The 'Butterfly Method' for Fractions 🦋

Struggling with adding or subtracting fractions? There's a super-fast way to do it without finding common denominators!

Subject: algebra • Classes: 6–12 • Difficulty: basic (6-8)

The Trick

The 'Butterfly Method' simplifies adding/subtracting fractions. For $\frac{a}{b} \pm \frac{c}{d}$, cross-multiply: $a \times d$ and $b \times c$. These are the butterfly 'wings'. The sum/difference of the wings becomes the new numerator, and $b \times d$ is the new denominator. So, $\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$ and $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$. It works because it's a shortcut to finding a common denominator ($bd$).

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