Stop Teaching the Butterfly Method: 5 Reasons It Hurts Fraction Sense (and What To Do Instead)

The Problem With “Butterfly”

The butterfly method tells students to cross-multiply numerators with opposite denominators, add or subtract, and toss the product of the denominators on the bottom. It “works” mechanically, but it bypasses the idea that fraction addition is about same-sized pieces. When students graduate to mixed numbers, three-fraction sums, or algebraic denominators, the trick collapses.

1) It ignores the common unit

Adding fractions means combining like units. The butterfly skips “equal pieces” entirely

What to say to students: “You can’t add fifths to tenths until you turn everything into the same unit.”

2) It inflates numbers unnecessarily

Butterfly always multiplies denominators, even when a smaller common denominator exists. Bigger numbers mean more arithmetic errors.

3) It encourages the wrong habits

Students learn “just cross something” and start canceling across addition, or they drop signs in subtraction.

We want: make equal units first, then combine. No crossing until you’re multiplying or simplifying factors.

4) It doesn’t scale well

Three fractions, mixed numbers, or like denominators? Butterfly turns into spaghetti (a mess).

5) It doesn’t prepare students for algebra

Adding rational expressions demands LCD thinking: factor, find the least common denominator, rewrite, then combine.

The Correct Way To Teach Adding/Subtracting Fractions

Core idea (say it every time)

Make the pieces match. Then combine.

Procedure students can remember

1. Find the LCD

2. Rewrite as equivalents with the LCD.

3. Add/subtract numerators, keep the denominator.

4. Simplify, if possible.

Remember: We don’t draw butterflies. We match units first, then add or subtract. That’s how fractions work, and it’s the same idea you’ll need for algebra!

Bottom line

Butterfly is a shortcut that skips the concept. If you want durable understanding that scales to algebra, teach students to make the pieces the same size and then combine. That’s math, not a drawing.