Benchmark Fractions

Benchmark fractions: how to work them out

Benchmark fractions are common reference values that help you compare or estimate fractions quickly. Typical benchmarks are 0, 1/2, and 1. The main idea is to decide which benchmark a fraction is closest to, or whether it lies between two benchmarks.

1) Identify the numerator and denominator

A fraction like (a/b) means (a) parts out of (b) equal parts. Ask:

• Is it less than (1/2)?
• Is it exactly (1/2)?
• Is it between (1/2) and (1)?
• Is it equal to or greater than (1)?

2) Compare with benchmark fractions

To compare quickly, think in equivalent parts:

• For fractions with denominator 2, 4, 5, 10, etc., use familiar benchmarks.
• If the numerator is much smaller than the denominator, the fraction is near (0).
• If the numerator is about half the denominator, it is near (1/2).
• If the numerator equals the denominator, the fraction is (1).

3) Simplify exact answers

If the exercise asks for an exact answer, reduce the fraction to lowest terms by dividing numerator and denominator by their greatest common factor.

4) Check your answer

Make sure your simplified fraction has the same value as the original and that your benchmark choice makes sense. A quick estimate should match the exact result.

Useful habit

When in doubt, compare the fraction to (0), (1/2), and (1) before trying anything more complicated.