how does drawing on a array help find different ways to decompose a number

Step-by-step explanation:

Breaking apart arrays is another effective strategy for students who are learning multiplication, and helps model distributive property.   For example: students usually learn their twos and their fives sooner than the larger times tables, so that when faced with a problem like 6 X 7, students can instead look at the 7 as a (5+2) instead.  Like this: 6 X (5+2) OR (6 X 2) + (6 X 5) = 12 + 30 = 42.  

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).