Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
14th Edition
ISBN: 9780134677972
Author: Barnett
Publisher: PEARSON
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Chapter DPT, Problem 1E

Replace each question mark with an appropriate expression that will illustrate the use of the indicated real number property:

A  Commutative   ( ) : x ( y + z ) = ? B  Associative      ( + ) : 2 + ( x + y ) = ? C  Distributive:    (2 + 3 ) x = ? :

Expert Solution & Answer
Check Mark
To determine

An appropriate expression that may replace each question mark, and illustrate the use of the indicated real number property:

(A) Commutative () : x(y+z)=?

(B) Associative (+) : 2+(x+y)=?

(C) Distributive: (2+3)x=?

Answer to Problem 1E

(A) The required expression for the Commutative property of multiplication is x(y+z)=(y+z)x.

(B) The required expression for the Associative property of addition is 2+(x+y)=(2+x)+y.

(C) The required expression for the Distributive property is (2+3)x=2x+3x.

Explanation of Solution

(A)

Consider the given expression,

x(y+z)=?

Now, commutative property of multiplication states that a,b, ab=ba.

Here, take x as a and (y+z) as b.

Then, by the commutative property,

x(y+z)=(y+z)x

Hence, the required expression for the Commutative property of multiplication is x(y+z)=(y+z)x.

(B)

Consider the given expression,

2+(x+y)=?

Now, associative property of addition states that a,b,c, a+(b+c)=(a+b)+c.

Here, take 2 as a and (x+y) as (b+c).

Then, by the associative property,

2+(x+y)=(2+x)+y

Hence, the required expression for the Associative property of addition is 2+(x+y)=(2+x)+y.

(C)

Consider the given expression,

(2+3)x=?

Now, distributive property states that for every a,b,c, (a+b)c=ac+bc.

Here, take (2+3) as (a+b) and x as c,

Then, by the distributive property,

(2+3)x=2x+3x

Hence, the required expression for the Distributive property is (2+3)x=2x+3x.

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Chapter DPT Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Ch. DPT - Write 0.35 as a fraction reduced to lowest terms.Ch. DPT - Write 78 in decimal form.Ch. DPT - Write in scientific notation:...Ch. DPT - Write in standard decimal form: A2.55108B4.06104Ch. DPT - Indicate true (T) or false (F): (A) A natural...Ch. DPT - Give an example of an integer that is not a...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 17-24, simplify and write answers...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - In Problems 25-30, perform the indicated operation...Ch. DPT - Each statement illustrates the use of one of the...Ch. DPT - Prob. 32ECh. DPT - Multiplying a number x by 4 gives the same result...Ch. DPT - Find the slope of the line that contains the...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - Find the x and y coordinates of the point at which...Ch. DPT - In Problems 37-40, solve for x. x2=5xCh. DPT - In Problems 37-40, solve for x. 3x221=0Ch. DPT - In Problems 37-40, solve for x. x2x20=0Ch. DPT - In Problems 37-40, solve for x. 6x2+7x1=0

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