Why do you think it isnecessary to study the order of operations and the laws of

Question

Why do you think it isnecessary to study the order of operations and the laws ofoperations before you start solving equations? Of the three laws, commutative, associative, and distributive,which one do you think is the most frequently used in algebra andwhy? Why do you think it isnecessary to study the order of operations and the laws ofoperations before you start solving equations? Of the three laws, commutative, associative, and distributive,which one do you think is the most frequently used in algebra andwhy? Of the three laws, commutative, associative, and distributive,which one do you think is the most frequently used in algebra andwhy?

Explanation / Answer

It's like playing a game. If you don't knowthe rules how will you play? The same is true for the order ofoperations and the laws of operations. You can't solve the problemuntil you understand the rules.
Simplify; 6 + 2 - 3 x 4
Answer = -4
You multiply before you add or subtract. PEMDAS

In ordinary high-school algebra all three of them are used all thetime.

Here is an example. I want to change 6x + 2y = 5x into x + 2y =0.

Step 1: Add -5x to the end of both sides.
I get (6x + 2y) + (-5x) = 5x + (-5x).

Step 2: Use the associative law for addition toget
6x +(2y + (-5x)) = 5x + (-5x).

Step 3: Use the commutative law for addition toget
6x +((-5x) +2y) = 5x + (-5x).

Step 4: Use the associative law for addition toget
(6x + (-5x)) +2y = 5x + (-5x).

Step 5: Use the distributive law on the left-handside to get
((6 + -5)x + 2y = 5x + (-5x).
Now, since 6 + (-5) = 1, and 1x = x, we get
x + 2y = 5x + (-5x).

Step 6: Use the distributive law on the right-handside to get
x + 2y = (5 + -5)x.
Since 5 + (-5) = 0, and 0x = 0, we finally get to
x + 2y = 0.

So I used all three laws. In Step 1, I added -5x rather thansubtracting 5x, because otherwise I would have to get involved withextra laws for subtraction as well as for addition.

It is difficult to pick out one law as "most frequently used" - allthree are vitally important.

The hardest law to spot is the associative law, because it ishidden in our notation. If I write an expression like x^2 + 3x + 2I am implicitly using the associative law for addition, becauseotherwise I could mean either
(x^2 + 3x) + 2 or x^2 + (3x +2),
and if I didn't have the associative law these two things could bedifferent.
(I am writing x^2 for x squared.)

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