In 1st through 3rd grade, children are taught that "multiplication makes numbers bigger" (3 × 4 = 12). So when they reach 5th grade and calculate 1/2 × 1/4 = 1/8, their brain revolts: "Wait! 1/8 is smaller than 1/2. Did I do something wrong?"

Replace the Word "Times" with "Of"

The easiest way to resolve this confusion is language. In math, whenever you multiply by a fraction, replace the multiplication symbol with the word "OF":

  • 1/2 × 8 means "half OF 8" = 4.
  • 1/2 × 1/4 means "half OF a quarter".

If you have a quarter of a candy bar and you take half of it, of course you have a smaller piece! When students translate multiplication into "taking a part of something," the confusion disappears.