Homework 3 Additional Properties of Real Numbers

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Can you help me understand this Algebra question?

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

2. Justify the statement (LaTeX: -

−
19)+19=0

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

Justify the statement LaTeX: displaystyle frac{-1}{7}_x000D_

−

1

7
(LaTeX: -

−
-54)LaTeX: displaystyle+ frac{1}{7}

+

1

7

(LaTeX: -

−
-54)=0

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

Justify the statement LaTeX: 0-

0

−
20LaTeX: =

=
20LaTeX: -0

−

0

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed, incorrect.

Justify the statement LaTeX: -

−
79LaTeX: +0=

+

0

=
LaTeX: -

−
79

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed, incorrect.

Justify the statement LaTeX: displaystyle left(frac{1}{17}right)cdot 0=0 cdot left(frac{1}{29}right)

(

1

17

)

⋅

0

=

0

⋅

(

1

29

)

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

If LaTeX: displaystyle left(frac{1}{a}right)cdot 0=0 cdot left(frac{1}{b}right)

(

1

a

)

⋅

0

=

0

⋅

(

1

b

)

then LaTeX: a=b

a

=

b
. True or false? Why?

(1) True because the two sides of an equation must be equal.

(2) True because the two sides of an equation must be 0.

(3) True because the two sides of the equation are 0.

(4) False because the two sides of the equation are 0 regardless of whether LaTeX: a=b

a

=

b
or not, as long as LaTeX: anot=0

a

≠

0
and/or LaTeX: bnot=0

b

≠

0

Justify the statement LaTeX: 1cdot (

1

⋅

(
5.6 LaTeX: )=(

)

=

(
5.6LaTeX: )cdot 1

)

⋅

1

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

Justify the statement LaTeX: 1div

1

÷
15LaTeX: =

=
15LaTeX: div 1

÷

1

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

Evaluate LaTeX: displaystyle frac{0}{a}

0

a
where a=84.

(1) 0

(2) undefined

(3) no solution

(4) infinity

Evaluate LaTeX: displaystyle frac{a}{0}

a

0
where a=2.

(1) 0

(2) undefined ( or infinity)

(3) no solution

(4) 1

Justify the statement LaTeX: displaystyle left( frac{a}{b}right)left( frac{b}{a}right)

(

a

b

)

(

b

a

)

=1 where a=7 and b=71

(1) Identity for addition

(2) Identity for subtraction

(3) Identity for multiplication

(4) Identity for division

(5) Zero property in addition

(6) Zero property in subtraction

(7) Zero prop. in multiplication

(8) Zero property in division

(9) Property of opposites

10) Property of reciprocals

(11) Rounding

(12) Inequalities

(13) Absolute value

(14) Interval notation

(15) Not listed

Subtract the opposite of 37 from the reciprocal of LaTeX: displaystyle frac{|-1|}{b}

|

−

1

|

b
where b=79

Every real number has an opposite.

Group of answer choices

Every real number has a reciprocal.

Group of answer choices

According to the definition of absolute value

<img src="https://ilearn.laccd.edu/equation_images/%255Cdisplaystyle%2520%257Cx%257C%253D%255Cleft%255C%257B%255Cbegin%257Barray%257D%257Brcl%2520lll%257D%250Ax%2520%2526%2520%255Chbox%257B%2520if%2520%257D%25260%255Cle%2520x%255C%255C%250A-x%2520%2526%255Chbox%257B%2520if%2520%257D%2526%2520x%253C0%255C%255C%250A%255Cend%257Barray%257D%255Cright." alt="LaTeX: displaystyle |x|=left{begin{array}{rcl lll}_x000D_
x & hbox{ if }&0le x_x000D_
-x &hbox{ if }& x

|

x

|

=

{

x

if

0

≤

x

−

x

if

x

<

0

Explain in your own words why LaTeX: |-9|=9

|

−

9

|

=

9
, Refrain from “negative and negative is positive”.

Use your calculator to evaluate the quotient of LaTeX: sqrt{a^2+b^2}

a

2

+

b

2

and 6.7. Use a=-10.7 and b=2.9.

Round to the nearest tenth.

Solve LaTeX: |x|=

|

x

|

=
-4

(1) x = -4

(2) x = LaTeX: -

−
-4

(3) x = LaTeX: pm

±
-4

(4) x is undefined.

Assume LaTeX: ale b

a

≤

b
and LaTeX: ble 0

b

≤

0
, Then

(1) LaTeX: ale 0

a

≤

0

(2) LaTeX: a=0

a

=

0

(3) LaTeX: 0le a

0

≤

a

(4) <img src="https://ilearn.laccd.edu/equation_images/0%253Ca" alt="LaTeX: 0

0

<

a

Mr. Baba earns at most $300 per week while Ms. Dede earns less than $200 week . Can Mr. Baba add his salary to Ms. Dede’s to buy a vase that costs $500 and they have no other source of revenue during the week and no additional expenses?

(1) Yes because 200+300 = 500

(2) Yes because Ms, Dede may only be a penny short, Mr. earns exactly $300, and the sales people want to make a commission.

(3) No because Ms. Dede and/or Mr. Baba may be substantially short.


(4) The answer is ambiguous. Case (2) and case (3) are possible.

A number is rounded to the nearest hundred. After rounding the number is 71,300. What could have been the largest number before rounding?

A number is rounded to the nearest hundred. After rounding the number is 31,300. What could have been the smallest number before rounding?