Guide · a method explained
The Butterfly Method for Comparing Fractions
To compare 3/4 and 5/7, multiply across the diagonals: 3 × 7 = 21 on the left, 5 × 4 = 20 on the right. The bigger product marks the bigger fraction, so 3/4 > 5/7. It's quick and correct, but teach it after kids understand common denominators.
How it works
Write the two fractions side by side. Multiply the left top by the right bottom and write the answer on the left. Multiply the right top by the left bottom and write the answer on the right. Draw loops around the diagonals and you get butterfly wings, which is where the name comes from. If the two answers match, the fractions are equal: for 2/3 and 4/6, you get 12 and 12.
Why it works
It's a common denominator in disguise. Rewrite 3/4 and 5/7 with the bottom 4 × 7 = 28, and you get 21/28 and 20/28. The butterfly's numbers, 21 and 20, are exactly those new tops. Once the bottoms match, you only compare the tops, so the method skips writing the bottoms down.
When to use it, and when not to
It's a fine shortcut for kids who already understand fractions. The risk is teaching it first: kids can get right answers with no idea what the numbers mean, then mix it up with other tricks that also involve crossing things. Many pairs don't need it at all. 3/8 and 4/6 fall on either side of 1/2, and 1/5 and 1/9 share a top. Try the quicker methods first.
How to do it with Fraction Bakery
- Learn the four methods in the comparing lesson.
- Play Bigger Slice to build a feel for which fraction is bigger.
- Print comparing worksheets. Have kids estimate first, then check with the butterfly.
- Ask “how could you tell without calculating?” for any pair.
Questions people ask
Is the butterfly method the same as cross-multiplying?
Yes, for comparing. The butterfly name is just a way to remember which numbers to multiply.
Can the butterfly method add fractions too?
Yes: for a/b + c/d, the top is a × d + c × b and the bottom is b × d. It works, but it often needs simplifying afterward, and it hides what's going on.
Take the bakery with you, soon
A Fraction Bakery app for iPhone is on the way. The plan: offline play for the car, a parent report of which fractions have stuck, and the full bakery shelf of prizes. Until then, the whole game is free right here.
Coming soon on theApp Store