Comparing & Ordering
📋 What it is
To compare fractions, give them the same denominator (or compare to a benchmark like 1/2), then the bigger numerator wins.
🗣️ Coach says
You can’t compare slices from differently-cut pizzas by eye. Make the bottoms match — a common denominator — and then it’s just comparing the tops. Or use a benchmark: is each one above or below 1/2?
🧠 Memory hook
Match the bottoms, then race the tops. Or ask: “above or below one-half?”
😂 Giggle
Why did the numerator break up with the denominator?
Because it felt like it was being divided!
😲 Whoa!
A common denominator is really just re-cutting both pizzas into the SAME number of slices so you can finally count fairly.
✅ Quick check: Which is bigger, 2/3 or 3/5? Make the bottoms match.
Say your answer out loud first — then reveal.
2/3 — with a common denominator of 15 they are 10/15 vs 9/15, so 2/3 is larger.
Equal denominators make the numerators directly comparable.
🪄 Trick question: A friend says 1/8 is bigger than 1/3 because 8 is bigger than 3. Right?
Careful — think it through, then reveal.
No — with the same numerator, a BIGGER bottom means SMALLER pieces, so 1/3 > 1/8.
More equal parts means each part is smaller.
🧪 Try it! (2 minutes)
Line up 1/2, 3/4, and 2/5 smallest to largest using a common denominator OR the “above/below 1/2” trick. Check on a number line.