Multiply 44 × 46 in two glances

Question

44 and 46 share a tens digit and their units add to 10, the ideal setup for the split trick. Solve in your head. What is 44 	imes 46? Aim: under 10 seconds.

Accepted Answer

Tens digit 4, units 4 + 6 = 10. Front is 4 	imes 5 = 20; back is 4 	imes 6 = 24: 44 	imes 46 = 2024. So 44 	imes 46 = \mathbf{2024}. Remember to pad the back part to two digits (here 24 already is). Difference-of-squares check: midpoint 45, gap 1, so 45^2 - 1 = 2025 - 1 = 2024. Confirmed. Takeaway. For same-tens numbers whose units sum to 10: front = a(a+1), back = b	imes c (two digits). It's also just 	ext{mid}^2 - 1 when the numbers are 2 apart.

Multiply 44 × 46 in two glances

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