide a variable through the same fraction Here's a fraction with letters: x(x+2) over x(x−1) . Top and bottom both contain a factor of x — their common factor. Drag the slider to choose a value for x , and watch: the original fraction and the canceled form (x+2)/(x−1) always come out to the same number . Canceling the shared x never changed the value — it just made the fraction simpler. A variable fraction is just a numeric fraction you haven't chosen the number for yet — so the same canceling holds. Factor, then cancel — exactly like the numbers

This is the written version of the interactive lesson above. See the full Algebra 1 course.