How do you add two fractions in your head with the butterfly method (no common denominator)?

Cross-multiply for the numerator, multiply the denominators: a/b + c/d = (ad + bc) / bd.

• ¾ + ⅖ → (3·5 + 4·2) / (4·5) = (15 + 8) / 20 = 23/20.
• ⅓ + ¼ → (1·4 + 3·1) / 12 = 7/12.

Check: 23/20 = 1.15 = 0.75 + 0.40. ✓ The same pattern with a minus subtracts: a/b − c/d = (ad − bc)/bd. Simplify the result at the end if it isn't already lowest terms.