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Chapter 2: Q4. (page 66)

Question: Evaluate the expression. Justify each of your steps.

鈭�鈥夆赌�4鈥夆赌�(鈥�9鈥�)鈥�(鈥�鈭�鈥�5)

Short Answer

Expert verified

The value of the expression is180.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Associative Property of Multiplication of Real Numbers: 

Suppose a, b, and c is three real numbers.

Associative property of Multiplication

Property:(a鈥夆赌�路鈥夆赌塨)鈥夆赌�路鈥夆赌塩=a鈥夆赌�路鈥夆赌�(鈥塨鈥夆赌�路鈥夆赌塩鈥�)

If you are multiplying three real numbers, the product is always the same regardless of their grouping.

Example:(6鈥夆赌�路鈥夆赌�4)鈥夆赌�路鈥夆赌�3=6鈥夆赌�路鈥夆赌�(鈥�4鈥夆赌�路鈥夆赌�3鈥�)鈥夆赌�=鈥夆赌�72

(a鈥夆赌�路鈥夆赌塨)鈥夆赌�路鈥夆赌塩=a鈥夆赌�路鈥夆赌�(鈥塨鈥夆赌�路鈥夆赌塩鈥�)
03

Step-3 – Evaluate the expression – 4 (9) (– 5) and justify each of your steps.

Associative property of Multiplication states thatif you are multiplying three real numbers, the product is always the same regardless of their grouping.

Property:(a鈥夆赌�路鈥夆赌塨)鈥夆赌�路鈥夆赌塩=a鈥夆赌�路鈥夆赌�(鈥塨鈥夆赌�路鈥夆赌塩鈥�)

Example:(6鈥夆赌�路鈥夆赌�4)鈥夆赌�路鈥夆赌�3=6鈥夆赌�路鈥夆赌�(鈥�4鈥夆赌�路鈥夆赌�3鈥�)鈥夆赌�=鈥夆赌�72

Associative Property of Multiplication: (a鈥夆赌�路鈥夆赌塨)鈥夆赌�路鈥夆赌塩=a鈥夆赌�路鈥夆赌�(鈥塨鈥夆赌�路鈥夆赌塩鈥�)

So, we can multiply the numbers in any order.

鈭�鈥夆赌�4(9)(鈭�鈥夆赌�5)(鈭�鈥夆赌�4鈥夆赌�路鈥夆赌�9)鈥�(鈭�5)鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌�(Associative鈥夆赌塒roperty鈥夆赌塷f鈥夆赌塎ultiplication)鈭�鈥夆赌�4鈥夆赌�(9鈥夆赌�路鈥夆赌�鈭�鈥夆赌�5)鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆��(Associative鈥夆赌塒roperty鈥夆赌塷f鈥夆赌塎ultiplication)鈭�鈥夆赌�4鈥夆赌�路鈥夆赌�鈭�鈥夆赌�45鈥夆赌�=鈥夆赌�180鈥夆赌�

Thus, the value of the expression is 180.

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