Flutter Through Fractions: The Butterfly Method!

Do you ever get tangled up adding or subtracting fractions with different denominators? What if there was a magical way to fly through them without finding the dreaded common denominator first?

Subject: mental-calculation • Classes: 6–12 • Difficulty: intermediate

The Trick

The 'Butterfly Method' helps you quickly add or subtract two fractions! Imagine two fractions like $\frac{a}{b} + \frac{c}{d}$. 1. Draw 'wings' by multiplying diagonally: $a \times d$ and $b \times c$. 2. Draw an 'antennae' by multiplying the denominators: $b \times d$. 3. The new numerator is the sum/difference of your 'wing' products: $(a \times d) \pm (b \times c)$. 4. The new denominator is the 'antennae' product: $b \times d$. Why it works: This method is a visual shortcut for finding a common denominator. $(a \times d)$ is equivalent to $a/b$ when multiplied by $d/d$, and $(b \times c)$ is equivalent to $c/d$ when multiplied by $b/b$. Both fractions get a common denominator of $b \times d$.

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