Compute 76 × 24 two different ways

Question

Solve in your head. What is 76 	imes 24? Aim: under 10 seconds.

Accepted Answer

Route 1, borrow a 25. 24 = 25 - 1, and multiplying by 25 is easy (	imes 100 / 4): 76 	imes 24 = 76 	imes 25 - 76 = \frac{7600}{4} - 76 = 1900 - 76 = 1824. Route 2, difference of squares. The factors straddle 50 at distance 26: 76 	imes 24 = 50^2 - 26^2 = 2500 - 676 = 1824. Route 1 is faster here because 26^2 is itself work; Route 2 wins when the offset is small. Takeaway. Factors like 24, 26, 49, 51 are round numbers in disguise. Check both "round one factor and correct" and "symmetric midpoint" before grinding, the best route depends on which correction is smaller.

Compute 76 × 24 two different ways

Your answer

More Mental Math questions