Benchmark Fractions: A Simple Definition

Is it near 0, 1/2 or 1?

Look at the top compared with the bottom. If the top is tiny next to the bottom, it's near 0, as with 1/9. If the top is about half of the bottom, it's near 1/2, as with 4/9 or 5/9. If the top is nearly the bottom, it's near 1, as with 8/9. A quick trick for 1/2: double the top. If that's more than the bottom, the fraction is over half.

Comparing with benchmarks

Which is bigger, 3/7 or 5/8? Double the tops: 6 is less than 7, so 3/7 is under half. 10 is more than 8, so 5/8 is over half. Done, with no common denominator needed. It also works near 1: 7/8 and 5/6 are each one piece short of a whole, and an eighth is smaller than a sixth, so 7/8 is bigger.

Estimating sums

Benchmarks catch silly answers. 3/8 + 4/9 is a bit under 1/2 plus a bit under 1/2, so the answer must be a bit under 1. If you get 7/17, which is less than a half, something went wrong. That sense of “does this make sense?” is worth more than any single rule.

How to do it with Fraction Bakery

1. Look at the fraction wall: which bricks end before the 1/2 line?
2. Each fraction's page says whether it's bigger or smaller than 1/2, and why.
3. Play Bigger Slice: the toughest pairs sit on either side of 1/2.
4. Try Delivery Line in the game, which puts fractions on a number line.

Questions people ask