Question

Define and give a visual example of the Commutative Property. 2. Explain the process ( Every Step ) that you would use to simplify the following expression. 7 ( c + 3 ) + -4 (3c -2 )

Answer 1

Problem 1

Imagine a rectangle that is 2 by 3. You would have an area of 2*3 = 6 and it is the same as saying 3*2 = 6. The order of multiplication doesn't matter. Visually, we can rotate the rectangle to have the shorter side be horizontal and then make it vertical, and the area is still the same. All we're doing is shifting things around.

Another example is say you had a marching band with 10 rows and 2 columns. That gives 10*2 = 20 people total. Then we could easily form the same number of people into 2 rows and 10 columns. The order of rows and columns doesn't matter because we get the same total number as a result.

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Problem 2

7(c+3) + -4(3c-2) ..... is the original expression

7(c+3) - 4(3c - 2) .... adding a negative is the same as subtracting

7*c + 7*3 - 4*3c - 4*(-2) .... distributive property

7c + 21 - 12c + 8 .... multiply

(7c-12c) + (21+8) .... group like terms

-5c + 29 ... combine like terms

The original expression simplifies to -5c+29

Answer 2

The Commutative Property is a property that states the order of the numbers in addition and multiplication don't matter. 2+3+7 = 7+2+3

Explanation:

7(c+3)+ -4(3c-2)

Distribute the 7 and the -4 to each of their parentheses.

7c+21-12c+8

You can use the Commutative Property to move the terms to places where they can be easily simplified.

7c-12c+21+8

Simplify.

-5c+29