Comparing and Ordering Fractions Calculator

How it works

Rewrite every fraction over the least common denominator (LCD = LCM of the denominators): a/b = (a × LCD/b)/LCD, then compare numerators · or cross-multiply two at a time: a/b < c/d ⇔ a·d < b·c (b, d > 0)

Fractions are easiest to compare when they share a denominator: then the one with the larger numerator is larger. The calculator finds the least common denominator (the LCM of all the denominators), rewrites each fraction over it, and sorts. Mixed numbers and decimals are converted to fractions first, equal values are joined with “=”, and every comparison is done in exact arithmetic.

Worked example

3/4, 5/8, 2/3 and 7/12 have LCD 24: 3/4 = 18/24, 5/8 = 15/24, 2/3 = 16/24 and 7/12 = 14/24. Ordering the numerators 14 < 15 < 16 < 18 gives 7/12 < 5/8 < 2/3 < 3/4. The difference between the largest and smallest is 18/24 − 14/24 = 1/6.

Sources: Common Core State Standards — 4.NF.2 (compare two fractions) · Khan Academy — Comparing fractions

Frequently asked questions