Final answer:
Casey's multiplication strategy is an application of the distributive property, breaking down a larger multiplication problem into simpler parts that can be easily calculated and then combined, such as turning 6x7 into 5x7 plus 1x7 to get 42.
Step-by-step explanation:
Casey's strategy works because it involves breaking down a multiplication problem into simpler parts that are easier to compute, known as the distributive property.
When Casey breaks down 6x7 into 5x7 and 1x7, she is essentially decomposing the problem into two parts that she finds easier to add together afterwards. By doing so, she calculates 5x7 to get 35 and 1x7 to get 7, and then adds those two results together to get 42, which is the same as 6x7.
This strategy can be applied to other multiplication problems as well. For instance, if we were to break down 32 x 35, we could expand this to (3x3) x (3-3-3-3-3), which is equivalent to multiplying seven threes together, or 37. Our general rule when combining powers with the same base is xpxq = x(p+q).