Final answer:
To mentally calculate 29 × 40 using the distributive property, first calculate 30 × 40 (1200), then subtract 1 × 40 (40) to get 1160.
Step-by-step explanation:
To calculate 29 × 40 mentally using the distributive property, we can start by finding the product of 30 × 40, which is easier to compute. To apply the distributive property, we write 29 × 40 as (30 - 1) × 40. Since 30 × 40 = 1200, we then subtract 1 × 40 from this product, which is 40, to get the final answer. The calculation is represented as 29 × 40 = (30 × 40) - (1 × 40), which simplifies to 1200 - 40 = 1160.
Esteeming a slightly larger or smaller number to make the calculation easier is a method encouraged for mental mathematics, and it is supported by the fact that multiplication by a whole number is distributive over addition and subtraction.