Number & Operations—Fractions
Comparing Unlike Fractions
Comparing fractions with different numerators and denominators.
Prerequisites
- Equivalent Fractions
Comparing Fractions That Don't Match
Grade 3 compared fractions that already shared a numerator or a denominator. Most pairs of fractions don't start out that convenient — comparing them takes one extra step first, using equivalent fractions to make a fair comparison possible.
To compare two fractions with different numerators and different denominators, rewrite both as equivalent fractions that share the same denominator. Once the denominators match, comparing the numerators directly decides which fraction is larger.
Worked Example — Comparing with a Common Denominator
Worked Example — Comparing Using Benchmark Fractions
Tip
Common Mistakes
Comparing the numerators or denominators of two unlike fractions directly, without first rewriting them with a shared denominator.
Fractions can only be compared directly once they share the same denominator (or the same numerator) — find equivalent fractions with a common denominator first.
Choosing a common denominator that isn't actually reachable from both original denominators using a whole-number multiplier.
A valid common denominator must be a multiple of both original denominators — check that a whole number, not a fraction, connects each original denominator to the new one.
Key Takeaways
- Comparing fractions with different denominators requires first rewriting them with a shared, common denominator.
- Once the denominators match, the fraction with the larger numerator is larger.
- Comparing both fractions to a simple benchmark, like 1/2, can sometimes decide the comparison faster.
Summary
Finding a common denominator makes it possible to fairly compare any two fractions. The next lesson introduces a special case of equivalent fractions — ones with a denominator of 10 or 100 — written in an entirely new form called a decimal.
Sign in to track your progress and mark this lesson complete.
Track your progress