Fractions shortcut
The butterfly method, explained.
What the butterfly (cross-multiply) method is, how it works, and when to use it for adding and subtracting fractions.
The butterfly method (also called the bowtie or cross-multiply method) is a popular shortcut for adding and subtracting two fractions. It's taught in many primary and elementary classrooms as a visual way to get started before learning the full common-denominator method.
How the butterfly method works
To add or subtract two fractions, say a/b and c/d:
- Cross-multiply the "wings": multiply a × d, and c × b. These give the two new numerators.
- Multiply the denominators: b × d gives the new bottom number.
- Add or subtract the two wing results over that denominator.
- Simplify the answer to lowest terms.
For example, for 1/2 + 1/3: the wings are 1×3 = 3 and 1×2 = 2; the new denominator is 2×3 = 6; so the answer is (3 + 2)/6 = 5/6.
Why it works
The butterfly method is really the common-denominator method in disguise. Multiplying the two denominators (b × d) always produces a shared denominator both fractions can use — it just isn't always the least common denominator, so you may need to simplify more at the end.
When to use it (and a caution)
The butterfly method is a helpful starting point, especially for younger learners, because it's quick and visual. But it has real limits worth knowing:
- It only works for two fractions at a time — it doesn't extend cleanly to three or more.
- Because it skips finding the least common denominator, answers often need more simplifying at the end.
- Many teachers treat it as a scaffold rather than a replacement, because understanding common denominators is a skill you'll need for later maths. If your teacher asks for the LCD method, use that — our calculator shows both.
Try it yourself
On our add fractions and subtract fractions calculators, use the Method switch above the steps to see any problem worked out the butterfly way or the standard LCD way, side by side with full step-by-step working.
Frequently asked
What is the butterfly method?
A shortcut for adding or subtracting two fractions: cross-multiply the numerators with the opposite denominators for the new top numbers, multiply the denominators for the new bottom, then combine and simplify.
Does the butterfly method always work?
It works for adding or subtracting any two fractions, but not for three or more at once. It also skips the least common denominator, so answers often need extra simplifying.
Is the butterfly method the same as cross-multiplying?
Yes — it's a visual way of remembering the cross-multiplication, with the crossing lines and denominators forming a butterfly or bowtie shape.
Should I use the butterfly method or LCD?
Use whichever your teacher asks for. The butterfly method is a quick starting shortcut; the LCD method builds understanding you'll need later. Our calculators show both.