Gary buys a 3 1/2 pound bag of cat food every 3 weeks. gary feeds his cat the same amount of food each day. which expression can gary use to determine the number of pounds of cat food his cat eats each year? (1 year = 52 weeks)

One expression that Gary can use,where y is the amount of food eaten in a year and x the amount of food eaten in a weeks is:
y=x*52

but we actually know that the cats eat one third of 3 1/2 pounds, that is:


 
So we can substitute this:
y=

which is y=7*13=91

So we actually know that the cats eat 91 pounds of food a year!

This law is sometimes called the grouping property. as you can see, regardless of how the numbers are grouped, the answer is still 13. the associative law of multiplication is similar to the same law for addition. it says that no matter how you group numbers you are multiplying together, you will get the same answer.