Because of the commutative property of multiplication, it is true that 3/4 x 4 = 4 x 3/4

. However, these expressions can be calculated in different ways even though the solutions will be the same. Below, show two different ways of solving this problem.

First, show how 3/4 x 4 can be solved using repeated addition. Then, show how 4 x 3/4 can be solved using multiplication and division.

a. For the repeated addition:

3/4 + 3/4 + 3/4 + 3/4 = 12/4 = 3

b. Using multiplication and division method:

3/4 × 4/1 = 12/4 = 3

Step-by-step explanation:

Commutative property literally has to do with moving terms or numbers or things around. The idea is just to show that an operation can still be performed successfully even after changing the manner the terms appear and still have same outcome. Example: 3+5 is the same as 5+3 , 9×4 is the same as 4×9 , F+B+C is the same as B+F+C and A×m×h is the same as h×A×m . It simply shows or displays the ability of expressions to be calculated in different ways or approaches without altering their outcomes.

In this particular case, we are asked to show different ways by which we can successfully perform the operation:

(3/4 × 4) [using repeated addition;

multiplication and division]

a. For the repeated addition: 3/4 is the same as:

3/4 + 3/4 + 3/4 + 3/4 = 12/4 = 3

So, 3/4 is the same as replicating the fraction "4" times and then finding their sum.

b. We can also use the operation of multiplication and then, division to still obtain the correct outcome:

3/4 × 4 is the same as:

3/4 × 4/1 = 12/4 = 3

Note, how "4" was made to have a denominator "1" and then we multiplied the numerators to give a common numerator "12". Later, the two denominators were multiplied to give a common denominator "4". We then divided the result's numerator by the denominator and obtained the same result (3) gotten when the operation was performed using the repeated addition method.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.