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Identify the property that the statement illustrates.

-  4ab=-  4ba

Short Answer

Expert verified

The statement-  4ab  =  -  4barepresents the Commutative property of Multiplication.

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 – Commutative Property of Multiplication of Real Numbers: 

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

Commutative Property of Multiplication:

Property: a  ·  b  =b  ·  a   or a  ·  b  ·  c=b  ·  c  ·  a

If you multiply two or three real numbers in any order, their product will always be the same.

Example: 12  ·  4  =4  ·  12  =  48 or 5  ·  6  ·  4=6  ·  4  ·  5  =  120

03

Step-3 – Identify the property that the statement – 4ab = – 4ba illustrates.

Commutative property of Multiplication states that If you multiply two or three real numbers in any order, their product will always be the same.

Property: a  ·  b  =b  ·  a  

Example: 12  ·  4  =4  ·  12  =  48

So, the expression -  4ab  =  -  4ba represents the Commutative Property of Multiplication.

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Most popular questions from this chapter

Crafts You make a decorative paper chain with n links by cutting a 9 inch by 12 inch sheet of construction paper into n strips.

a. Write an expression in terms of n for the width of each paper strip.

b. Suppose you want each strip to be 0.75 inch wide. Use the problem solving strategy guess, check, and revise to find the number of links your paper chain will have.

Challenge The problem below is a variation of one that appears in the ancient Chinese text Nine Chapters on the Mathematical Art. (In the problem, a tou is a Chinese unit of measure.)

A goat, a horse, and a cow mistakenly enter a farmer’s wheat field and eat some stalks of wheat. The horse eats twice as many stalks as the goat, and the cow eats twice as many stalks as the horse. The farmer demands 5 tou of wheat from the owners of the animals to replace what was eaten. How much wheat should be replaced by the goat’s owner? by the horse’s owner? by the cow’s owner?

a. Let x be the amount of wheat (in tou) that should be replaced by the goat’s owner. What is an expression in terms of x for the amount that should be replaced by the horse’s owner? by the cow’s owner?

b. Write and solve an equation to find x. To the nearest tenth of a tou, how much wheat should be replaced by each animal’s owner?

Simplify the expression.

x+6+11

Evaluate the expression. Justify each of your steps.

5. (- 6) ( 1 ) ( 10)

Extended Problem Solving You are making a rectangular rug. You want the rug to be twice as long as it is wide. Let w represent the width (in feet) of the rug.

a. Write an expression in terms of w for the perimeter of the rug.

b. Write an expression in terms of w for the area of the rug.

c. Calculate Copy and complete the table.

d. Writing Explain how doubling the width of the rug affects the perimeter and the area

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