Multiply 26 × 34 by finding the midpoint

Question

The factors 26 and 34 differ by 8, which hides that they are symmetric about a clean center. Solve in your head. What is 26 	imes 34? Aim: under 10 seconds.

Accepted Answer

Their midpoint is (26+34)/2 = 30, and each is 4 away. Use (30+4)(30-4) = 30^2 - 4^2: 26 	imes 34 = 900 - 16 = 884. So 26 	imes 34 = \mathbf{884}. Just "nine hundred minus sixteen." Check: 26 	imes 34 = 26 	imes 30 + 26 	imes 4 = 780 + 104 = 884. Matches. Takeaway. Even when the two numbers look far apart, average them: a round midpoint means 	ext{mid}^2 - 	ext{gap}^2 still applies.

Multiply 26 × 34 by finding the midpoint

Your answer

More Mental Math questions