Please My Dear Aunt Sally. The first letter of the words are for the order of mathematical operations. P M D A S

Parentheses, Multiplication, Division, Addition, Subtraction

So, for the first equation: 35 / 7 – 9 / 3

According to PMDAS, we would do the division first.

35/7 = 5 and 9/3 = 3

We would take those answers and perform the next operation, which would be subtraction

5 – 3 = 2 So the answer is 2

Now, there are three properties for operations. These are associative and communtative and distributive. You were asked to apply the associative property for the multiplication problem.

The associative property applies only to multiplication and addition. It means that, in order to simplify the problem, numbers may be organized in any way you want, because the product is going to be the same.

So, (19 * 20) * 5 can be also written as (5 * 20) * 19 and it still equals the same thing. The directions state that you are to write an expression that is equivalent. This does not mean to actually solve the problem, but just to rewrite it given the associative property. So, really, you can rewrite this problem any way you like, and it should be correct.

Lastly. Add, 13 + (-8). I hated these problems in school because they are meant to “trick” the eyes. It is uncommon for the signs of addition and subtraction to be side-by-side in equations because they are natural opposites. Now, given that we discussed the associative property, we can “fix” this to look better and to be easier to read because the associative property, remember, can be applied to both multiplication and addition problems.

So, we can say (-8) + 13 and the answer will be the same.

There is also another “trick” you can do. If a positive is in front of a negative, you can cancel the positive out.

Meaning, the negative can be considered stronger than the positive. So, we can say 13 – 8 and get the same answer which is 5.

I hope these explanations helped. It’s one thing to just give you the answers, but you asked HOW to do them, which is important, as in future math, you will better understand the why behind the what.

Good Luck!

LilD

35 / 7 = 5

9 / 3 = 3

then 5 -3 = 2

Your next two statements are not very clear to me though.

The associative prop of multiplication is shown in the above example …

(19*20)* 5 = 19*(20*5)

These two should give the same results although one might say it is easier to multiply 20*5.

Add 13+(-8) …. that’s simply 13 – 8 or 5.

(19 x 20) x 5= 900

13 + (- 8)= 5

5-9+3

5-3

2

(MDAS)

(MULTIPLICATION, DIVISION, ADDITION, SUBTRACTION)